Method and apparatus for MPEG artifact reduction

0001This invention generally relates to improving video and graphics quality.

0002MPEG compression is a widely used algorithm for digital video signal transmission and storage. MPEG encoded and decoded streams of video can be used in various applications including cable television, satellite television, and digital video discs (DVD).

0003The content of a video signal generally comprises a sequence of image frames for a progressive video sequence and image fields for an interlaced video sequence. Each frame/field consists of a rectangular spatial area of pixels. When video content is encoded using MPEG, generally an 8X8 window of pixels (64 pixels) in an image frame of the video signal is processed as follows. First, a Discrete Cosine Transform (DCT) is applied to the window to generate a 2-D spatial spectrum representation of the 8X8 window. This 2-D spatial spectrum is often referred to as a Fourier image, as it is a representation of the image in the Fourier domain. The Fourier image also has 64 pixels. The pixel values in the Fourier image represent a DC component and various frequencies or AC components. The DC component is generally situated in a top left corner pixel of the Fourier image. The other 63 pixels in the Fourier image represent the AC components. After generating the Fourier image, an MPEG encoder quantization is applied so that all the 64 pixels in the Fourier image are quantized.

0004The MPEG-2 standard provides for intraframe compression. In a video sequence, neighboring image frames are grouped into one or more Groups of Pictures ("GOP"). In a GOP, one image frame is encoded spatially, namely the I-frame. For other frames, differences are encoded. There are two types of frames where differences are encoded: P-frame and B-frame. For a P-frame, the difference between a current frame and a modified by motion vectors I-frame is spatially encoded. For a B-frame, the difference between a current frame and a weighting sum of a modified by motion vectors I-frame and P-frame or two P-frames is spatially encoded. "Modified by motion vectors" means that the currently encoded P- (or B-) frame is split by 16x16 pixel squares, and for each square the best matched square located with some spatial offset from the reference frame is searched. The searching happens in some local area. The spatial offset (vertical and horizontal) for the best matching block is kept in the MPEG stream and called the motion vector. Each 16x16 block of P-frame has one motion vector, and the B-frame has two motion vectors. MPEG compression for an interlaced signal processes fields instead of frames.

0005When an image is decoded using MPEG and MPEG-2 standards, the image frame is converted back from the Fourier domain to the spatial domain. The encoding and decoding of image frames using MPEG compression causes artifacts to appear in a processed image frame. The compression ratio, i.e. bit rate used in the MPEG encoding and decoding defines the level and behavior of the artifacts. That is, the visually perceived effect of the artifacts is a function of the bit rate.

0006There are various types of artifacts which can appear in image frames. When low compression rates are used, for example, less than 2 Megabits per second (Mbits/sec) the most perceivable are blocking artifacts which appear in certain areas of the image frame, particularly textured areas and etched or line areas. These blocking artifacts are often visually perceived as an image or object that appears to be divided into blocks. Pixel values inside the image frame are affected, introducing artifacts which appear as abrupt transitions between neighboring windows or blocks of the image frame. These abrupt transitions are generally aligned vertically and horizontally in the image frame and make the artifact very perceivable. In edge (line) areas, blocking artifacts are caused by transitions between neighboring windows or blocks in the presence of natural edges and lines, for instance, tree branches, wires, or edges between objects. In these edge areas, additional jaggedness is visually perceived. Increasing the bit rate to an intermediate or high level, for instance, higher than 2 Mbits/sec, can effectively reduce blocking artifacts occurring at low bit rates. For low bit rates, other artifacts such as mosquito noise, and flat area blocking artifact, can also take place.

0007For bit rates greater than 2 Mbits/sec, the blocking artifact is less perceivable. The main artifact appearing at these and higher bit rates is mosquito noise. Mosquito noise is a high frequency pattern that appears inside a window or block of pixels particularly in a more or less flat area in the presence of a high edge in a neighborhood or any other high transition between pixel values. The mosquito noise appears as a small checkerboard mixed with delta-impulse pattern that is clearly visible in areas within the window. Mosquito noise becomes visible due to the uniform spatial distribution of quantization noise appearing in blocks which contain generally smooth areas in the presence of strong edges. The mosquito noise is perceptually visible in the smooth areas. Pure vertical and horizontal intrablock ringing is one type of the mosquito noise. Here, mosquito noise appears close to vertical and horizontal edges in the image frame. The mosquito noise caused by pure vertical or horizontal edges is less severe than that caused by diagonal structures, but is still visible as vertical and horizontal ringing of the edges.

0008Also, in flat or smooth areas of the image frame, a flat area (DC) blocking artifact is perceptually visible at intermediate and high bit rates (greater than about 2 Mbits/sec). The flat area blocking artifact is caused by the quantized block essentially containing only one DC component, i.e. values of the pixels of the decoded block are the same. Perceptually, the smooth flat area appears as tiled 8x8 squares having close but different values. Thus, there is a distinguishable blocking pattern with smooth areas inside the blocks and rectangular transitions between neighboring blocks. The transitions are clearly visible because the transitions are generally aligned vertically and horizontally.

0009In modern video processing applications, often the source of a video signal is unknown. The video signal maybe digital or analog, and it could be transmitted from a DVD player, cable television source, satellite, or a montage of images from different sources. For instance, the video signal may be a combination from several analog and digital sources. Thus, any technique for artifacts reduction needs to perform effectively independent of any knowledge about the source of the video signal, including any knowledge about window or block boundaries in an image frame or video signal. Such knowledge might include information about edges, texture information and other information. If such knowledge was required, MPEG artifacts reduction techniques would be unnecessarily complex and hardware and time consuming.

0010Video sequences can also be affected by channel additive Gaussian Noise independent from MPEG artifacts.

0011<patcit id="pcit0001" dnum="EP0772365A2"><text>EP-A2-0772365</text></patcit> describes a method of filtering a picture signal and encoding/decoding using the same to decrease a step (i.e. block distortion) on a block boundary.

0012Therefore, what is needed is a technique for reducing artifacts occurring at intermediate and higher compression rates in the context of MPEG compression that is effective without knowledge about block boundaries or other information as to the content of the image frames in the video signal with or without the presence of Gaussian Noise.

0013Aspects of the invention are set out in the independent claims and preferred features are set out in the dependent claims.

0014There are described herein methods and apparatus, including computer program products, implementing and using techniques for reducing mosquito noise in an image frame of a video signal. A window of the image frame is provided. The window includes a plurality of pixel values. One of the pixel values is selected from the pixel values in the window to define a modified window of pixel value differences. A local mean (DC) value is computed based on the pixel value differences. A mosquito noise reduction value is also computed based on the pixel value differences. An artifact attenuation factor is computed as a function of a dynamic range measure of the pixel value differences. A weighted sum of the mosquito noise reduction value and the local mean value, applying the artifact attenuation factor, and the selected pixel value, is computed to generate a modified pixel value.

