arXiv subjects

Jun-Feng Yin

Publications and source records attributed to Jun-Feng Yin.

6 recordsLinked to original sources

arXiv2026

Iterative Thresholding Pursuit with Continuation for $\ell_{1-2}$-Regularized Sparse Recovery

Sparse recovery aims to reconstruct sparse signals from underdetermined and possibly noisy linear measurements. Existing $\ell_{1-2}$ iterative thresholding schemes are first-order methods. We propose an iterative thresholding pursuit method with continuation (ITP-C) for $\ell_{1-2}$-regularized sparse recovery. The method goes beyond first-order thresholding by combining the active-set identification capability of the $\ell_{1-2}$ proximal step with a restricted least-squares pursuit step that provides a second-order update on the identified support. The support is generated adaptively by the thresholding update, and no prior knowledge of the true sparsity level is required. To control the possible instability of the pursuit step while preserving the descent structure of the continuation scheme, we impose a strict descent check with respect to the dynamic objective. We establish convergence of the generated sequence under the Kurdyka-Lojasiewicz framework and prove a local oracle-type property after correct support identification. Numerical experiments on synthetic sparse recovery and image reconstruction illustrate the descent preservation of the proposed safeguard and demonstrate the improved recovery performance of ITP-C over the state-of-the-art baselines.

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arXiv2026

Residual-based Kaczmarz methods for tensor linear equations with t-product

Tensor linear systems widely arise from high-dimensional data mining and computing, for instance, natural language processing and machine learning. A class of residual-based tensor Kaczmarz method is proposed for tensor linear equations with t-product. Theoretical analyses prove the convergence and give an upper bound of the convergence rate of the proposed method. Furthermore, an accelerated residual-based Kaczmarz method with heavy ball momentum is developed. Numerical experiments verify the efficiency of the proposed methods and demonstrate that they are faster than the existing tensor Kaczmarz methods.

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arXiv2025

A fast block nonlinear Bregman-Kaczmarz method with averaging for nonlinear sparse signal recovery

Recovery of a sparse signal from a nonlinear system arises in many practical applications including compressive sensing, image reconstruction and machine learning. In this paper, a fast block nonlinear Bregman-Kaczmarz method with averaging is presented for nonlinear sparse signal recovery problems. Theoretical analysis proves that the averaging block nonlinear Bregman-Kaczmarz method with both constant stepsizes and adaptive stepsizes are convergent. Numerical experiments demonstrate the effectiveness of the averaging block nonlinear Bregman-Kaczmarz method, which converges faster than the existing nonlinear Bregman-Kaczmarz methods.

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arXiv2024

The sparse Kaczmarz method with surrogate hyperplane for the regularized basis pursuit problem

The Sparse Kaczmarz method is a famous and widely used iterative method for solving the regularized basis pursuit problem. A general scheme of the surrogate hyperplane sparse Kaczmarz method is proposed. In particular, a class of residual-based surrogate hyperplane sparse Kaczmarz method is introduced and the implementations are well discussed. Their convergence theories are proved and the linear convergence rates are studied and compared in details. Numerical experiments verify the efficiency of the proposed methods.

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arXiv2022

A stabilized GMRES method for singular and severely ill-conditioned systems of linear equations

Consider using the right-preconditioned GMRES (AB-GMRES) for obtaining the minimum-norm solution of inconsistent underdetermined systems of linear equations. Morikuni (Ph.D. thesis, 2013) showed that for some inconsistent and ill-conditioned problems, the iterates may diverge. This is mainly because the Hessenberg matrix in the GMRES method becomes very ill-conditioned so that the backward substitution of the resulting triangular system becomes numerically unstable. We propose a stabilized GMRES based on solving the normal equations corresponding to the above triangular system using the standard Cholesky decomposition. This has the effect of shifting upwards the tiny singular values of the Hessenberg matrix which lead to an inaccurate solution. We analyze why the method works. Numerical experiments show that the proposed method is robust and efficient, not only for applying AB-GMRES to underdetermined systems, but also for applying GMRES to severely ill-conditioned range-symmetric systems of linear equations.

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arXiv2021

Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems

We propose using greedy and randomized Kaczmarz inner-iterations as preconditioners for the right-preconditioned flexible GMRES method to solve consistent linear systems, with a parameter tuning strategy for adjusting the number of inner iterations and the relaxation parameter. We also present theoretical justifications of the right-preconditioned flexible GMRES for solving consistent linear systems. Numerical experiments on overdetermined and underdetermined linear systems show that the proposed method is superior to the GMRES method preconditioned by NE-SOR inner iterations in terms of total CPU time.

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