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