LAUSR

Sparsity-regularized linear inverse problem has served as the base in many disciplines, such as remote sensing imaging, image processing and analysis, seismic deconvolution, compressed sensing, medical imaging, and so forth. The iterative hard thresholding algorithm (IHTA) and iterative soft thresholding algorithm (ISTA) are two frequently used methods to solve sparsity-regularized linear inverse problems. They are also the basic unit of other more complex methods. IHTA and ISTA are derived under the steepest descent method, i.e., iteratively perform gradient descent and thresholding shrinkage. The steepest descent method is a first-order algorithm, which is a powerful way to solve optimization due to its relatively simple implementation. However, a known issue of the first-order method is the possible poor convergence rate. Fast iterative thresholding-like algorithms have been proposed to overcome this issue in the existing works of literature. In history, another alternative way is second-order algorithms or quasi-second-order algorithms. In this letter, we include a quasi-Newton’s method, i.e., Davidon–Fletcher–Powell (DFP) formulations in the framework of iterative thresholding-like algorithms to replace gradient descent to form a hybrid method to further increase convergence rate. The proposed method has been performed on two numerical examples and a real-life application in sparse-spike seismic deconvolution. The numerical examples and real-life application showed that it provides an effective alternative method to solve sparsity-regularized linear inverse problems.