Compressed Sensing Recoverability In Imaging Modalities

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.