Abstract
Recently, compressed sensing (CS) has aroused much attention for that sparse signals can be retrieved from a small set of linear samples. Algorithms for CS reconstruction can be roughly classified into two categories: (1) optimization-based algorithms and (2) greedy search ones. In this paper, we propose an algorithm called the preconditioned generalized orthogonal matching pursuit (Pre-gOMP) to promote the recovery performance. We provide a sufficient condition for exact recovery via the Pre-gOMP algorithm, which says that if the mutual coherence of the preconditioned sampling matrix Φ satisfies mu ({Phi }) < frac {1}{SK -S + 1}, then the Pre-gOMP algorithm exactly recovers any K-sparse signals from the compressed samples, where S (>1) is the number of indices selected in each iteration of Pre-gOMP. We also apply the Pre-gOMP algorithm to the application of ghost imaging. Our experimental results demonstrate that the Pre-gOMP can largely improve the imaging quality of ghost imaging, while boosting the imaging speed.
Highlights
Compressed sensing (CS) has gained a lot of interests and promoted the applications of many fields, such as the imaging signal processing, applied mathematics, and statistics [1–5]
Our experimental results demonstrate that the Pre-generalized OMP (gOMP) can largely improve the imaging quality of ghost imaging, while boosting the imaging speed
The primary contributions of this paper are summarized as follows: 1. Based on the mutual coherence framework, we develop a sufficient condition for the Pre-gOMP algorithm
Summary
Compressed sensing (CS) has gained a lot of interests and promoted the applications of many fields, such as the imaging signal processing, applied mathematics, and statistics [1–5]. 1 − S + 1, the Pre-gOMP algorithm exactly recovers any K-sparse signals from the compressed samples, where S (> 1) is the number of indices selected in each iteration of Pre-gOMP. We apply the Pre-gOMP algorithm to the application of ghost imaging. We propose a preconditioned gOMP (Pre-gOMP) algorithm for the recovery of sparse signals. The Pre-gOMP algorithm consists of (i) a preconditioning step and (ii) a conventional signal reconstruction step.
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