Introduction1 - JPEG2000 Algorithm1.1 - Architecture1.2 – 2D-DWT2 – Implementation2-1 – Non optimized version2.2 – Optimizations3 – Verification4 – Profiler5 – Results6 – ReferencesImplementation of JPEG2000Using SSE Instruction SetECE 734VLSI Array StructuresFor Digital Signal ProcessingAmi MehtaGilles Muller Spring 20040Table of ContentsIntroduction.....................................................................................................21 - JPEG2000 Algorithm.................................................................................31.1 - Architecture.........................................................................................31.2 – 2D-DWT.............................................................................................32 – Implementation.........................................................................................52-1 – Non optimized version.......................................................................52.2 – Optimizations......................................................................................63 – Verification................................................................................................84 – Profiler.......................................................................................................95 – Results.......................................................................................................96 – References...............................................................................................111IntroductionJPEG2000 is a new image compression standard being developed by the JointPhotographic Experts Group (JPEG), part of the International Organization forStandardization (ISO). It is designed for different types of still images (bi-level, gray-level, color, multicomponent) allowing different imaging models (client/server, real-timetransmission, image library archival, limited buffer and bandwidth resources, etc), withina unified system. JPEG2000 is intended to provide low bit rate operation with rate-distortion and subjectiveimage quality performance superior to existing standards, without sacrificingperformance at other points in the rate-distortion spectrum. JPEG2000 addresses areas where current standards fail to produce the best quality ofperformance, such as: - Low bit rate compression performance (rates below 0.25 bpp for highly-detailedgray-level images) - Lossless and lossy compression in a single code stream - Seamless quality and resolution scalability, without having to download the entirefile. The major benefit is the conservation of bandwidth - Large images: JPEG is restricted to 64k x 64k images (without tiling). JPEG2000will handle image sizes up to ( 232-1 ) - Single decompression architecture - Error resilience for transmission in noisy environments, such as wireless and theInternet - Computer generated imagery - Compound documents - Region of Interest coding - Improved compression techniques to accommodate richer content and higherresolutions - Metadata mechanisms for incorporating additional non-image data as part of thefile - JPEG2000 will be able to handle up to 256 channels of information, as comparedto JPEG, which is limited to only RGB data. Thus, JPEG2000 will be capable ofdescribing complete alternate color models, such as CMYK, and full ICC(International Color Consortium). 21 - JPEG2000 Algorithm1.1 - ArchitectureThe encoding procedure is as follows:--The source image is decomposed into components.--The image and its components are decomposed into rectangular tiles. The tile-component is the basic unit of the original or reconstructed image.--The wavelet transform is applied on each tile. The tile is decomposed in differentresolution levels.--These decomposition levels are made up of subbands of coefficients that describe thefrequency characteristics of local areas (rather than across the entire tile-component) ofthe tile component. --Markers are added in the bitstream to allow error resilience.--The codestream has a main header at the beginning that describes the original imageand the various decomposition and coding styles that are used to locate, extract, decodeand reconstruct the image with the desired resolution, fidelity, region of interest and othercharacteristics.--The optional file format describes the meaning of the image and its components in thecontext of the application.1.2 – 2D-DWTThis process decomposes the original image into two sub-bands, usually denoted as thecoarse scale approximation (lower band) and the detail signal (higher band). Thistransform can be easily extended to multiple dimensions by using separable filters, i.e. byapplying separate 1-D transforms along each dimension. In particular, we haveimplemented the most common approach, commonly known as the squaredecomposition. This scheme alternates between operations on rows and columns, i.e. onestage of the 1-D DWT is applied first to the rows of the image and then to the columns. 3This process is applied recursively to the quadrant containing the coarse scaleapproximation in both directions. In this way, the data on which computations areperformed is reduced to a quarter in each step.From a performance point of view, the main bottleneck of this transformation is causedby the vertical filtering (the processing of image columns) or the horizontal one (theprocessing of image rows), depending on whether we assume a row-major or a column-major layout for the images.The lifting filter computes the low frequency and high frequency coefficients in 1-D.The following filter coefficients are used for JPEG2000 lossy filter:42 – Implementation2-1 – Non optimized versionWe chose to implement the lifting transform using Daubichies 9/7 Analysis. This wasdone mainly because lifting requires less working memory and fewer arithmeticcomputations. The lossy filter was implemented since our focus is to make JPEG2000faster on general purpose architectures, where some loss of resolution is tolerable andlossy compression gives a better compression ratio.This version was implemented only using C code. The lifting filter described abovecomputes high and low frequency coefficients in the same
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