Adaptive transform coding as constrained vector quantization

We investigate the application of local principal component analysis (PCA) to transform coding for fixed-rate image compression. Local PCA transform coding adapts to differences in correlations between signal components by partitioning the signal space into regions and compressing signal vectors in each region with a separate local transform coder. Previous researchers optimize the signal space partition and transform coders independently and consequently underestimate the potential advantage of using adaptive transform coding methods. We propose a new algorithm that concurrently optimizes the signal space partition and local transform coders. This algorithm is simply a constrained version of the LBG algorithm for vector quantizer design. Image compression experiments show that adaptive transform coders designed with our integrated algorithm compress an image with less distortion than previous related methods. We saw improvements in compressed image signal-to-noise ratio of 0.5 to 2.0 dB compared to other tested adaptive methods and 2.5 to 3.0 dB compared to global PCA transform coding.