Previous optical implementations of the two-dimensional fractional Fourier transform have assumed identical transform orders in both dimensions. We let the orders in the two orthogonal dimensions to be different and present general design formulae for optically implementing such transforms. This design formulae allows us to specify the two orders and the input, output scale parameters simultane...

In this article, an image feature extraction method based on two-dimensional (2D) Mellin cepstrum is introduced. The concept of one-dimensional (1D) mel-cepstrum that is widely used in speech recognition is extended to two-dimensions using both the ordinary 2D Fourier transform and the Mellin transform. The resultant feature matrices are applied to two different classifiers such as common matri...

This paper extends the concepts of the Sparse Fast Fourier Transform (sFFT) Algorithm introduced in [1] to work with two dimensional (2D) data. The 2D algorithm requires several generalizations to multiple key concepts of the 1D sparse Fourier transform algorithm. Furthermore, several parameters needed in the algorithm are optimized for the reconstruction of sparse image spectra. This paper add...

Optical implementation of a three-dimensional (3-D) Fourier transform is proposed and demonstrated. A spatial 3-D object, as seen from the paraxial zone, is transformed to the 3-D spatial frequency space. Based on the new procedure, a 3-D joint transform correlator is described that is capable of recognizing targets in the 3-D space.

It is a consensus in signal processing that the Gaussian kernel and its partial derivatives enable the development of robust algorithms for feature detection. Fourier analysis and convolution theory have central role in such development. In this paper we collect theoretical elements to follow this avenue but using the q-Gaussian kernel that is a nonextensive generalization of the Gaussian one. ...

We develop a harmonic analysis on objects of some category C 2 of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. The main result is the theory of the Fourier transform on these objects and two-dimensional Poisson formulas.

Following the ideas from a paper by same author, we prove abstract maximal restriction results for Fourier transform. Our deal mainly with operators of convolution-type and $r-$average functions. As by-product our techniques obtain spherical estimates, as well estimates $2-$average functions, answering thus points left open V. Kovac Muller, Ricci Wright.

We propose RSFT, which is an extension of the one dimensional Sparse Fourier Transform algorithm to higher dimensions in a way that it can be applied to real, noisy data. The RSFT allows for off-grid frequencies. Furthermore, by incorporating Neyman-Pearson detection, the frequency detection stages in RSFT do not require knowledge of the exact sparsity of the signal and are more robust to noise...

We develop a harmonic analysis on objects of some category C 2 of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. The main result is the theory of the Fourier transform on these objects and two-dimensional Poisson formulas.