Backtracking-Based Iterative Regularization Method for Image Compressive Sensing Recovery

Abstract

This paper presents a variant of the iterative shrinkage-thresholding (IST) algorithm, called backtracking-based adaptive IST (BAIST), for image compressive sensing (CS) reconstruction. For increasing iterations, IST usually yields a smoothing of the solution and runs into prematurity. To add back more details, the BAIST method backtracks to the previous noisy image using L2 norm minimization, i.e., minimizing the Euclidean distance between the current solution and the previous ones. Through this modification, the BAIST method achieves superior performance while maintaining the low complexity of IST-type methods. Also, BAIST takes a nonlocal regularization with an adaptive regularizor to automatically detect the sparsity level of an image. Experimental results show that our algorithm outperforms the original IST method and several excellent CS techniques.

A Novel Iterative Thresholding Algorithm Based on Plug-and-Play Priors for Compressive Sampling

“…There are two algorithms based on iterative shrinkage-thresholding method FCSA [1] (using wavelet sparsity and gradient sparsity), WaTMRI [2] (using wavelet sparsity, gradient sparsity and tree sparsity) and two Bayesian CS methods Turbo-AMP [3] (using tree sparsity), D-AMP [6] (using nonlocal sparsity via BM3D denoiser). Three experiments are carried on both natural images and MR (Magnetic Resonance) images with size 256 × 256 at four sampling ratios (18,20,22, and 25%). The eight natural images and four MR images used in our experiments are shown in Figure 1.…”

“…For representing the global sparsity, we use the wavelet and gradient denoiser. This multiple denoisers problem is then solved based on fast composite splitting technique [5] and the fast proximal method FISTA (fast iterative shrinkage-thresholding algorithm) [20,21]. In the frame of FISTA, the original composite regularization problem is firstly decomposed into three simpler regularization sub-problems via fast composite splitting technique; then each of them is separately solved by thresholding methods.…”

A Preliminary Comparison Between Compressive Sampling and Anisotropic Mesh-based Image Representation

“…CS has been applied to computed tomography (CT) [9,10] and MRI [11,12,13] reconstructions to improve the acquisition speed. It has also been applied to represent digital images obtained from different sources [14,15], although many images are not sparse on their own.…”