Enhancement of transform coding by nonlinear interpolation

In conventional transform coding, a linear transformation generates a set of transform coefficients for each image block, followed by quantization of the transform coefficients and inverse transformation. We show that for a given transform encoder, the conventional decoder employing inverse transformation is a special case of a nonlinear interpolative decoder that performs table lookups to reconstruct the image blocks from the code indexes. In the nonlinear interpolative decoder, each received code index of an image block addresses a particular codebook to fetch a component block. The image block is then reconstructed as the vector sum of the component blocks. Hence with a set of well designed codebooks, this new decoding technique will be superior to the conventional decoder. In this paper, we develop an iterative algorithm for designing a set of locally optimal codebooks. We also present a hybrid decoder which combines conventional decoding with nonlinear interpolative decoding to reduced the memory requirement for codebook storage. Computer simulations with the JPEG image compression algorithm demonstrate that this new decoding technique can decode enhanced quality pictures from the bit stream generated by the standard encoding scheme.