0015Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.

0016The details of one or more embodiments of the invention will now be described, by way of example only, and with reference to the accompanying drawings, in which: <ul id="ul0001" list-style="none" compact="compact"><li><figref idref="f0001">Fig. 1</figref> shows a block diagram of an apparatus 100 for modifying a pixel value in an image frame, according to one embodiment of the present invention.</li><li><figref idref="f0002">Fig. 2</figref> shows a flow diagram of a method 200 for modifying a pixel value in an image frame, performed in accordance with one embodiment of the present invention.</li><li><figref idref="f0003">Fig. 3A</figref> shows an illustration of an aperture window 300 of pixel values in an image frame, for a 3x3 case, according to one embodiment of the present invention.</li><li><figref idref="f0003">Fig. 3B</figref> shows an illustration of a modified aperture window 350 of pixel value differences, for a 3x3 case, according to one embodiment of the present invention.</li><li><figref idref="f0004">Fig. 4</figref> shows a block diagram of a mosquito noise reduction module 110, for a 3x3 case, according to one embodiment of the present invention.</li><li><figref idref="f0005">Fig. 5</figref> shows a flow diagram of a method 500 for performing a mosquito noise reduction operation, performed in accordance with one embodiment of the present invention.</li><li><figref idref="f0006">Fig. 6A</figref> shows a nonlinear processing module 115 for generating a nonlinear function, according to one embodiment of the present invention.</li><li><figref idref="f0006">Fig. 6B</figref> shows a limitation module 650 of the nonlinear processing module, according to one embodiment of the present invention.</li><li><figref idref="f0007">Fig. 6C</figref> shows a flow diagram of a method 600 for performing a nonlinear processing operation, according to one embodiment of the present invention.</li><li><figref idref="f0008">Fig. 7</figref> shows a graphical illustration of a nonlinear function 700, according to one embodiment of the present invention.</li><li><figref idref="f0009">Fig. 8A</figref> shows a smooth attenuation module 120, according to one embodiment of the present invention.</li><li><figref idref="f0010">Fig. 8B</figref> shows a flow diagram of a method 800 for performing a smooth attenuation operation, performed in accordance with one embodiment of the present invention.</li><li><figref idref="f0011">Fig. 9A</figref> shows a graphical illustration of an MPEG artifact attenuation factor λ, according to one embodiment of the present invention.</li><li><figref idref="f0011">Fig. 9B</figref> shows a graphical illustration of a Gaussian Noise attenuation factor λ₁, according to one embodiment of the present invention.</li><li><figref idref="f0012">Fig. 10</figref> shows a flow diagram of a method 1000 performed by output module 125, performed in accordance with one embodiment of the present invention.</li></ul>

0017Like reference symbols in the various drawings indicate like elements.

0018Embodiments of the present invention provide methods, apparatus, including computer program products, for modifying pixel values in an image frame of a video signal to reduce artifacts in the image frame. The methods and apparatus described herein are generally performed in the context of MPEG compression in which intermediate and high bit rates are used, generally above 2 Mbits/sec. These techniques are particularly well suited for removing mosquito noise, including pure vertical and horizontal intrablock ringing, and flat area (DC) blocking artifacts.

0019Embodiments of the invention provide methods and apparatus, including computer program products, implementing and using techniques for modifying pixel values of an image frame of a video signal to reduce artifacts in the image frame. According to some embodiments, an input image frame is received and processed pixel by pixel by one or more of several modules to reduce the above-described artifacts in the image frame. The modules cooperate to correct pixel values of the image frame so that the artifacts are reduced while preserving the natural details of the image frame as much as possible.

0020Embodiments of methods and apparatus disclosed herein process, pixel by pixel, a square sliding window as a processing aperture wherein the modifying pixel is generally a central pixel of the window. This window includes a plurality of pixel values. For a hardware implementation, linestores are cost consuming; therefore, the size of the sliding window is preferably small, e.g. 3x3. Generally, a nxn window is used, where n is a small odd value. The goal is to modify the pixel value located at the center of the window to reduce artifacts. As an initial step, the central pixel value is subtracted from the pixel values in the window to define a modified window of pixel value differences. The central pixel difference is zero.

0021A mosquito noise reduction module is provided to identify the mosquito noise component of a pixel. As will be shown below, the mosquito noise reduction processing is based on knowledge that mosquito noise has high frequency patterns in vertical and horizontal directions, and assumes that its dynamic range is limited to the value defined by a threshold. The mosquito noise reduction module performs a mosquito noise reduction operation on the pixel value differences in the modified window to generate two signals. First is a mosquito noise reduction value. Second is a local DC value based on the sliding window aperture. These two values are provided to a nonlinear processing module.

0022At the nonlinear processing module, a nonlinear function is applied to the difference between the mosquito noise reduction value and the local DC value. In this way, the nonlinear processing module reduces residual noise, pure vertical and horizontal ringing, DC blocking artifacts, and residual mosquito noise remaining in the pixel after processing by the mosquito noise reduction module. The nonlinear processing module has an adaptive threshold and operates to essentially force the value computed by the mosquito noise reduction module towards a local DC value, using techniques explained below. The nonlinear processing module effectively reduces pure vertical and horizontal ringing and DC blocking artifacts without introducing much blur into the image.

0023The output value of the nonlinear processing module is multiplied by a static blurriness parameter γ to control the overall blurriness of the image details. The product is multiplied by a Gaussian Noise attenuation factor generated by a smooth attenuation module, described below, and controls the Gaussian Noise reduction strength. This product is added back to the local DC value, since the local DC value was subtracted in the nonlinear processing module. The result is multiplied by an MPEG artifact attenuation factor, also generated by the smooth attenuation module, and controls the MPEG artifact reduction strength. The result of the multiplication is added to the aperture window central pixel input value, since the central pixel value was subtracted from the pixel values of the sliding window. This value is the output of the MPEG artifact reduction method and apparatus, according to some embodiments of the present invention.

0024The smooth attenuation module is provided to generate the MPEG artifact attenuation factor and Gaussian Noise attenuation factor based on MPEG artifact and Gaussian Noise reducing dynamic ranges. These dynamic ranges are defined by an MPEG artifact threshold and a Gaussian Noise threshold. The attenuation factors have three working zones: maximum value, zero and smooth transition between maximum and zero. The absence of the smooth transition zone can provide additional flickering. The flickering happens because values of pixels may change from frame-to-frame from slightly below the threshold to slightly above it, and the hard switch from zero to maximum takes place. Small changes up and down cause big changes up and down. The smooth attenuation module outputs attenuation factors having these zones, and additional flickering does not take place.

0025Embodiments of the methods and apparatus disclosed herein provide for a spatial method, which is generally practiced in a two-dimensional area or window representing part of an image frame in a video signal. This frame is generally processed on a pixel-by-pixel basis.

