Entropy-Regularized Iterative Weighted Shrinkage-Thresholding Algorithm (ERIWSTA) for inverse problems in imaging

The iterative shrinkage-thresholding algorithm (ISTA) is a classic optimization algorithm for solving ill-posed linear inverse problems. Recently, this algorithm has continued to improve, and the iterative weighted shrinkage-thresholding algorithm (IWSTA) is one of the improved versions with a more evident advantage over the ISTA. It processes features with different weights, making different features have different contributions. However, the weights of the existing IWSTA do not conform to the usual definition of weights: their sum is not 1, and they are distributed over an extensive range. These problems may make it challenging to interpret and analyze the weights, leading to inaccurate solution results. Therefore, this paper proposes a new IWSTA, namely, the entropy-regularized IWSTA (ERIWSTA), with weights that are easy to calculate and interpret. The weights automatically fall within the range of [0, 1] and are guaranteed to sum to 1. At this point, considering the weights as the probabilities of the contributions of different attributes to the model can enhance the interpretation ability of the algorithm. Specifically, we add an entropy regularization term to the objective function of the problem model and then use the Lagrange multiplier method to solve the weights. Experimental results of a computed tomography (CT) image reconstruction task show that the ERIWSTA outperforms the existing methods in terms of convergence speed and recovery accuracy.