Element-Wise Adaptive Thresholds for Learned Iterative Shrinkage Thresholding Algorithms

In this paper, we propose element-wise adaptive threshold methods for learned iterative shrinkage thresholding algorithms. The threshold for each element is adapted in such a way that it is set to be smaller when the previously recovered estimate or the current one-step gradient descent at that element has a larger value. This adaptive threshold gives a lower misdetection probability of the true support, which speedups the convergence to the optimal solution. We show that the proposed element-wise threshold adaption method has better convergence rate than the existing non-adaptive threshold methods. Numerical results show that the proposed neural network has the best recovery performance among the tested algorithms. In addition, it is robust to the sparsity mismatch, which is very desirable in the case of unknown signal sparsity.