Wavelet Based Image Coding
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 seminar class Active In SP Posts: 5,361 Joined: Feb 2011 23-02-2011, 11:07 AM   631pub04_sec11waveletCoding.ppt (Size: 1.82 MB / Downloads: 100) Wavelet Based Image Coding Overview and Logistics  Last Time: – Transform coding  Today: – JPEG compression standard: Baseline block-DCT based algorithm u lossy part: quantization with different step size for each coeff. Band u lossless part: differential coding, run-length coding, Huffman => Continued with the class notes handed out in last lecture – Subband and Wavelet based compression u Exploiting the structures between coefficients for removing redundancy Wavelet Transform for Image Compression  ENEE631 emphasis – Focus on conceptual aspects related to image compression – Wavelet is also useful for denoising, enhancement, and image analysis – Build upon filterbank and subband coding from ENEE630 (For more in-depth info. on wavelet: wavelet course offered in Math Dept.)  K-level 1-D wavelet/subband decomposition – Successive lowpass/highpass filtering and downsampling u on different level: capture transitions of different frequency bands u on the same level: capture transitions at different locations Successive Wavelet/Subband Decomposition Successive lowpass/highpass filtering and downsampling u on different level: capture transitions of different frequency bands u on the same level: capture transitions at different locations Examples of 1-D Wavelet Transform 2-D Wavelet Transform via Separable Filters 2-D Example Subband Coding Techniques  General coding approach – Allocate different bits for coeff. in different frequency bands – Encode different bands separately – Example: DCT-based JPEG and early wavelet coding  Some difference between subband coding and early wavelet coding ~ Choices of filters – Subband filters aims at (approx.) non-overlapping freq. response – Wavelet filters has interpretations in terms of basis and typically designed for certain smoothness constraints (=> will discuss more )  Shortcomings of subband coding – Difficult to determine optimal bit allocation for low bit rate applications – Not easy to accommodate different bit rates with a single code stream – Difficult to encode at an exact target rate Smoothness Conditions on Wavelet Filter – Ensure the low band coefficients obtained by recursive filtering can provide a smooth approximation of the original signal Embedded Zero-Tree Wavelet Coding (EZW)  Modern” lossy wavelet coding exploits multi-resolution and self-similar nature of wavelet decomposition – Energy is compacted into a small number of coeff. – Significant coeff. tend to cluster at the same spatial location in each frequency subband  Two set of info. to code: – Where are the significant coefficients? – What values are the significant coefficients?