相关论文: Generalized Structure Preserving Preconditioners f…

Thresholding iterative methods are recently successfully applied to image deblurring problems. In this paper, we investigate the modified linearized Bregman algorithm (MLBA) used in image deblurring problems, with a proper treatment of the…

Circulant preconditioners are commonly used to accelerate the rate of convergence of iterative methods when solving linear systems of equations with a Toeplitz matrix. Block extensions that can be applied when the system has a block…

This paper presents a couple of preconditioning techniques that can be used to enhance the performance of iterative regularization methods applied to image deblurring problems with a variety of point spread functions (PSFs) and boundary…

In recent works several authors have proposed the use of precise boundary conditions (BCs) for blurring models and they proved that the resulting choice (Neumann or reflective, anti-reflective) leads to fast algorithms both for deblurring…

By applying the linearly implicit conservative difference scheme proposed in [D.-L. Wang, A.-G. Xiao, W. Yang. J. Comput. Phys. 2014;272:670-681], the system of repulsive space fractional coupled nonlinear Schr\"odinger equations leads to a…

Purpose: Design of a preconditioner for fast and efficient parallel imaging and compressed sensing reconstructions. Theory: Parallel imaging and compressed sensing reconstructions become time consuming when the problem size or the number of…

In this paper, we study the problem of recovering a sharp version of a given blurry image when the blur kernel is unknown. Previous methods often introduce an image-independent regularizer (such as Gaussian or sparse priors) on the desired…

In recent years, large convolutional neural networks have been widely used as tools for image deblurring, because of their ability in restoring images very precisely. It is well known that image deblurring is mathematically modeled as an…

The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…

Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their…

Spectral computed tomography (CT) has a great potential in material identification and decomposition. To achieve high-quality material composition images and further suppress the x-ray beam hardening artifacts, we first propose a one-step…

Image restoration is typically addressed through non-convex inverse problems, which are often solved using first-order block-wise splitting methods. In this paper, we consider a general type of non-convex optimisation model that captures…

Blind image deblurring is a challenging problem in computer vision, which aims to restore both the blur kernel and the latent sharp image from only a blurry observation. Inspired by the prevalent self-example prior in image…

Tikhonov regularization is a widely used technique in solving inverse problems that can enforce prior properties on the desired solution. In this paper, we propose a Krylov subspace based iterative method for solving linear inverse problems…

Non-blind image deblurring is typically formulated as a linear least-squares problem regularized by natural priors on the corresponding sharp picture's gradients, which can be solved, for example, using a half-quadratic splitting method…

Training deep neural networks has become a common approach for addressing image restoration problems. An alternative for training a "task-specific" network for each observation model is to use pretrained deep denoisers for imposing only the…

This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…

We consider the task of image reconstruction while simultaneously decomposing the reconstructed image into components with different features. A commonly used tool for this is a variational approach with an infimal convolution of…

In this study, a novel preconditioner based on the absolute-value block $\alpha$-circulant matrix approximation is developed, specifically designed for nonsymmetric dense block lower triangular Toeplitz (BLTT) systems that emerge from the…

Model-based iterative reconstruction plays a key role in solving inverse problems. However, the associated minimization problems are generally large-scale, nonsmooth, and sometimes even nonconvex, which present challenges in designing…