QISTA-NET: DNN ARCHITECTURE TO SOLVE l_q-NORM MINIMIZATION PROBLEM

In this paper, we reformulate the non-convex $\ell_q$-norm minimization problem with $q\in(0,1)$ into a 2-step problem, which consists of one convex and one non-convex subproblems, and propose a novel iterative algorithm called QISTA ($\ell_q$-ISTA) to solve the $\left(\ell_q\right)$-problem. By taking advantage of DNN in accelerating optimization algorithms, we also design a DNN architecture associated with QISTA, called QISTA-Net, which is then further speeded up as QISTA-Net$^+$ using the momentum from all previous layers. Extensive experimental comparisons demonstrate that the proposed methods yield better reconstruction qualities than state-of-the-art $\ell_1$-norm optimization (plus learning) algorithms even if the original sparse signal is noisy.