Periodic Gabor Functions with Biorthogonal Exchange: A Highly Accurate and Efficient Method for Signal Compression

TL;DR

This paper introduces a novel periodic Gabor basis set with biorthogonal exchange for signal compression, offering high accuracy and efficiency, especially for band-limited functions, demonstrated through various signal examples.

Contribution

The paper presents a new formalism for signal compression using a periodic Gabor basis and biorthogonal exchange, overcoming limitations of traditional Gabor methods.

Findings

Achieves high compression factors with stable coefficient calculation

Exact representation for band-limited functions with finite support

Effective on signals including audio and image processing examples

Abstract

We propose a new formalism for signal compression based on the Gabor basis set. By convolving the conventional Gabor functions with Dirichlet functions we obtain a periodic version of the Gabor basis set (pg). The pg basis is exact for functions that are band-limited with finite support, bypassing the Balian-Low theorem. The calculation of the pg coefficients is trivial and numerically stable, but the representation does not allow compression. However, by exchanging the pg basis with its biorthogonal basis and using the localized pg basis to calculate the coefficients, large compression factors are achieved. We illustrate the method on three examples: a rectangular pulse, an audio signal and a benchmark example from image processing.