Natural Thresholding Algorithms for Signal Recovery With Sparsity

Abstract

The algorithms based on the technique of optimal k-thresholding (OT) were recently proposed for signal recovery, and they are very different from the traditional family of hard thresholding methods. However, the computational cost for OT-based algorithms remains high at the current stage of their development. This stimulates the development of the so-called natural thresholding (NT) algorithm and its variants in this paper. The family of NT algorithms is developed through the first-order approximation of the so-called regularized optimal k-thresholding model, and thus the computational cost for this family of algorithms is significantly lower than that of the OT-based algorithms. The guaranteed performance of NT-type algorithms for signal recovery from noisy measurements is shown under the restricted isometry property and concavity of the objective function of regularized optimal kthresholding model. Empirical results indicate that the NT-type algorithms are robust and very comparable to several mainstream algorithms for sparse signal recovery.

Recovery of Sparse Signals via Modified Hard Thresholding Pursuit Algorithms

“…However, this modification causes a significant increase in runtime because the subproblem is not easy to solve. Recently, using a binary regularization and linearization technique, Zhao and Luo [27] proposed Natural Thresholding algorithm to reduce the computational cost. In addition, Liu and Barber introduced a new operator called the Reciprocal Thresholding [28], which lies between hard and soft thresholding.…”