The hierarchical signal dependent transform: Creating orthonormal basis that match local signal characteristics

Hierarchical transforms are widely used in image and video coding to produce multilevel decomposition of signals. After applying these transforms, same level signals are typically uncorrelated. However, there is often still significant cross level information. Traditionally, this cross-level information is exploited at the entropy coding step, but not at the transform step. The main contribution of this work is an energy compaction technique/transform that can also exploit these cross-resolution-level structural similarities. The core idea of the technique is to include in the hierarchical transform a number of adaptive basis functions derived from the lower resolution of the signal. A full image codec was developed in order to measure the performance of the new transform. Results are presented in terms of transform coding gain, energy concentration and distortion versus rate curves compared with standard JPEG, JPEG 2000 and JPEG XR.