Related papers: The structure of optimal parameters for image rest…
Total Generalized Variation (TGV) has recently been proven certainly successful in image processing for preserving sharp features as well as smooth transition variations. However, none of the existing works aims at numerically calculating…
Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and…
Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…
This paper considers the constrained total variation (TV) denoising problem for complex-valued images. We extend the definition of TV seminorms for real-valued images to dealing with complex-valued ones. In particular, we introduce two…
This paper continues earlier work and is concerned with the inverse problem of parameter identification in variational inequalities of the second kind that does not only treat the parameter linked to a bilinear form, but importantly also…
Total variation (TV) regularization is popular in image restoration and reconstruction due to its ability to preserve image edges. To date, most research activities on TV models concentrate on image restoration from blurry and noisy…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
We introduce a novel regulariser based on the natural vector field operations gradient, divergence, curl and shear. For suitable choices of the weighting parameters contained in our model it generalises well-known first- and second-order…
We present some results of geometric convergence of level sets for solutions of total variation denoising as the regularization parameter tends to zero. The common feature among them is that they make use of explicit constructions of…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…
We present a new vectorial total variation method that addresses the problem of color consistent image filtering. Our approach is inspired from the double-opponent cell representation in the human visual cortex. Existing methods of…
$\ell_1$ regularization is used to preserve edges or enforce sparsity in a solution to an inverse problem. We investigate the Split Bregman and the Majorization-Minimization iterative methods that turn this non-smooth minimization problem…
In this work we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation…
We develop a statistical-mechanical formulation for image restoration and error-correcting codes. These problems are shown to be equivalent to the Ising spin glass with ferromagnetic bias under random external fields. We prove that the…
Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. It allows one to recover any element in any finite-dimensional subspace given finitely many of its samples with…
We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Data-driven approaches for inverse problems aim for learning model and regularization parameters from observed data samples, and…
Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor…
Regularization plays a crucial role in reliably utilizing imaging systems for scientific and medical investigations. It helps to stabilize the process of computationally undoing any degradation caused by physical limitations of the imaging…