Research On The Problem Of Nonconvex Convolutional Sparse Coding Based On Slices

Convolutional dictionary learning aims to learn the convolutional dictionary and the corresponding sparse coefficient mapping from the given signal.Most traditional convolutional dictionary learning algorithms use image blocks for dictionary learning.Most of them are performed in the context of convex optimization for solution convenience,which leads to ignoring the correlation between image blocks and the problem of non-sparse sparse coefficients.With continuous research,the nonconvex optimization problem has been further developed.And convergence proofs can also be obtained from a mathematical point of view.Based on this,this paper investigates the nonconvex optimization problem.In this paper,we analyze and study two algorithms based on the slicing-based convex optimization dictionary learning algorithm,namely the SBDL algorithm and Fourier domain-based adaptive nonconvex forward–backward splitting algorithm,namely the AFB algorithm.For nonconvex optimization problems this paper applies the slicing idea to solve the nonconvex optimization problem.It proposes a nonconvex forward and backward splitting adaptive algorithm based on slicing,which is concurrent and based on the time domain,namely the ANFBA algorithm.And this paper proves the convergence of the algorithm from a mathematical point of view,and the algorithm is proved experimentally.It is experimentally demonstrated that the ANFBA algorithm can obtain smaller objective function values and lower sparsity.To further demonstrate the performance of nonconvex optimization,this paper also compares the convex optimization problems in the corresponding cases.It is demonstrated by experiments that the objective function values and the sparsity of the nonconvex optimization are lower than the convex optimization results.To further illustrate the performance of the ANFBA algorithm in application areas,this paper applies the ANFBA algorithm to image fusion and conduct experiments for multi-focusing and so on.The experimental results show that the ANFBA algorithm has excellent performance.Finally,this paper applies the ANFBA algorithm to compressed-sensing image reconstruction.To better solve the image reconstruction problem,this paper combines the ANFBA algorithm with the cartoon texture separation model and proposes the CSTVISO-Net,a compressed sensing image separation network based on the isotropic total variation.To speed up the convergence,this paper adopts the generalized accelerated proximal gradient method.It is demonstrated by experimental results that our CSTVISO-Net algorithm can obtain higher-quality reconstructed images,especially at low measurement rates.