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We propose a new fast algorithm for solving one of the standard formulations of frame-based image deconvolution: an unconstrained optimization problem, involving an $\ell_2$ data-fidelity term and a non-smooth regularizer. Our approach is…
"Classical" First Order (FO) algorithms of convex optimization, such as Mirror Descent algorithm or Nesterov's optimal algorithm of smooth convex optimization, are well known to have optimal (theoretical) complexity estimates which do not…
Variational segmentation algorithms require a prior imposed in the form of a regularisation term to enforce smoothness of the solution. Recently, it was shown in the Deep Image Prior work that the explicit regularisation in a model can be…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed…
This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image…
In this paper,we present an inexact primal-dual method with correction step for a saddle point problem by introducing the notations of inexact extended proximal operators with symmetric positive definite matrix $D$. Relaxing requirement on…
The quadratic penalty alternating minimization (AM) method is widely used for solving the convex $\ell_1$ total variation (TV) image deblurring problem. However, quadratic penalty AM for solving the nonconvex nonsmooth $\ell_p$, $0 < p < 1$…
In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…
In recent years, the removal of motion blur in photographs has seen impressive progress in the hands of deep learning-based methods, trained to map directly from blurry to sharp images. For this reason, approaches that explicitly use a…
Image deblurring is a challenging problem in imaging due to its highly ill-posed nature. Deep learning models have shown great success in tackling this problem but the quest for the best image quality has brought their computational…
Blind image deblurring is an important yet very challenging problem in low-level vision. Traditional optimization based methods generally formulate this task as a maximum-a-posteriori estimation or variational inference problem, whose…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
Separable nonlinear least squares problems appear in many inverse problems, including semi-blind image deblurring. The variable projection (VarPro) method provides an efficient approach for solving such problems by eliminating linear…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
This paper concerns a class of composite image reconstruction models for impluse noise removal, which is rather general and covers existing convex and nonconvex models proposed for reconstructing images with impluse noise. For this…
This paper proposes using a Gaussian mixture model as a prior, for solving two image inverse problems, namely image deblurring and compressive imaging. We capitalize on the fact that variable splitting algorithms, like ADMM, are able to…
Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters,…
Blind image deblurring is the process of recovering a sharp image from a blurred one without prior knowledge about the blur kernel. It is a small data problem, since the key challenge lies in estimating the unknown degrees of blur from a…
Structured convex optimization on weighted graphs finds numerous applications in machine learning and computer vision. In this work, we propose a novel adaptive preconditioning strategy for proximal algorithms on this problem class. Our…