Related papers: Non-local image deconvolution by Cauchy sequence
In recent years, algorithm unrolling has emerged as a powerful technique for designing interpretable neural networks based on iterative algorithms. Imaging inverse problems have particularly benefited from unrolling-based deep network…
Given a (possibly approximate) Cauchy matrix, how can we efficiently compute its generators? Expanding on previous work by Liesen and Luce [Linear Algebra Appl. 493 (2016) 261--280], we present a general family of algorithms for Cauchy…
Current techniques for explainable AI have been applied with some success to image processing. The recent rise of research in video processing has called for similar work n deconstructing and explaining spatio-temporal models. While many…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
We introduce a new projection-free (Frank-Wolfe) method for optimizing structured nonconvex functions that are expressed as a difference of two convex functions. This problem class subsumes smooth nonconvex minimization, positioning our…
We generalize Richardson-Lucy (RL) deblurring to 4-D light fields by replacing the convolution steps with light field rendering of motion blur. The method deals correctly with blur caused by 6-degree-of-freedom camera motion in complex 3-D…
In this paper, we propose a very deep fully convolutional encoding-decoding framework for image restoration such as denoising and super-resolution. The network is composed of multiple layers of convolution and de-convolution operators,…
We propose an optimization algorithm called Frictionless Hamiltonian Descent, which is a direct counterpart of classical Hamiltonian Monte Carlo in sampling. We analyze Frictionless Hamiltonian Descent for strongly convex quadratic…
We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models were successfully applied for real-valued images, we introduce…
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…
The aim of this paper is to develop an efficient algorithm for solving a class of unconstrained nondifferentiable convex optimization problems in finite dimensional spaces. To this end we formulate first its Fenchel dual problem and…
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
Recent successes in deep learning based deformable image registration (DIR) methods have demonstrated that complex deformation can be learnt directly from data while reducing computation time when compared to traditional methods. However,…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
In this paper we study the the Gauss image problem, which is a generalization of the Aleksandrov problem in convex geometry. By considering a geometric flow involving Gauss curvature and functions of normal vectors and radial vectors, we…
Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as…
We investigate a one-dimensional nonlinear wave system which arises from a variational principle modeling a type of cholesteric liquid crystals. The problem treated here is the Cauchy problem for the same wave speed case with initial data…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…