0026Embodiments of the methods and apparatus described herein can be implemented in various combinations of software and hardware. In one embodiment, the methods and apparatus are implemented in a video controller for use with a television or other display device. The methods and apparatus described herein are particularly well suited for processing video signals from any of various sources, including analog sources, digital sources, and a montage of analog and digital signals. For instance, the methods and apparatus are applicable to TV sets, DVD players, cable television systems, and satellite transmission of television signals. Artifacts associated with intermediate and high bit rates encoding, including mosquito noise and flat area blocking artifacts, are reduced regardless of the source of the video signal. No knowledge of window or block boundaries used in MPEG compression is required. Thus, embodiments of the methods and apparatus are computationally less complex, less time consuming, and less hardware consuming than conventional techniques requiring knowledge of block boundaries.

0027<figref idref="f0001">Fig. 1</figref> shows an apparatus 100 for modifying a pixel value in an image frame of an input video signal to reduce artifacts in the image frame. In <figref idref="f0001">Fig. 1</figref>, the apparatus 100 includes a windowing and pixel subtraction module 105 which receives an input image frame. The apparatus 100 further includes a mosquito noise reduction and local mean determination module 110 which receives pixel values a'-i' from windowing and pixel subtraction module 105. In addition, apparatus 100 includes nonlinear processing module 115 which receives information from mosquito noise reduction and local mean determination module 110 and outputs a value to a multiplier module 130 to be multiplied by a static blurriness parameter γ. The apparatus 100 also includes smooth attenuation module 120, which receives pixel values a' - i' from module 105 and outputs MPEG artifact and Gaussian Noise attenuation factors λ and λ₁ to an output module 125. Output module 125, which receives output values from module 130 and module 120 and the local DC value from module 110 provides a modified pixel value e as output. As shown in <figref idref="f0001">Fig. 1</figref>, windowing and pixel subtraction module 105 outputs central pixel value "e" to output module 125 for modification of that pixel value "e." Parameters <i>T</i>₂, <i>T</i>₁, <i>T</i>₀, and γ are control parameters for the method 200 and apparatus 100, and are discussed below.

0028<figref idref="f0002">Fig. 2</figref> provides a method 200 of the operation of the apparatus 100 for modifying a pixel value in an image frame to reduce artifacts in the image frame. In step 205, the input image frame is provided to windowing and pixel subtraction module 105. In this embodiment, windowing and pixel subtraction module 105 provides two functions: (1) a sliding windowing operation, and (2) a pixel subtraction operation. Those skilled in the art will appreciate, in another embodiment, there is a separate module for each function; that is, the windowing operation is provided by a windowing module, and the pixel subtraction operation is performed by a separate pixel subtraction module.

0029In step 210 of <figref idref="f0002">Fig. 2</figref>, windowing module 105 provides a window 300 of the input image frame. In one example, window 300 is a 3x3 sliding window described below with reference to <figref idref="f0003">Fig. 3A</figref>. The window includes a plurality of pixel values from a portion of the input image frame. In step 215, the pixel subtraction module in module 105 subtracts a central pixel value in the window from the other pixel values in the window to define a modified window of pixel value differences a'-i', as described below with reference to <figref idref="f0003">Fig. 3B</figref>.

0030In <figref idref="f0001">Fig. 1</figref>, mosquito noise reduction and local mean determination module 110 provides two functions: (1) a mosquito noise reduction operation, and (2) a local mean determination operation. Those skilled in the art will appreciate, in another embodiment, the local mean determination module is a submodule of mosquito noise reduction module. In step 220 of <figref idref="f0002">Fig. 2</figref>, the local mean determination module determines a local mean value "E_DC" based on the input pixel value differences a'-i'. In step 225, the mosquito noise reduction module 110 performs a mosquito reduction operation on the pixel value differences a'-i' in the modified window of <figref idref="f0003">Fig. 3B</figref> to generate a mosquito noise reduction value "u." This mosquito noise reduction operation is described below with respect to <figref idref="f0004">Figs. 4</figref> and <figref idref="f0005">5</figref>.

0031In step 230 of <figref idref="f0002">Fig. 2</figref>, nonlinear processing module 115 determines the difference between local mean value "E_DC" and mosquito noise reduction value "u" and generates a nonlinear function based on this difference to reduce the DC blocking artifact, and pure vertical and horizontal ringing. In step 235 of <figref idref="f0002">Fig. 2</figref>, the value output from nonlinear processing module 115 is multiplied in multiplier block 130 by a blurriness parameter γ which controls overall blurriness. The output result is received by module 125.

0032In step 240, the processing in the output module 125 takes place. At the output module 125, the input value 134 is multiplied by Gaussian Noise attenuation factor λ₁ received from smooth attenuation module 120. Then the local mean received from module 110 is added to the product. The result is multiplied by MPEG artifact attenuation factor λ, also received from the smooth attenuation module 120. The obtained product is added to the central pixel value of the sliding window received from the module 105 and outputs a modified pixel value <i>e̅</i>. The attenuation factors λ and λ₁ provided to the output module 125 control the strength of the MPEG artifact and Gaussian Noise reduction done by previous modules to the pixel value e. In step 245, the modified pixel value e is allocated in the output image frame.

0033<figref idref="f0003">Fig. 3A</figref> shows an illustration of a window 300 of pixel values a-i in the input image frame provided to windowing and pixel subtraction module 105 of <figref idref="f0001">Fig. 1</figref>. In this particular embodiment, window 300 is a 3X3 window of pixels from the input image frame. Those skilled in the art will appreciate that other window sizes of nxn, where n is preferably a small odd number, may be used in other embodiments. In this embodiment, a central pixel "e" of the 3X3 window is selected as the pixel for processing. The sliding window 300 is moved along the entire image frame in both horizontal and vertical directions, i.e. pixel by pixel in each line, line by line, to process all of the pixels in the image frame. The window 300 enables apparatus 100 to provide a modification of the central pixel value "e" based on the 9 pixel values a-i in the window 300.

