A Min-Max Approach to the Multidimensional Nonuniform FFT: Application to Tomographic Image Reconstruction

Abstract

The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) over a set of uniformly spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e., a nonuniform FT. Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents a method for the nonuniform FT that is optimal in a min-max sense. The proposed method minimizes the worst-case approximation error over all signals of unit norm. Unlike many previous methods for the nonuniform FT, the proposed method easily generalizes to multidimensional signals. We are investigating this method as a fast algorithm for computing the Radon transform in 2D iterative tomographic image reconstruction.