Multiresolution Lattice Discrete Fourier Transform (MRL-DFT)
Fred L. Fontaine, Cooper Union, New York City, USA
In many imaging applications, including sensor arrays, MRI and CT,data is often sampled on non-rectangular point sets with non-uniform density. Moreover, in image and video processing, a mix of non-rectangular sampling structures naturally arise. Multirate processing typically utilizes a normalized integer indexing scheme, which masks the true physical dimensions of the points. However, the spatial correlation of such signals often contains important information.This paper presents a theory of signals defined on regular discrete sets called lattices, and presents an associated form of a finite Fourier transform denoted here as multiresolution lattice discrete Fourier transform (MRL-DFT). Multirate processing techniques such as decimation, interpolation and polyphase representations are presented in a context which preserves the true spatial dimensions of the sampling structure.Moreover, the polyphase formulation enables systematic representation and processing for sampling patterns with variable spatial density, and provides a framework for developing generalized FFT and regridding algorithms.