0034<figref idref="f0003">Fig. 3B</figref> shows a modified window 350 of pixel value differences a'-i' after the pixel subtraction operation 215 is performed on window 300 by module 105 in <figref idref="f0001">Fig. 1</figref>. In this embodiment, the central pixel "e" is subtracted from each pixel a-i in window 300 to define pixel value differences a'-i' as shown in <figref idref="f0003">Fig. 3B</figref>. In particular, the differences between the pixel values a-i of the window 300 and the central coefficient e are represented as:<maths id="math0001"><math display="block"><mtable><mtr><mtd><mi mathvariant="italic">eʹ</mi><mo>=</mo><mn>0</mn><mo>;</mo><mi mathvariant="italic">aʹ</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>e</mi><mo>;</mo><mi mathvariant="italic">bʹ</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>e</mi><mo>;</mo><mi mathvariant="italic">cʹ</mi><mo>=</mo><mi>c</mi><mo>-</mo><mi>e</mi><mo>;</mo><mi mathvariant="italic">dʹ</mi><mo>=</mo><mi>d</mi><mo>-</mo><mi>e</mi><mo>;</mo></mtd></mtr><mtr><mtd><mi mathvariant="italic">fʹ</mi><mo>=</mo><mi>f</mi><mo>-</mo><mi>e</mi><mo>;</mo><mi mathvariant="italic">gʹ</mi><mo>=</mo><mi>g</mi><mo>-</mo><mi>e</mi><mo>;</mo><mi mathvariant="italic">hʹ</mi><mo>=</mo><mi>h</mi><mo>-</mo><mi>e</mi><mo>;</mo><mi mathvariant="italic">iʹ</mi><mo>-</mo><mi>i</mi><mo>-</mo><mn>.</mn></mtd></mtr></mtable></math><img file="EP1545134B1_D0001.tif" /></maths>

0035<figref idref="f0004">Fig. 4</figref> shows a block diagram of mosquito noise reduction and local mean determination module 110 constructed according to one embodiment of the present invention. The module 110 includes limiting modules 405, local mean determination module 410, 2D - highpass filter 415, and a variance module 420 for computing a weighting coefficient α. <figref idref="f0005">Fig. 5</figref> provides a flow diagram of a method 500 for performing a mosquito noise reduction operation, described with reference to <figref idref="f0004">Fig. 4</figref>. The mosquito noise reduction and local mean determination module 110 decreases intrablock ringing while preserving as much as possible the natural details of the input image frame. The mosquito noise reduction operation is based on knowledge that mosquito noise is a high frequency process both in vertical and horizontal directions, appears as a mixture of checkerboard and delta-impulse patterns, and the assumption that the mosquito noise dynamic range is located in the range of e - T₁ to e + T₁.

0036In <figref idref="f0004">Fig. 4</figref>, pixel value differences a'-i' of modified window 350 are provided to the limiting modules 405.

0037In step 505 of <figref idref="f0005">Fig. 5</figref>, the limiting modules 405 limit the pixel value differences by a threshold - T₁ from the bottom and + T₁ from the top to define limited pixel value differences. This threshold T₁ defines the working dynamic range for mosquito noise reduction. The limiting modules output a group of the limited pixel value differences, b", d", f", h", a", c", g", and i". In particular, a mathematical representation of the derivation of these limited pixel value differences is as follows:<maths id="math0002"><math display="block"><mi mathvariant="italic">aʺ</mi><mo>=</mo><mi mathvariant="italic">Lim</mi><mfenced><mi mathvariant="italic">aʹ</mi><msub><mi>T</mi><mn>1</mn></msub></mfenced><mo>,</mo><mi mathvariant="italic">bʺ</mi><mo>=</mo><mi mathvariant="italic">Lim</mi><mfenced><mi mathvariant="italic">bʹ</mi><msub><mi>T</mi><mn>1</mn></msub></mfenced><mo>,</mo><mi mathvariant="italic">cʺ</mi><mo>=</mo><mi mathvariant="italic">Lim</mi><mfenced><mi mathvariant="italic">cʹ</mi><msub><mi>T</mi><mn>1</mn></msub></mfenced><mo>,</mo><mi mathvariant="italic">dʺ</mi><mo>=</mo><mi mathvariant="italic">Lim</mi><mfenced><mi mathvariant="italic">dʹ</mi><msub><mi>T</mi><mn>1</mn></msub></mfenced><mo>,</mo></math><img file="EP1545134B1_D0002.tif" /></maths><maths id="math0003"><math display="block"><mi mathvariant="italic">fʺ</mi><mo>=</mo><mi mathvariant="italic">Lim</mi><mfenced><mi mathvariant="italic">fʹ</mi><msub><mi>T</mi><mn>1</mn></msub></mfenced><mo>,</mo><mi mathvariant="italic">gʺ</mi><mo>=</mo><mi mathvariant="italic">Lim</mi><mfenced><mi mathvariant="italic">gʹ</mi><msub><mi>T</mi><mn>1</mn></msub></mfenced><mo>,</mo><mi mathvariant="italic">hʺ</mi><mo>=</mo><mi mathvariant="italic">Lim</mi><mfenced><mi mathvariant="italic">hʹ</mi><msub><mi>T</mi><mn>1</mn></msub></mfenced><mo>,</mo><mi mathvariant="italic">iʺ</mi><mo>=</mo><mi mathvariant="italic">Lim</mi><mfenced><mi mathvariant="italic">iʹ</mi><msub><mi>T</mi><mn>1</mn></msub></mfenced><mo>,</mo></math><img file="EP1545134B1_D0003.tif" /></maths> where<maths id="math0004"><math display="block"><mi mathvariant="italic">Lim</mi><mfenced><mi mathvariant="italic">x</mi><msub><mi>T</mi><mn>1</mn></msub></mfenced><mo>=</mo><mrow><mo>{</mo><mtable><mtr><mtd><mi>x</mi><mo>,</mo></mtd><mtd><mfenced open="|" close="|"><mi>x</mi></mfenced><mo>≤</mo><msub><mi>T</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><mi mathvariant="italic">sign</mi><mfenced><mi>x</mi></mfenced><mo>⁢</mo><msub><mi>T</mi><mn>1</mn></msub><mo>,</mo></mtd><mtd><mfenced open="|" close="|"><mi>x</mi></mfenced><mo>></mo><msub><mi>T</mi><mn>1</mn></msub></mtd></mtr></mtable></mrow><mn>.</mn></math><img file="EP1545134B1_D0004.tif" /></maths>

0038In step 510, the 2D - highpass filter 415 computes a reducing value of the checkerboard pattern <i>E</i>_cb. In step 511, local mean determination module 410 computes the local DC value E_DC.

0039In step 515 of <figref idref="f0005">Fig. 5</figref>, variance module 420 of <figref idref="f0004">Fig. 4</figref> computes a weighting coefficient α as a function of a variance of the limited pixel value differences a"-i". In step 520, the weighting coefficient α is provided to a summing module 425, along with the reducing value of the checkerboard pattern <i>E</i>_cb and local DC value E_DC to compute a weighted sum to generate a mosquito noise reduction value "u."<maths id="math0005"><math display="block"><mi>u</mi><mo>=</mo><mi>α</mi><mo>⁢</mo><msub><mi>E</mi><mi mathvariant="italic">cb</mi></msub><mo>+</mo><mfenced><mn>1</mn><mo>-</mo><mi>a</mi></mfenced><mo>⁢</mo><msub><mi>E</mi><mi mathvariant="italic">DC</mi></msub><mo>,</mo></math><img file="EP1545134B1_D0005.tif" /></maths>

