The Improvement of Compressive Sampling and Matching Pursuit Algorithm Based on Pre-estimation

This paper presents a novel iterative greedy reconstruction algorithm for compressed sensing, called the compressive sampling and matching pursuit algorithm based on pre-estimation (PCoSaMP). Compression sampling matching pursuit algorithm (CoSaMP) is widely applied to image reconstruction owing to its high precision of reconstruction, robustness, and simple operation. In this paper, we propose a new method, the PCoSaMP, to properly overcome the shortcomings in CoSaMP for choosing too much optional atoms and imprecise choice. The concept of the maximum estimation, which is called M, is proposed as a key point. The M is calculated from the current support set of target signals in each iteration using the largest correlation test method. At the next step, the M is regard as a selection condition for the optional atoms to decrease the number of candidate atoms and increase its accuracy. The simulation results show that this algorithm can precisely reconstruct the original signal. Under the same sampling rate, compared to the original algorithm, the proposed method can greatly shorten the recovery time, improve the PSNR and reconstruction performance.