Multiwavelet Image Compression

Poster summary

Goal: compare lossy image compression performance of multiwavelets vs. biorthogonal scalar wavelets
Multiwavelets (MW) allow for linear phase, finite impulse response filters which are orthogonal (impossible to achieve with scalar wavelets)
Orthogonality is necessary for coefficient decorrelation
Use state of the art compressor (SPIHT) as comparison platform
Change transform, keep prediction tree and entropy coding stage (makes fair comparison)
Result: multiwavelets do very well—- within 0.5 dB PSNR from SPIHT - but they are not the best ;-)

Iterated wavelet transform
Hierarchical prediction of coefficient magnitudes to exploit self-similarity across scales
Quantization with octavely decreasing thresholds
(coding of "bitplanes")
Arithmetic coding with context modeling
Produces fully embedded bitstream

View MW transform as time-varying filterbank
(see balanced multiwavelet poster)
Interleave coefficients at output (1-D transform):
L₀[0]L₁[0]…L₀[N/4-1]L₁[N/4-1] | H₀[0]H₁[0]…H₀[N/4-1]H₁[N/4-1]
Separable 2-D transform (vectorization would introduce noise, thus kill performance)
Main issue: yield non-expansive transform via symmetric extension at borders
Downsampling by four and filter symmetries restrict filter centering: unavoidable 0.5 pixel phase shift in lowpass

Remarkably good PSNR performance compared to SPIHT with 9/7-tap biorthogonal wavelets
Performance limited by lowpass phase shift and very dissimilar characteristics of highpass filters
Changing tree structure (but not branch factors) to predict like coeffs does not improve compression
Confirms rule of thumb: strict orthogonality is not a key factor in image transform coding

Test pictures: caution, this page contains more than 600 kB distorted Lena pictures
Balanced multiwavelet filter coefficients (Matlab files)
SPIHT homepage
Our source code is not available, because we used copyrighted code from SPIHT :-(

Claudio Weidmann, Jerome Lebrun and Martin Vetterli, ``Significance tree image coding using balanced multiwavelets'', to appear in Proc. of ICIP-98, Chicago, Illinois, October 1998. [Abstract] [pdf]