Transform/subband representations for signals with arbitrarily shaped regions of support

Transform/subband representations form a basic building block for many signal processing algorithms and applications. Most of the effort has focused on developing representations for infinite-length signals, with simple extensions to finite-length 1-D and rectangular support 2-D signals. However, many signals may have arbitrary length or arbitrarily shaped (AS) regions of support (ROS). We present a novel framework for creating critically sampled perfect reconstruction transform/subband representations for AS signals. Our method selects an appropriate subset of vectors from an (easily obtained) basis for a larger (superset) signal space, in order to form a basis for the AS signal. In particular, we have developed a number of promising wavelet representations for arbitrary-length l-D signals and AS 2-D/M-D signals that provide high performance with low complexity.