Orthogonal matching pursuit vs. iterative hard thresholding: addressing phase discontinuities in digital holography

Abstract

This paper presents a novel comparative study between two prominent compressed sensing algorithms -Orthogonal Matching Pursuit (OMP) and Iterative Hard Thresholding (IHT) -within the context of digital holography, specifically focusing on their efficacy in handling phase discontinuities. Previous research has predominantly centered on Gibbs ringing artifacts in image reconstruction and their mitigation. However, the aspect of phase discontinuities, which are critical in holographic imaging, has not been extensively explored. Our study implement both OMP and IHT algorithms in a simulated digital holographic environment, where phase discontinuities are inherent due to the nature of holographic imaging. We analyze how these algorithms perform in the presence of phase discontinuities. We quantitatively analyze the performance of each algorithm in handling phase discontinuities. Additionally, our study delves into the computational efficiency of both algorithms, considering their practical applicability in real-time holographic imaging systems. The results of our comparative analysis provide insights into the advantages and limitations of OMP and IHT in the context of phase discontinuities. Our findings have significant implications for advancing digital holography, particularly in applications requiring precise phase information, such as medical imaging, microscopy, and non-destructive testing.