Weighted universal transform coding: universal image compression with the Karhunen-Loeve transform

We introduce a two-stage universal transform code for image compression. The code combines Karhunen-Lo eve transform coding with weighted universal bit allocation (WUBA) 1] in a two-stage algorithm analogous to the algorithm for weighted universal vector quantization (WUVQ) 2, 3]. The encoder uses a collection of transform / bit allocation pairs rather than a single transform / bit allocation pair (as in JPEG) or a single transform with a variety of bit allocations (as in WUBA). We describe both an encoding algorithm for achieving optimal compression using a collection of transform / bit allocation pairs and a technique for designing locally optimal collections of transform / bit allocation pairs. We demonstrate performance using the mean squared error distortion measure. On a sequence of combined text and gray scale images, the algorithm achieves up to 2 dB improvement over a JPEG style coder using the discrete cosine transform (DCT) and an optimal collection of bit allocations, up to 3 dB improvement over a JPEG style coder using the DCT and a single (optimal) bit allocation, up to 6 dB over an en-tropy constrained WUVQ with rst-and second-stage vector dimensions equal to 16 and 4 respectively, and up to 10 dB improvement over an entropy constrained vector quantizer (ECVQ) with vector dimension 4.