0040The value of α generated by variance module 420 desirably satisfies the condition 0 ≤ α ≤ 1 and depends on the closeness of the pixels surrounding the center pixel e to each other. In particular, α is determined by variance module 420 according to the following nonlinear function:<maths id="math0006"><math display="block"><mi>a</mi><mo>=</mo><mi>exp</mi><mfenced><mo>-</mo><msub><mi>β</mi><mn>1</mn></msub><mo>⁢</mo><mfrac><mi>V</mi><mfenced open="|" close="|"><msub><mi>E</mi><mn>0</mn></msub></mfenced></mfrac></mfenced><mo>,</mo></math><img file="EP1545134B1_D0006.tif" /></maths> where<maths id="math0007"><math display="block"><msub><mi>E</mi><mn>0</mn></msub><mo>=</mo><mn>0.5</mn><mo>⋅</mo><mfenced><msub><mi>E</mi><mn>1</mn></msub><mo>+</mo><msub><mi>E</mi><mn>2</mn></msub></mfenced></math><img file="EP1545134B1_D0007.tif" /></maths>

0041"V" is an estimation of the expectation of all surrounding pixels,<maths id="math0008"><math display="block"><mi>V</mi><mo>=</mo><mfenced open="|" close="|"><msub><mi>E</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="italic">aʹ</mi></mfenced><mo>+</mo><mfenced open="|" close="|"><msub><mi>E</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="italic">bʹ</mi></mfenced><mo>+</mo><mfenced open="|" close="|"><msub><mi>E</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="italic">cʹ</mi></mfenced><mo>+</mo><mfenced open="|" close="|"><msub><mi>E</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="italic">dʹ</mi></mfenced><mo>+</mo><mfenced open="|" close="|"><msub><mi>E</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="italic">fʹ</mi></mfenced><mo>+</mo><mfenced open="|" close="|"><msub><mi>E</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="italic">gʹ</mi></mfenced><mo>+</mo><mfenced open="|" close="|"><msub><mi>E</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="italic">hʹ</mi></mfenced><mo>+</mo><mfenced open="|" close="|"><msub><mi>E</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="italic">iʹ</mi></mfenced></math><img file="EP1545134B1_D0008.tif" /></maths>

0042β₁ is a predetermined constant positive value, obtained on the basis of subjective experimentation. In one example, to decrease the mosquito noise value significantly, while preserving natural image details as much as possible, β₁=5 was chosen. Decreasing β₁, it is possible to reduce artifacts with more blurring of natural details of the image.

0043In one example, local mean determination module 410 includes a two-dimensional lowpass filter for local mean determination, for a 3x3 window obtained from the one-dimensional filter: <tables id="tabl0001" num="0001"><table frame="none"><tgroup cols="3" rowsep="0"><colspec colnum="1" colname="col1" colwidth="10mm" colsep="0" /><colspec colnum="2" colname="col2" colwidth="10mm" colsep="0" /><colspec colnum="3" colname="col3" colwidth="10mm" colsep="0" /><tbody><row rowsep="1"><entry align="center">1/4</entry><entry align="center">1/2</entry><entry align="center">1/4</entry></row></tbody></tgroup></table></tables> having the following impulse response: <tables id="tabl0002" num="0002"><table frame="none"><tgroup cols="3" rowsep="0"><colspec colnum="1" colname="col1" colwidth="12mm" /><colspec colnum="2" colname="col2" colwidth="10mm" /><colspec colnum="3" colname="col3" colwidth="12mm" /><tbody><row><entry colsep="0" align="center">1/16</entry><entry colsep="0" align="center">1/8</entry><entry colsep="0" align="center">1/16</entry></row><row><entry colsep="0" align="center">1/8</entry><entry colsep="0" align="center">1/4</entry><entry colsep="0" align="center">1/8</entry></row><row rowsep="1"><entry colsep="0" align="center">1/16</entry><entry colsep="0" align="center">1/8</entry><entry colsep="0" align="center">1/16.</entry></row></tbody></tgroup></table></tables>

0044Therefore, the local DC value <i>E_DC</i> is as follows.<maths id="math0009"><math display="block"><msub><mi>E</mi><mi mathvariant="italic">DC</mi></msub><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>⋅</mo><msub><mi>E</mi><mn>1</mn></msub><mo>+</mo><mn>1</mn><mo>/</mo><mn>4</mn><mo>⋅</mo><msub><mi>E</mi><mn>2</mn></msub><mo>,</mo></math><img file="EP1545134B1_D0009.tif" /></maths> where <i>E</i>₁ = <i>Avr</i>(<i>b"</i>,<i>d"</i>,<i>f"</i>,<i>h"</i>), and <i>E</i>₂ = ·<i>Avr</i>(<i>a"</i>,<i>c"</i>,<i>g"</i>,<i>i"</i>), and where <i>Avr</i>( ) means average.

0045A two-dimensional highpass filter for the reducing value of the checkerboard pattern <i>E</i>_cb. for a 3x3 window obtained from the one-dimensional filter: <tables id="tabl0003" num="0003"><table frame="none"><tgroup cols="3" rowsep="0"><colspec colnum="1" colname="col1" colwidth="10mm" colsep="0" /><colspec colnum="2" colname="col2" colwidth="10mm" colsep="0" /><colspec colnum="3" colname="col3" colwidth="10mm" colsep="0" /><tbody><row rowsep="1"><entry align="center">-1/4</entry><entry align="center">1/2</entry><entry align="center">-1/4</entry></row></tbody></tgroup></table></tables> has the following impulse response: <tables id="tabl0004" num="0004"><table frame="none"><tgroup cols="3" rowsep="0"><colspec colnum="1" colname="col1" colwidth="13mm" /><colspec colnum="2" colname="col2" colwidth="10mm" /><colspec colnum="3" colname="col3" colwidth="14mm" /><tbody><row><entry colsep="0" align="center">-1/16</entry><entry colsep="0" align="center">1/8</entry><entry colsep="0" align="center">-1/16</entry></row><row><entry colsep="0" align="center">1/8</entry><entry colsep="0" align="center">1/4</entry><entry colsep="0" align="center">1/8</entry></row><row rowsep="1"><entry colsep="0" align="center">-1/16</entry><entry colsep="0" align="center">1/8</entry><entry colsep="0" align="center">-1/16.</entry></row></tbody></tgroup></table></tables>

0046Therefore, the value <i>E_cb</i> is as follows:<maths id="math0010"><math display="block"><msub><mi>E</mi><mi mathvariant="italic">cb</mi></msub><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>⋅</mo><msub><mi>E</mi><mn>1</mn></msub><mo>-</mo><mn>1</mn><mo>/</mo><mn>4</mn><mo>⋅</mo><msub><mi>E</mi><mn>2</mn></msub><mo>,</mo></math><img file="EP1545134B1_D0010.tif" /></maths> where <i>E,</i> = <i>Avr</i>(<i>b"</i>,<i>d"</i>,<i>f"</i>,<i>h"</i>), and <i>E</i>₂ = ·<i>Avr</i>(<i>a"</i>,<i>c"</i>,<i>g"</i>,<i>i"</i>), and where <i>Avr</i>( ) means average.

