Spark Deficient Gabor Frames for Inverse Problems

TL;DR

This paper introduces a star-Digital Gabor Transform that creates spark deficient Gabor frames with many linear dependencies, improving performance in compressed sensing and speech denoising tasks compared to traditional methods.

Contribution

The paper presents a novel star-Digital Gabor Transform that generates spark deficient frames with linear dependencies, enhancing analysis in compressed sensing and speech denoising.

Findings

Star-Gabor transform outperforms baseline Gabor transforms in all tested signal cases.

Generated frames have many linear dependencies, beneficial for inverse problems.

Experimental results on synthetic and real signals validate the proposed method's effectiveness.

Abstract

In this paper, we apply star-Digital Gabor Transform in analysis Compressed Sensing and speech denoising. Based on assumptions on the ambient dimension, we produce a window vector that generates a spark deficient Gabor frame with many linear dependencies among its elements. We conduct computational experiments on both synthetic and real-world signals, using as baseline three Gabor transforms generated by state-of-the-art window vectors and compare their performance to star-Gabor transform. Results show that the proposed star-Gabor transform outperforms all others in all signal cases.