Learning optimal nonlinearities for iterative thresholding algorithms
This work addresses the challenge of enhancing sparse signal recovery for applications in inverse problems, but it is incremental as it builds on the well-established ISTA method.
The authors tackled the problem of improving sparse signal estimation by learning optimal thresholding functions for the iterative shrinkage/thresholding algorithm (ISTA), resulting in potential gains in estimation quality as demonstrated in simulations on sparse statistical signals.
Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems. In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA. The proposed scheme is obtained by relating iterations of ISTA to layers of a simple deep neural network (DNN) and developing a corresponding error backpropagation algorithm that allows to fine-tune the thresholding functions. Simulations on sparse statistical signals illustrate potential gains in estimation quality due to the proposed data adaptive ISTA.