0047The E_DC value is output to nonlinear processing module 115 along with the mosquito noise reduction value u, as shown in <figref idref="f0001">Fig. 1</figref>. The nonlinear processing module 115 of <figref idref="f0001">Figs. 1</figref> and <figref idref="f0006">6A, 6B</figref> reduces any residual amounts of mosquito noise remaining after the mosquito noise reduction operation is performed, as well as DC blocking artifacts and pure vertical or horizontal ringing. As will be shown below, the nonlinear processing module 115 essentially forces the modified pixel value towards the local DC value E_DC to reduce remaining high frequency components associated with mosquito noise, DC blocking artifacts and pure vertical or horizontal ringing.

0048<figref idref="f0006">Fig. 6A</figref> shows nonlinear processing module 115 for generating a nonlinear function Ψ(Δ) of the difference between the mosquito noise reduction value and local DC value, Δ = <i>u - E_DC</i>, according to one embodiment of the present invention. <figref idref="f0006">Fig. 6B</figref> shows a limitation module 650 of nonlinear processing module 115, according to one embodiment of the present invention. <figref idref="f0007">Fig. 6C</figref> provides a flow diagram of a method 600 for performing a nonlinear processing operation, described with reference to <figref idref="f0006">Fig. 6A</figref>.

0049In step 660 of <figref idref="f0007">Fig. 6C</figref>, the difference is computed between the mosquito noise reduction value and local DC value, Δ=<i>u</i>-<i>E_DC</i>. In step 670, a dynamic dead zone threshold T_DC is computed based on: (1) a DC blocking artifact threshold, To, also referred to as a static dead zone threshold, and (2) the input mosquito noise reduction value. In step 680, a nonlinear function Ψ(Δ) is applied, forcing the input value to or toward zero.

0050A graphical illustration of the exemplary nonlinear function Ψ(Δ) 700 applied by nonlinear processing module 115 is shown in <figref idref="f0008">Fig. 7</figref>. A mathematical representation of the nonlinear function Ψ(Δ) 700 is as follows:<maths id="math0011"><math display="block"><mtable><mtr><mtd><mi mathvariant="normal">Ψ</mi><mfenced><mi mathvariant="normal">Δ</mi></mfenced><mo>=</mo><mrow><mo>{</mo><mtable><mtr><mtd><mn>0</mn><mo>,</mo></mtd><mtd><mfenced open="|" close="|"><mi mathvariant="normal">Δ</mi></mfenced><mo>≤</mo><msub><mi>T</mi><mi mathvariant="italic">DC</mi></msub></mtd></mtr><mtr><mtd><mn>2</mn><mo>⁢</mo><mi mathvariant="italic">sign</mi><mfenced><mi mathvariant="normal">Δ</mi></mfenced><mo>⁢</mo><mfenced><mfenced open="|" close="|"><mi mathvariant="normal">Δ</mi></mfenced><mo>-</mo><msub><mi>T</mi><mi mathvariant="italic">DC</mi></msub></mfenced></mtd><mtd><msub><mi>T</mi><mi mathvariant="italic">DC</mi></msub><mo>≤</mo><mfenced open="|" close="|"><mi mathvariant="normal">Δ</mi></mfenced><mo>≤</mo><mn>2</mn><mo>⁢</mo><msub><mi>T</mi><mi mathvariant="italic">DC</mi></msub></mtd></mtr><mtr><mtd><mi mathvariant="normal">Δ</mi><mo>,</mo></mtd><mtd><mfenced open="|" close="|"><mi mathvariant="normal">Δ</mi></mfenced><mo>≥</mo><mn>2</mn><mo>⁢</mo><msub><mi>T</mi><mi mathvariant="italic">DC</mi></msub></mtd></mtr></mtable></mrow><mo>,</mo></mtd></mtr><mtr><mtd><msub><mi>T</mi><mi mathvariant="italic">DC</mi></msub><mo>=</mo><mrow><mo>{</mo><mtable><mtr><mtd><msub><mi>γ</mi><mn>1</mn></msub><mfenced open="|" close="|"><mi>u</mi></mfenced><mo>,</mo></mtd><mtd><msub><mi>γ</mi><mn>1</mn></msub><mfenced open="|" close="|"><mi>u</mi></mfenced><mo>></mo><msub><mi>T</mi><mn>0</mn></msub></mtd></mtr><mtr><mtd><msub><mi>T</mi><mn>0</mn></msub><mo>,</mo></mtd><mtd><msub><mi>γ</mi><mn>1</mn></msub><mfenced open="|" close="|"><mi>u</mi></mfenced><mo>≤</mo><msub><mi>T</mi><mn>0</mn></msub></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math><img file="EP1545134B1_D0011.tif" /></maths>

0051The nonlinear function above avoids hard thresholding at T_DC, as shown in <figref idref="f0008">Fig. 7</figref>. Thresholding can cause flickering. The nonlinear function has a linear transition between T_DC and 2T_DC instead of a hard switch, helping to reduce any such flickering.

0052In the preceding nonlinear function Ψ(Δ), the control parameter To is a predetermined threshold, defining a static dead zone of the nonlinear function. Subjective experiments show that optimal values for T₀≈ 2,...,3. As shown in <figref idref="f0006">Fig. 6B</figref>, the value of the threshold T_DC is determined based on the output of the mosquito noise reduction block γ₁|<i>u</i>|. The parameter γ₁ is a weighting coefficient preferably satisfying the condition 0 ≤ γ₁ ≤ 1, which provides a tradeoff between image smoothness versus reduction of MPEG artifacts in the image. γ₁ defines the strength of the MPEG artifact adaptive reduction feature, i.e., controls the adaptive threshold T_DC. When the γ₁|<i>u</i>| value is smaller than T₀, T_DC becomes equal to T₀.

0053This modification adds an additional filtration property, efficiently decreasing DC blocking artifacts and pure vertical and horizontal ringing without introducing any significant blurring to the image. In one example, the value of the parameter γ₁ that provides satisfactory results is γ₁ ≈ 0.5, based on subjective testing.

0054Returning to <figref idref="f0001">Fig. 1</figref>, at multiplier block 130, the result of the nonlinear function Ψ(Δ) that is the output of nonlinear processing module 115 is multiplied by parameter γ. γ is a weighting coefficient which preferably satisfies the condition 0 ≤ γ ≤ 1 and defines the strength of the MPEG artifact static reduction feature, i.e. portion of the local DC value blended with the mosquito noise reduction value. In fact, γ is a blurriness parameter that controls a static blurriness property of the whole frame from a minimum to a maximum defined by the local DC value. For instance, when γ is 1.0, an artifacts reduction value 135 of output module 125 is nonlinear function Ψ(Δ). When γ is 0, the artifacts reduction value 135 of output module 125 is the local DC value E_DC. Those skilled in the art will appreciate, that when γ is zero or close to zero, small details in the image frame are blurred because they are made equal to local DC value. In one example, the values of the control parameter γ that provide satisfactory results are γ = 0.8, ..., 1, based on subjective testing.

