Iterative Hard Thresholding Using Minimum Mean Square Error Step Size

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 manipulation of search step size. In this work, a numerical search is used to find an optimal step size in the sense of minimal signal recovery error for the normalized IHT algorithm. The performance of the proposed step size is compared to that of a randomly chosen fixed one as in the former works. Numerical examples illustrate that the optimal parameters that form up a good step size can provide lower root-mean-square-relative error of the acquired signal than the arbitrary chosen step size method. The performance improvement is obvious for numerous nonzero elements hidden in the sparse signal.