Low-complexity iterative equalization for OTFS based on alternating minimization

To achieve robust communication in high mobility scenarios,an iterative equalization algorithm based on alternating minimization(AM)is proposed for the orthogonal time frequency space(OTFS)system.The algorithm approximates the equalization problem to a convex function optimization problem in the real-valued domain and solves the problem iteratively using the AM algorithm.In the iterative process,the complexity of the proposed algorithm is reduced further based on the study of the cyclic structure and sparse property of the OTFS channel matrix in the delay-Doppler(DD)domain.The new method for OTFS is simulated and verified in a high-speed mobile scenario and the results show that the proposed equalization algorithm has excellent bit error rate performance with low complexity.

Alternating minimization for data-driven computational elasticity from experimental data: kernel method for learning constitutive manifold

Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected to a specified external load.Provided that a data set comprising stress-strain pairs of material is available,a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie(Kanno 2021,Jpn.J.Ind.Appl.Math.).From the perspective of physical experiments,stress field cannot be directly measured,while displacement and force fields are measurable.In this study,we extend the previous kernel method to the situation that pairs of displacement and force,instead of pairs of stress and strain,are available as an input data set.A new regularized least-squares problem is formulated in this problem setting,and an alternating minimization algorithm is proposed to solve the problem.

TWO-PHASE IMAGE SEGMENTATION BY NONCONVEX NONSMOOTH MODELS WITH CONVERGENT ALTERNATING MINIMIZATION ALGORITHMS

Two-phase image segmentation is a fundamental task to partition an image into foreground and background.In this paper,two types of nonconvex and nonsmooth regularization models are proposed for basic two-phase segmentation.They extend the convex regularization on the characteristic function on the image domain to the nonconvex case,which are able to better obtain piecewise constant regions with neat boundaries.By analyzing the proposed non-Lipschitz model,we combine the proximal alternating minimization framework with support shrinkage and linearization strategies to design our algorithm.This leads to two alternating strongly convex subproblems which can be easily solved.Similarly,we present an algorithm without support shrinkage operation for the nonconvex Lipschitz case.Using the Kurdyka-Lojasiewicz property of the objective function,we prove that the limit point of the generated sequence is a critical point of the original nonconvex nonsmooth problem.Numerical experiments and comparisons illustrate the effectiveness of our method in two-phase image segmentation.

The convergence properties of infeasible inexact proximal alternating linearized minimization

The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real applications.In the cases where subproblems do not have closed-form solutions,e.g.,due to complex constraints,infeasible subsolvers are indispensable,giving rise to an infeasible inexact PALM(PALM-I).Numerous efforts have been devoted to analyzing the feasible PALM,while little attention has been paid to the PALM-I.The usage of the PALM-I thus lacks a theoretical guarantee.The essential difficulty of analysis consists in the objective value nonmonotonicity induced by the infeasibility.We study in the present work the convergence properties of the PALM-I.In particular,we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact criterion.Based upon these,we manage to establish the stationarity of any accumulation point,and moreover,show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz property.The prominent advantages of the PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3-dimensional anisotropic frictional contact.

Alternating Minimization Method for Total Variation Based Wavelet Shrinkage Model

In this paper,we introduce a novel hybrid variational model which generalizes the classical total variation method and the wavelet shrinkage method.An alternating minimization direction algorithm is then employed.We also prove that it converges strongly to the minimizer of the proposed hybrid model.Finally,some numerical examples illustrate clearly that the new model outperforms the standard total variation method and wavelet shrinkage method as it recovers better image details and avoids the Gibbs oscillations.

Sparse approximate solution of fitting surface to scattered points by MLASSO model

The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the principal shift invariant(PSI) space and the l_1 norm minimization. In order to obtain different sparsity of the approximation solution, the problem is represented as a multilevel LASSO(MLASSO)model with different regularization parameters. The MLASSO model can be solved efficiently by the alternating direction method of multipliers. Numerical experiments indicate that compared to the AGLASSO model and the basic MBA algorithm, the MLASSO model can provide an acceptable compromise between the minimization of the data mismatch term and the sparsity of the solution. Moreover, the solution by the MLASSO model can reflect the regions of the underlying surface where high gradients occur.

Image Denoising via Improved Simultaneous Sparse Coding with Laplacian Scale Mixture

Image denoising is a well-studied problem closely related to sparse coding. Noticing that the Laplacian distribution has a strong sparseness, we use Laplacian scale mixture to model sparse coefficients. With the observation that prior information of an image is relevant to the estimation of sparse coefficients, we introduce the prior information into maximum a posteriori（MAP） estimation of sparse coefficients by an appropriate estimate of the probability density function. Extending to structured sparsity, a nonlocal image denoising model： Improved Simultaneous Sparse Coding with Laplacian Scale Mixture（ISSC-LSM） is proposed. The centering preprocessing, which admits biased-mean of sparse coefficients and saves expensive computation, is done firstly. By alternating minimization and learning an orthogonal PCA dictionary, an efficient algorithm with closed-form solutions is proposed. When applied to noise removal, our proposed ISSC-LSM can capture structured image features, and the adoption of image prior information leads to highly competitive denoising performance. Experimental results show that the proposed method often provides higher subjective and objective qualities than other competing approaches. Our method is most suitable for processing images with abundant self-repeating patterns by effectively suppressing undesirable artifacts while maintaining the textures and edges.

An Efficient Variational Model for Multiplicative Noise Removal

In this paper,an efficient variational model for multiplicative noise removal is proposed.By using a MAP estimator,Aubert and Aujol[SIAM J.Appl.Math.,68(2008),pp.925-946]derived a nonconvex cost functional.With logarithmic transformation,we transform the image into a logarithmic domain which makes the fidelity convex in the transform domain.Considering the TV regularization term in logarithmic domain may cause oversmoothness numerically,we propose the TV regularization directly in the original image domain,which preserves more details of images.An alternative minimization algorithm is applied to solve the optimization problem.The z-subproblem can be solved by a closed formula,which makes the method very efficient.The convergence of the algorithm is discussed.The numerical experiments show the efficiency of the proposed model and algorithm.

The Convex Relaxation Method on Deconvolution Model with Multiplicative Noise

In this paper,we consider variational approaches to handle the multiplicative noise removal and deblurring problem.Based on rather reasonable physical blurring-noisy assumptions,we derive a new variational model for this issue.After the study of the basic properties,we propose to approximate it by a convex relaxation model which is a balance between the previous non-convex model and a convex model.The relaxed model is solved by an alternating minimization approach.Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed method.