M-band filtering and nonredundant directional wavelets

This article introduces families of nonadaptive directional wavelets. Unlike curvelets and contourlets, they are nonredundant and form orthonormal bases for L2(R2). Their implementation derives from a single nonseparable filter bank structure with nonuniform sampling. We give several examples of frequency partitioning, including constructions based on separable multiresolution analyses. We show how to obtain orthonormal bases of wavelets with fast decay and compactly supported, biorthogonal wavelet bases. Some aliasing phenomena that can occur in these constructions are discussed.