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lectureDCT.220.06.4up - The Discrete Cosine Transform...

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Hemami JPEG lec.-1-10/2/06 The Discrete Cosine Transform: the “basis” for Baseline JPEG Outline Motivation: image compression & JPEG. Block based transforms in 1-D and 2-D. DCT definition & properties. Example applications to images. ECE 220 Fall 2006 Prof. Hemami Hemami JPEG lec.-2-10/2/06 Lossy Image Compression 1. Data transform is invertible and most commonly a frequency transform... Block-based (e.g., JPEG with a DCT). Wavelet-based (e.g., JPEG-2000). 2. Quantization reduces the amount of data (this is the “loss” ) (and should consider human visual system characteristics for best performance). Data Transform Quantization Entropy Code 1 2 3 Hemami JPEG lec.-3-10/2/06 Lossy Image Compression, ctd. 3. Entropy coding is lossless and compacts the bit stream (coding is variable-length). Data Transform Quantization Entropy Code 1 2 3 Hemami JPEG lec.-4-10/2/06 Baseline JPEG image component Q 8 x 8 D C T Q u a n t i z e D P C M Z i g - Z a g S c a n R u n - l e n g t h e n c o d e DC AC E n t r o p y C o d e 001 0001 (3,14) (3,21) ... arrange into bitstream Entropy Coding Transform Quantization
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Hemami JPEG lec.-5-10/2/06 Block-based Transforms for DT Signals For a finite duration signal, DTFT transforms N samples (which we can easily store) into a continuous function on — now we need an “infinite” number of points to represent it! A block-based transform analyzes N samples at a time, and represents them by N coefficients in frequency. We say it has “block-length N. Example: the DFT! Break signal into separate blocks & transform. Representing a signal by its transform is called block-based transform coding . ω π π) , [ Hemami JPEG lec.-6-10/2/06 Block-based Transform Coding Each transform coefficient for a block is formed as the inner product of the block and an basis vector : n p n ( ) block
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