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In this paper we present a spatially-adaptive method for image reconstruction that is based on the concept of statistical multiresolution estimation as introduced in [Frick K, Marnitz P, and Munk A. "Statistical multiresolution Dantzig…

While convergence of the Alternating Direction Method of Multipliers (ADMM) on convex problems is well studied, convergence on nonconvex problems is only partially understood. In this paper, we consider the Gaussian phase retrieval problem,…

We introduce a new paradigm for solving regularized variational problems. These are typically formulated to address ill-posed inverse problems encountered in signal and image processing. The objective function is traditionally defined by…

This work explores the search for heterogeneous approximate multiplier configurations for neural networks that produce high accuracy and low energy consumption. We discuss the validity of additive Gaussian noise added to accurate neural…

Focus of this work is solving a non-smooth constraint minimization problem by a primal-dual splitting algorithm involving proximity operators. The problem is penalized by the Bregman divergence associated with the non-smooth total variation…

This paper presents an Accelerated Preconditioned Proximal Gradient Algorithm (APPGA) for effectively solving a class of Positron Emission Tomography (PET) image reconstruction models with differentiable regularizers. We establish the…

The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [{\tt Math. Prog. Comput., 2018}] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of…

Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered backprojection, time reversal and least squares suffer from…

Patch-based low rank is an important prior assumption for image processing. Moreover, according to our calculation, the optimization of l0 norm corresponds to the maximum likelihood estimation under random-valued impulse noise. In this…

Adaptive optics (AO) corrected ood imaging of the retina is a popular technique for studying the retinal structure and function in the living eye. However, the raw retinal images are usually of poor contrast and the interpretation of such…

We consider the problem of max-min beamforming (MMB) for cell-free massive multi-input multi-output (MIMO) systems, where the objective is to maximize the minimum achievable rate among all users. Existing MMB methods are mainly based on…

Recently, many variance reduced stochastic alternating direction method of multipliers (ADMM) methods (e.g.\ SAG-ADMM, SDCA-ADMM and SVRG-ADMM) have made exciting progress such as linear convergence rates for strongly convex problems.…

The Alternating Direction Method of Multipliers (ADMM) provides a natural way of solving inverse problems with multiple partial differential equations (PDE) forward models and nonsmooth regularization. ADMM allows splitting these…

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…

The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners,…

Recent work in image processing suggests that operating on (overlapping) patches in an image may lead to state-of-the-art results. This has been demonstrated for a variety of problems including denoising, inpainting, deblurring, and…

A novel formulation of the hyperspectral broadband phase retrieval is developed for the scenario where both object and modulation phase masks are spectrally varying. The proposed algorithm is based on a complex domain version of the…

We consider a problem that recovers a 2-D object and the underlying view angle distribution from its noisy projection tilt series taken at unknown view angles. Traditional approaches rely on the estimation of the view angles of the…

This paper introduces a novel numerical method for the inverse problem of electroencephalography(EEG). We pose the inverse EEG problem as an optimal control (OC) problem for Poisson's equation. The optimality conditions lead to a…

We propose a general deep plug-and-play (PnP) algorithm with a theoretical convergence guarantee. PnP strategies have demonstrated outstanding performance in various image restoration tasks by exploiting the powerful priors underlying…