Negentropy-Based Sparsity-Promoting Reconstruction with Fast Iterative Solution from Noisy Measurements

Compressed sensing provides an elegant framework for recovering sparse signals from compressed measurements. This paper addresses the problem of sparse signal reconstruction from compressed measurements that is more robust to complex, especially non-Gaussian noise, which arises in many applications. For this purpose, we present a method that exploits the maximum negentropy theory to promote the adaptability to noise. This problem is formalized as a constrained minimization problem, where the objective function is the negentropy of measurement error with sparse constraint ℓp(0<p<1)-norm. On the minimization issue of the problem, although several promising algorithms have been proposed in the literature, they are very computationally demanding and thus cannot be used in many practical situations. To improve on this, we propose an efficient algorithm based on a fast iterative shrinkage-thresholding algorithm that can converge fast. Both the theoretical analysis and numerical experiments show the better accuracy and convergent rate of the proposed method.