Iterative Hard Thresholding with Nonzero Index Initialization

Abstract

Several methods for signal acquisition in compressed sensing were proposed in the past. Iterative hard thresholding (IHT) algorithm and its variants can be considered as a kind of those methods based on gradient descent. Unfortunately, when the objective function has many local minima, the steepest descent typically suffers from being misled into attaining those local minima. One way to facilitate the nonlinear search to be close to the global solution is the preparation for good initialization. In this work, a nonzero index according to signal sparsity is applied as the initial value for the IHT algorithms, instead of all zeros as in the former works. Numerical examples illustrate that the nonzero index initialization can provide lower normalized root-mean-square error of the acquired signal than the conventional all-zeros initialization, especially for numerous nonzero elements in the signal. © 2021 IEEE.