相关论文: On deconvolution problems: numerical aspects

We consider the problems of compressed sensing and optimal denoising for signals $\mathbf{x_0}\in\mathbb{R}^N$ that are monotone, i.e., $\mathbf{x_0}(i+1) \geq \mathbf{x_0}(i)$, and sparsely varying, i.e., $\mathbf{x_0}(i+1) >…

Optimization techniques have been widely used in deformable registration, allowing for the incorporation of similarity metrics with regularization mechanisms. These regularization mechanisms are designed to mitigate the effects of trivial…

In this paper we investigate the non-linear and ill-posed inverse problem of simultaneously identifying the conductivity and the reaction in diffuse optical tomography with noisy measurement data available on an accessible part of the…

Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…

In this paper, we investigate in a unified way the structural properties of solutions to inverse problems. These solutions are regularized by the generic class of semi-norms defined as a decomposable norm composed with a linear operator,…

High resolution ultrasound image reconstruction from a reduced number of measurements is of great interest in ultrasound imaging, since it could enhance both the frame rate and image resolution. Compressive deconvolution, combining…

Image deconvolution is still to be a challenging ill-posed problem for recovering a clear image from a given blurry image, when the point spread function is known. Although competitive deconvolution methods are numerically impressive and…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

Max-norm regularizer has been extensively studied in the last decade as it promotes an effective low-rank estimation for the underlying data. However, such max-norm regularized problems are typically formulated and solved in a batch manner,…

Multibang regularization and combinatorial integral approximation decompositions are two actively researched techniques for integer optimal control. We consider a class of polyhedral functions that arise particularly as convex lower…

We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…

We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…

We propose a fast algorithm to approximate the optimal transport distance. The main idea is to add a Fisher information regularization into the dynamical setting of the problem, originated by Benamou and Brenier. The regularized problem is…

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,…

Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve…

This paper proposes a new framework for the optimization of excitation inputs for system identification. The optimization problem considered is to maximize a reduced Fisher information matrix in any of the classical D-, E-, or A-optimal…

We study the non-parametric estimation of an unknown density f with support on R+ based on an i.i.d. sample with multiplicative measurement errors. The proposed fully-data driven procedure consists of the estimation of the Mellin transform…

Consider a polynomial optimisation problem, whose instances vary continuously over time. We propose to use a coordinate-descent algorithm for solving such time-varying optimisation problems. In particular, we focus on relaxations of…

A standard way to solve linear algebraic systems $Au=f,\,\,(*)$ with ill-conditioned matrices $A$ is to use variational regularization. This leads to solving the equation $(A^*A+aI)u=A^*f_\d$, where $a$ is a regularization parameter, and…

In this study, the problem of computing a sparse representation of multi-dimensional visual data is considered. In general, such data e.g., hyperspectral images, color images or video data consists of signals that exhibit strong local…