It is popular to use multiresolution systems for image coding and compression. However, general-purpose techniques such as filter banks and wavelets are linear. While these systems are rigorous, nonlinear features in the signals cannot be utilized in a single entity for compression. Linear filters are known to blur the edges. Thus, the low-resolution images are typically blurred, carrying little information. We propose and demonstrate that edge- preserving filters such as median filters can be used in generating a multiresolution system using the Laplacian pyramid. The signals in the detail images are small and localized in the edge areas. Principal component vector quantization (PCVQ) is used to encode the detail images. PCVQ is a tree-structured VQ which allows fast codebook design and encoding/decoding. In encoding, the quantization error at each level is fed back through the pyramid to the previous level so that ultimately all the error is confined to the first level. With simple coding methods, we demonstrate that images with PSNR 33 dB can be obtained at 0.66 bpp without the use of entropy coding. When the rate is decreased to 0.25 bpp, the PSNR of 30 dB can still be achieved. Combined with an earlier result, our work demonstrate that nonlinear filters can be used for multiresolution systems and image coding.
"Combining nonlinear multiresolution system and vector quantization for still image compression", Proc. SPIE 2186, Image and Video Compression, (1 May 1994); doi: 10.1117/12.173916; https://doi.org/10.1117/12.173916