Compressed Sensing Recoverability In Imaging Modalities

TL;DR

This paper presents a framework using the Spherical Section Property to analyze the recoverability of compressed sensing in imaging modalities, evaluating sampling patterns for sparse image recovery.

Contribution

It introduces a new recoverability analysis framework based on SSP for imaging applications, aiding in the design and evaluation of sampling patterns.

Findings

SSP provides a lower bound for unique sparse recovery.

Different sampling paradigms are evaluated for their effectiveness.

Numerical experiments validate the analysis of sampling pattern effectiveness.

Abstract

The paper introduces a framework for the recoverability analysis in compressive sensing for imaging applications such as CI cameras, rapid MRI and coded apertures. This is done using the fact that the Spherical Section Property (SSP) of a sensing matrix provides a lower bound for unique sparse recovery condition. The lower bound is evaluated for different sampling paradigms adopted from the aforementioned imaging modalities. In particular, a platform is provided to analyze the well-posedness of sub-sampling patterns commonly used in practical scenarios. The effectiveness of the various designed patterns for sparse image recovery is studied through numerical experiments.