Critically sampled wavelet representations for multidimensional signals with arbitrary regions of support

Transform/subband representations form an important element of many signal processing algorithms and applications. Until recently, representations have typically been designed for signals with convenient supports, e.g. 2-D signals with rectangular supports. However, a number of applications require representations for signals with arbitrary (non-rectangular) regions of support. We present a novel algorithm for creating critically sampled perfect reconstruction wavelet representations for signals defined over arbitrary supports. The proposed algorithm selects a subset of vectors from a convenient superset basis which under appropriate conditions provides a basis over the given arbitrary support. The algorithm can be interpreted as solving a corresponding sampling problem