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Unsupervised Anomaly Detection (UAD) aims to identify abnormal regions by establishing correspondences between test images and normal templates. Existing methods primarily rely on image reconstruction or template retrieval but face a…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
Phase retrieval refers to algorithmic methods for recovering a signal from its phaseless measurements. Local search algorithms that work directly on the non-convex formulation of the problem have been very popular recently. Due to the…
We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm (RAGD), and show that for geodesically smooth and strongly convex problems, within a neighborhood of the minimizer whose radius depends on the condition number as…
We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…
The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…
This paper introduces a novel computational approach termed the Reduced Augmentation Implicit Low-rank (RAIL) method by investigating two predominant research directions in low-rank solutions to time-dependent partial differential equations…
We study the problem of recovering the underlining sparse signals from clean or noisy phaseless measurements. Due to the sparse prior of signals, we adopt an L0regularized variational model to ensure only a small number of nonzero elements…
Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function.…
The problem of reconstructing a sparse signal vector from magnitude-only measurements (a.k.a., compressive phase retrieval), emerges naturally in diverse applications, but it is NP-hard in general. Building on recent advances in nonconvex…
Regularization-based image restoration has remained an active research topic in computer vision and image processing. It often leverages a guidance signal captured in different fields as an additional cue. In this work, we present a general…
Depth estimation is an essential component in understanding the 3D geometry of a scene, with numerous applications in urban and indoor settings. These scenes are characterized by a prevalence of human made structures, which in most of the…
Companion paper [118] developed a powerful \emph{Random duality theory} (RDT) based analytical program to statistically characterize performance of \emph{descending} phase retrieval algorithms (dPR) (these include all variants of gradient…
This paper presents new variants of the averaged alternating modified reflections (AAMR) method for the best approximation problem. Under a mild constraint qualification, we first show its weak convergence and then establish a convergence…
We propose a new space-variant anisotropic regularisation term for variational image restoration, based on the statistical assumption that the gradients of the target image distribute locally according to a bivariate generalised Gaussian…
We study a class of real robust phase retrieval problems under a Gaussian assumption on the coding matrix when the received signal is sparsely corrupted by noise. The goal is to establish conditions on the sparsity under which the input…
Phase retrieval aims at reconstructing unknown signals from magnitude measurements of linear mixtures. In this paper, we consider the phase retrieval with dictionary learning problem, which includes an additional prior information that the…
Penalized selection criteria like AIC or BIC are among the most popular methods for variable selection. Their theoretical properties have been studied intensively and are well understood, but making use of them in case of high-dimensional…
Model-free deep reinforcement learning (RL) algorithms have been widely used for a range of complex control tasks. However, slow convergence and sample inefficiency remain challenging problems in RL, especially when handling continuous and…