Globally optimal algorithms for multiple-transform signal compression

Abstract

In video compression, a single transform such as the DCT is typically used. Multiple-transforms such as directional 1-D DCTs have been proposed to exploit the different statistical characteristics of motion compensation residuals. Many issues are associated with this scenario. In this thesis, we will focus on the issue of selecting the appropriate number of coefficients and transforms to be allocated for each block of the signal to optimize the energy compaction. We propose two new methods to select optimal transforms for different blocks in a signal. The first method is based on thresholding, while the second method is based on dynamic programming and related to the multiple-choice knapsack problem. These algorithms are then compared to two other previous algorithms. We analyze the energy compaction performance of these algorithms in terms of different block-sizes and different input characteristics. We then extend all of these algorithms to quantizated coefficients being transmitted, as well as to take a bit-rate constraint into account.