Wavelets on Irregular Grids with Arbitrary Dilation Matrices, and Frame Atoms for L2(Rd)

ALDROUBI, AKRAM; CABRELLI, CARLOS; MOLTER, URSULA

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS

Elsevier

Lugar: San Diego, California USA; Año: 2004 vol. 17 p. 119 - 140

1063-5203

In this article, we develop a general method for constructing wa- velets {|detAj|1/2ψ(Ajx − xj,k) : j ∈ J,k ∈ K} on irregular lattices of the form X = {xj,k ∈ Rd : j ∈ J,k ∈ K}, and with an arbitrary countable family of invertible d × d matrices {Aj ∈ GLd(R) : j ∈ J} that do not nec- essarily have a group structure. This wavelet construction is a particular case of general atomic frame decompositions of L2(Rd) developed in this article, that allow other time frequency decompositions such as non-harmonic Gabor frames with non-uniform covering of the Euclidean space Rd. Possible applica- tions include image and video compression, speech coding, image and digital data transmission, image analysis, estimations and detection, and seismology.