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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?