Related papers: Rapid, Robust, and Reliable Blind Deconvolution vi…
Optimization problems under affine constraints appear in various areas of machine learning. We consider the task of minimizing a smooth strongly convex function F(x) under the affine constraint Kx=b, with an oracle providing evaluations of…
Richardson-Lucy deconvolution is widely used to restore images from degradation caused by the broadening effects of a point spread function and corruption by photon shot noise, in order to recover an underlying object. In practice, this is…
We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as…
Super-resolution and denoising are ill-posed yet fundamental image restoration tasks. In blind settings, the degradation kernel or the noise level are unknown. This makes restoration even more challenging, notably for learning-based…
We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows…
We consider the problem of calibrating a compressed sensing measurement system under the assumption that the decalibration consists in unknown gains on each measure. We focus on {\em blind} calibration, using measures performed on a few…
The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in reconstruction quality. Unfortunately, these new methods often lack reliability and explainability, and there is a…
Gradient descent methods are fundamental first-order optimization algorithms in both Euclidean spaces and Riemannian manifolds. However, the exact gradient is not readily available in many scenarios. This paper proposes a novel inexact…
Optimization problems occurring in a wide variety of physical design problems, including but not limited to optical engineering, quantum control, structural engineering, involve minimization of a simple cost function of the state of the…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
Recent results suggest that quantum computers possess the potential to speed up nonconvex optimization problems. However, a crucial factor for the implementation of quantum optimization algorithms is their robustness against experimental…
We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective…
Blind super-resolution can be cast as low rank matrix recovery problem by exploiting the inherent simplicity of the signal. In this paper, we develop a simple yet efficient nonconvex method for this problem based on the low rank structure…
This paper studies decentralized stochastic nonconvex optimization problem over row-stochastic networks. We consider the heavy-tailed gradient noise which is empirically observed in many popular real-world applications. Specifically, we…
We consider the task of minimizing the sum of smooth and strongly convex functions stored in a decentralized manner across the nodes of a communication network whose links are allowed to change in time. We solve two fundamental problems for…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest $\mathbf{x}^{\natural}\in\mathbb{R}^{n}$ from $m$ quadratic equations/samples…
Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…
Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training…
Blind deconvolution is an ubiquitous non-linear inverse problem in applications like wireless communications and image processing. This problem is generally ill-posed since signal identifiability is a key concern, and there have been…