Related papers: Generalized Structure Preserving Preconditioners f…

Image deblurring continues to achieve impressive performance with the development of generative models. Nonetheless, there still remains a displeasing problem if one wants to improve perceptual quality and quantitative scores of recovered…

Blind image deblurring remains a topic of enduring interest. Learning based approaches, especially those that employ neural networks have emerged to complement traditional model based methods and in many cases achieve vastly enhanced…

Non-blind deblurring methods achieve decent performance under the accurate blur kernel assumption. Since the kernel uncertainty (i.e. kernel error) is inevitable in practice, semi-blind deblurring is suggested to handle it by introducing…

Currently, many blind deblurring methods assume blurred images are noise-free and perform unsatisfactorily on the blurry images with noise. Unfortunately, noise is quite common in real scenes. A straightforward solution is to denoise images…

We propose a simple, interpretable framework for solving a wide range of image reconstruction problems such as denoising and deconvolution. Given a corrupted input image, the model synthesizes a spatially varying linear filter which, when…

In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper invstigates the more general problem of putting a set of matrices into block triangular or block-diagonal form…

Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…

In image deconvolution problems, the diagonalization of the underlying operators by means of the FFT usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard…

We begin by showing that any $n \times n$ matrix can be decomposed into a sum of $n$ circulant matrices with periodic relaxations on the unit circle. This decomposition is orthogonal with respect to a Frobenius inner product, allowing…

When a linear system Ax = y is solved by means of iterative methods (mainly CG and GMRES) and the convergence rate is slow, one may consider a preconditioner P. The use of such preconditioner changes the spectrum of the matrix defining the…

In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…

Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This helps to avoid the staircasing effect of Total Variation…

While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…

Image deblurring aims to remove undesired blurs from an image captured in a dynamic scene. Much research has been dedicated to improving deblurring performance through model architectural designs. However, there is little work on data…

This paper studies the spectral properties of large matrices and the preconditioning of linear systems, arising from the finite difference discretization of a time-dependent space-fractional diffusion equation with a variable coefficient…

Deconvolution is the most commonly used image processing method to remove the blur caused by the point-spread-function (PSF) in optical imaging systems. While this method has been successful in deblurring, it suffers from several…

The inherent ill-posed nature of image reconstruction problems, due to limitations in the physical acquisition process, is typically addressed by introducing a regularisation term that incorporates prior knowledge about the underlying…

In recent literature there are plenty of works that combine handcrafted and learnable regularizers to solve inverse imaging problems. While this hybrid approach has demonstrated promising results, the motivation for combining handcrafted…

Blind face restoration is a challenging task due to the unknown and complex degradation. Although face prior-based methods and reference-based methods have recently demonstrated high-quality results, the restored images tend to contain…

We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the skew-symmetric part and makes the main diagonal of the coefficient matrix as close…