Related papers: Inexact Alternating Direction Method Based on Newt…

In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…

We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…

In this paper, we consider a strongly convex finite-sum minimization problem over a decentralized network and propose a communication-efficient decentralized Newton's method for solving it. We first apply dynamic average consensus (DAC) so…

In this work, we address the problem of Hessian inversion bias in distributed second-order optimization algorithms. We introduce a novel shrinkage-based estimator for the resolvent of gram matrices which is asymptotically unbiased, and…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…

We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…

In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…

Due to the high flexibility and remarkable performance, low-rank approximation methods has been widely studied for color image denoising. However, those methods mostly ignore either the cross-channel difference or the spatial variation of…

This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…

Machine learning problems such as neural network training, tensor decomposition, and matrix factorization, require local minimization of a nonconvex function. This local minimization is challenged by the presence of saddle points, of which…

The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how…

This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to…

Diffusion posterior sampling conditions diffusion priors on measurements, but data-consistency updates are typically scaled by hand-tuned guidance weights and can destabilize sampling under stiff, operator-dependent curvature. We replace…

We propose NAMA (Newton-type Alternating Minimization Algorithm) for solving structured nonsmooth convex optimization problems where the sum of two functions is to be minimized, one being strongly convex and the other composed with a linear…

A new algorithmic framework is presented for holographic phase retrieval via maximum likelihood optimization, which allows for practical and robust image reconstruction. This framework is especially well-suited for holographic coherent…

An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…

Deep neural network based methods are the state of the art in various image restoration problems. Standard supervised learning frameworks require a set of noisy measurement and clean image pairs for which a distance between the output of…

Image enhancement approaches often assume that the noise is signal independent, and approximate the degradation model as zero-mean additive Gaussian. However, this assumption does not hold for biomedical imaging systems where sensor-based…

Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…