0055Mosquito noise reduction processing is based on the assumption that its dynamic range is limited to the value defined by the threshold T₁. A dynamic range measure <i>M</i> is a function of all absolute values of pixel differences a'-i' inside the sliding window. <i>M</i> is a nonlinear function <i>F_DA</i>() of absolute values of differences that takes into account the influence of the particular difference a'-i' to the dynamic range measure. For a 3x3 window, <i>M</i> can be represented as<maths id="math0012"><math display="block"><mi>M</mi><mo>=</mo><msub><mi>F</mi><mi mathvariant="italic">DR</mi></msub><mfenced><mfenced open="|" close="|"><mi mathvariant="italic">aʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">bʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">cʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">dʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">fʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">gʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">fʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">hʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">iʹ</mi></mfenced></mfenced><mo>,</mo></math><img file="EP1545134B1_D0012.tif" /></maths>

0056When the dynamic range measure is less than or equal to the threshold, it has a unity value. When the dynamic range measure of the sliding window exceeds the threshold, the output modified pixel value has to be reduced as follows:<maths id="math0013"><math display="block"><mover><mi>e</mi><mo>‾</mo></mover><mo>=</mo><mi>e</mi><mo>+</mo><mi mathvariant="italic">λuʹ</mi><mo>,</mo></math><img file="EP1545134B1_D0013.tif" /></maths> where λ is an MPEG artifact attenuation factor. When the output modified pixel value is reduced to zero immediately after the threshold is exceeded, the hard switch case occurs. It is possible that from frame to frame, the pixel values at the same spatial location change from slightly smaller than the threshold to slightly larger than it. Therefore, for the hard switch case, the values of the same location output pixels in the neighboring frames will have quite different values. More over slightly smaller and then larger than the threshold from frame to frame may have a repetitive pattern. Therefore, some level of flickering can occur. To avoid this phenomenon, a smooth attenuation operation is performed. When M is below or equal to the threshold T₁, the MPEG artifact attenuation factor is 1. As soon as <i>M</i> exceeds the threshold, the value of λ starts to decrease linearly. When <i>M</i> reach the value <i>T</i>₁ + <i>T</i>₁/<i>K</i>, λ is equal zero for all greater values. K is a steepness coefficient of the linear smooth transition

0057<figref idref="f0009">Fig. 8A</figref> shows a block diagram of smooth attenuation module 120 for a 3x3 sliding window that performs a smooth attenuation operation 800. <figref idref="f0010">Fig. 8B</figref> shows a flow diagram of a method 800 for performing the smooth attenuation operation.

0058In step 810 of <figref idref="f0010">Fig. 8B</figref>, the dynamic range measure M is calculated from the pixel value differences, as explained above. The nonlinear function <i>F_DR</i>( ) takes into account the amount of the influence of a particular pixel difference to the output value based on the spatial location closeness to the central pixel, and is represented as:<maths id="math0014"><math display="block"><mi>M</mi><mo>=</mo><mrow><mo>{</mo><mtable><mtr><mtd><msub><mi>M</mi><mn>1</mn></msub></mtd><mtd><msub><mi>M</mi><mn>1</mn></msub><mo>≥</mo><msub><mi>M</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><msub><mi>M</mi><mn>1</mn></msub><mo>+</mo><mn>0.5</mn><mo>⁢</mo><mfenced><msub><mi>M</mi><mn>2</mn></msub><mo>-</mo><msub><mi>M</mi><mn>1</mn></msub></mfenced><mo>,</mo></mtd><mtd><msub><mi>M</mi><mn>1</mn></msub><mo>&lt;</mo><msub><mi>M</mi><mn>2</mn></msub></mtd></mtr></mtable></mrow><mo>,</mo></math><img file="EP1545134B1_D0014.tif" /></maths><maths id="math0015"><math display="block"><msub><mi>M</mi><mn>1</mn></msub><mo>=</mo><mi>max</mi><mfenced><mfenced open="|" close="|"><mi mathvariant="italic">bʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">dʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">fʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">hʹ</mi></mfenced></mfenced><mo>,</mo><msub><mi>M</mi><mn>2</mn></msub><mo>=</mo><mi>max</mi><mfenced><mfenced open="|" close="|"><mi mathvariant="italic">aʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">cʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">gʹ</mi></mfenced><mfenced open="|" close="|"><mi mathvariant="italic">iʹ</mi></mfenced></mfenced><mn>.</mn></math><img file="EP1545134B1_D0015.tif" /></maths>

0059The corner pixel differences <i>a'</i>,<i>c'</i>,<i>g'</i>,<i>i'</i> have twice less influence and contribution than "cross" pixel differences <i>b',d', f',h'</i> to the output value.

0060In step 820, the smoothing coefficient value λ is based on <i>M</i> and <i>T</i>₁ and calculated as follows:<maths id="math0016"><math display="block"><mi>λ</mi><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left"><mtr><mtd><mspace width="1em" /><mn>1</mn><mo>,</mo><mi>r</mi><mo>≥</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>r</mi><mo>,</mo><mn>0</mn><mo>&lt;</mo><mi>r</mi><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>where</mi><mspace width="1em" /><mi>r</mi><mo>=</mo><mn>1</mn><mo>-</mo><mi>K</mi><mo>⁢</mo><mfenced><mfrac><mi>M</mi><msub><mi>T</mi><mn>1</mn></msub></mfrac><mo>-</mo><mn>1</mn></mfenced><mn>.</mn></mtd></mtr><mtr><mtd><mspace width="1em" /><mn>0</mn><mo>,</mo><mi>r</mi><mo>≤</mo><mn>0</mn></mtd></mtr></mtable></mrow></math><img file="EP1545134B1_D0016.tif" /></maths>

0061<figref idref="f0009 f0010">Fig. 8</figref> shows the case for K = 1 that, based on the subjective experimentation, provides satisfactory results. The output value of the MPEG artifact attenuation factor λ is applied to limit application of the nonlinear function to the selected pixel value e.

0062<figref idref="f0011">Fig. 9A</figref> shows a graphical illustration of the smoothing coefficient λ as a function of M for various values of <i>T</i>₁ and K=1 and K=2.

