QISTANet: DNN Architecture to Solve $\ell_q$norm Minimization Problem and Image Compressed Sensing
Abstract
In this paper, we reformulate the nonconvex $\ell_q$norm minimization problem with $q\in(0,1)$ into a 2step problem, which consists of one convex and one nonconvex subproblems, and propose a novel iterative algorithm called QISTA ($\ell_q$ISTA) to solve the $\left(\ell_q\right)$problem. By taking advantage of deep learning in accelerating optimization algorithms, together with the speedup strategy that using the momentum from all previous layers in the network, we propose a learningbased method, called QISTANets, to solve the sparse signal reconstruction problem. Extensive experimental comparisons demonstrate that the QISTANets yield better reconstruction qualities than stateoftheart $\ell_1$norm optimization (plus learning) algorithms even if the original sparse signal is noisy. On the other hand, based on the network architecture associated with QISTA, with considering the use of convolution layers, we proposed the QISTANetn for solving the image CS problem, and the performance of the reconstruction still outperforms most of the stateoftheart natural images reconstruction methods. QISTANetn is designed in unfolding QISTA and adding the convolutional operator as the dictionary. This makes QISTANets interpretable. We provide complete experimental results that QISTANets and QISTANetn contribute the better reconstruction performance than the competing.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 DOI:
 10.48550/arXiv.2010.11363
 arXiv:
 arXiv:2010.11363
 Bibcode:
 2020arXiv201011363L
 Keywords:

 Computer Science  Computer Vision and Pattern Recognition;
 Computer Science  Machine Learning;
 Electrical Engineering and Systems Science  Image and Video Processing