Related papers: Parallel Proximal Algorithm for Image Restoration …
Crucial information barely visible to the human eye is often embedded in a series of low-resolution images taken of the same scene. Super-resolution enables the extraction of this information by reconstructing a single image, at a high…
This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…
We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…
This paper presents a general method for applying hierarchical matrix skeletonization factorizations to the numerical solution of boundary integral equations with possibly rank-deficient integral operators. Rank-deficient operators arise in…
Based on the joint bidiagonalization process of a large matrix pair $\{A,L\}$, we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-posed problems in general-form regularization: $\min\|Lx\| \…
Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based…
The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…
In this work, we propose a framework to learn a local regularization model for solving general image restoration problems. This regularizer is defined with a fully convolutional neural network that sees the image through a receptive field…
The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
Recent work in image processing suggests that operating on (overlapping) patches in an image may lead to state-of-the-art results. This has been demonstrated for a variety of problems including denoising, inpainting, deblurring, and…
In this paper we present a new method for solving optimization problems involving the sum of two proper, convex, lower semicontinuous functions, one of which has Lipschitz continuous gradient. The proposed method has a hybrid nature that…
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…
Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum,…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
Regularization techniques are necessary to compute meaningful solutions to discrete ill-posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped with a discretization of the gradient operator as regularization…
We address the image restoration problem under Poisson noise corruption. The Kullback-Leibler divergence, which is typically adopted in the variational framework as data fidelity term in this case, is coupled with the second-order Total…