0063In step 830 of <figref idref="f0010">Fig. 8B</figref>, the smooth attenuation module 120 also computes and outputs a Gaussian Noise attenuation factor λ₁ that is one of the inputs to the output module 125. When Gaussian Noise attenuation is disabled, by switch 145 in <figref idref="f0001">Fig. 1</figref>, the value of λ₁ has to be equal to unity, and the residual value inside the output module 125 is not modified as will be described below. When the value of λ₁ equals 0, the residual value inside the output module 125 is forced to the local DC value. The zone where λ₁ equals 0 is defined by the dynamic range measure M and the threshold T₂ when <i>M</i> ≤ <i>T</i>₂. In a similar manner to MPEG artifact attenuation factor λ, to avoid the hard switch between cases when <i>M ≤ T</i>₂<i>and M</i> > <i>T</i>₂, the smooth attenuation is done by applying a linear transition zone for <i>T</i>₂ ≤ <i>M ≤</i> 2<i>T</i>₂. Thus the value of λ₁ is determined as<maths id="math0017"><math display="block"><msub><mi>λ</mi><mn>1</mn></msub><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left"><mtr><mtd><mspace width="1em" /><mn>1</mn><mo>,</mo><mi>p</mi><mo>≥</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>p</mi><mo>,</mo><mn>0</mn><mo><</mo><mi>p</mi><mo><</mo><mn>1</mn><mo>,</mo><mi>p</mi><mo>=</mo><mfenced><mfrac><mi>M</mi><msub><mi>T</mi><mn>2</mn></msub></mfrac><mo>-</mo><mn>1</mn></mfenced><mn>.</mn></mtd></mtr><mtr><mtd><mspace width="1em" /><mn>0</mn><mo>,</mo><mi>p</mi><mo>≤</mo><mn>0</mn></mtd></mtr></mtable></mrow></math><img file="EP1545134B1_D0017.tif" /></maths>

0064<figref idref="f0011">Fig. 9B</figref> shows a graphical illustration of the smoothing coefficient λ₁ as a function of M for various values of <i>T</i>₂.

0065In <figref idref="f0001">Fig. 1</figref>, the output module 125 provides application of the nonlinear function Ψ(Δ), multiplied by the parameter γ in module 130 and entered to a first input of the MPEG artifact reduction on/off switch 140 in <figref idref="f0001">Fig. 1</figref>. The second input of the switch 140 is a Local DC value with the reversed -<i>E_DC</i>. When switch 140 is in the 'on' position, MPEG artifact reduction mode is enabled. When switch 140 is in the 'off' position, MPEG artifact reduction mode is disabled. When the MPEG artifact reduction mode is enabled, the input value 134 to the output module 125 is γΨ(Δ), and when the MPEG artifact reduction mode is disabled, the input value is - <i>E_DC</i>.

0066<figref idref="f0012">Fig. 10</figref> shows a flow diagram of a method 1000 performed by the output module 125 <figref idref="f0001">Fig. 1</figref>. In step 1010, the input value 134 from switch 140 is multiplied by input value 133, that is, the Gaussian Noise attenuation factor λ₁. In step 1020, the result is added to input signal 132, that is, the local DC value, to compute value 135. When both MPEG artifact reduction mode and Gaussian Noise reduction mode are enabled, the value 135 equals<maths id="math0018"><math display="block"><mi mathvariant="italic">uʹ</mi><mo>=</mo><msub><mi>λ</mi><mn>1</mn></msub><mo>⁢</mo><mi>γ</mi><mo>⁢</mo><mi mathvariant="normal">Ψ</mi><mfenced><mi mathvariant="normal">Δ</mi></mfenced><mo>+</mo><msub><mi>E</mi><mi mathvariant="italic">DC</mi></msub><mo>,</mo></math><img file="EP1545134B1_D0018.tif" /></maths>

0067When MPEG artifact reduction mode is disabled and Gaussian Noise reduction mode is enabled, the value 135 equals <maths id="math0019"><math display="block"><mi mathvariant="italic">uʹ</mi><mo>=</mo><mo>-</mo><msub><mi>λ</mi><mn>1</mn></msub><mo>⁢</mo><msub><mi>E</mi><mi mathvariant="italic">DC</mi></msub><mo>+</mo><msub><mi>E</mi><mi mathvariant="italic">DC</mi></msub><mo>=</mo><msub><mi>E</mi><mi mathvariant="italic">DC</mi></msub><mo>⁢</mo><mfenced><mn>1</mn><mo>-</mo><msub><mi>λ</mi><mn>1</mn></msub></mfenced><mn>.</mn></math><img file="EP1545134B1_D0019.tif" /></maths>

0068When both the MPEG Artifact Reduction mode and Gaussian Noise reduction mode are disabled, λ₁ = 1 and the value 135 equals<maths id="math0020"><math display="block"><mi mathvariant="italic">uʹ</mi><mo>=</mo><msub><mi>E</mi><mi mathvariant="italic">DC</mi></msub><mo>⁢</mo><mfenced><mn>1</mn><mo>-</mo><mn>1</mn></mfenced><mo>=</mo><mn>0.</mn></math><img file="EP1545134B1_D0020.tif" /></maths>

0069When MPEG artifact reduction mode is enabled, and the Gaussian Noise reduction mode is disabled, the value 135 equals<maths id="math0021"><math display="block"><mi mathvariant="italic">uʹ</mi><mo>=</mo><mi>γ</mi><mo>⁢</mo><mi mathvariant="normal">Ψ</mi><mfenced><mi mathvariant="normal">Δ</mi></mfenced><mo>+</mo><msub><mi>E</mi><mi mathvariant="italic">DC</mi></msub><mn>.</mn></math><img file="EP1545134B1_D0021.tif" /></maths>

0070In step 1030, the value 135 is multiplied by the MPEG artifact attenuation factor λ, that is, value 104, to control the applicability of the artifact reduction with respect to the dynamic range measure <i>M.</i> In step 1040, the result is added to the value of the input pixel e to compute the output modified pixel value <i>e̅</i>. Therefore,<maths id="math0022"><math display="block"><mover><mi>e</mi><mo>‾</mo></mover><mo>=</mo><mi>e</mi><mo>+</mo><mi mathvariant="italic">λuʹ</mi></math><img file="EP1545134B1_D0022.tif" /></maths>

0071Embodiments of the invention, including the apparatus disclosed herein, can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations of them. Apparatus embodiments of the invention can be implemented in a computer program product tangibly embodied in a machine-readable storage device for execution by a programmable processor; and method steps of the invention can be performed by a programmable processor executing a program of instructions to perform functions of the invention by operating on input data and generating output. Embodiments of the invention can be implemented advantageously in one or more computer programs that are executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. Each computer program can be implemented in a high-level procedural or object-oriented programming language, or in assembly or machine language if desired; and in any case, the language can be a compiled or interpreted language.

0072Suitable processors include, by way of example, both general and special purpose microprocessors. Generally, a processor will receive instructions and data from a read-only memory and/or a random access memory. Generally, a computer will include one or more mass storage devices for storing data files; such devices include magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM disks. Any of the foregoing can be supplemented by, or incorporated in, ASICs (application-specific integrated circuits).