相关论文: Wirtinger gradient descent methods for low-dose Po…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
The properties of gradient techniques for the phase retrieval problem have received a considerable attention in recent years. In almost all applications, however, the phase retrieval problem is solved using a family of algorithms that can…
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…
Low-count positron emission tomography (PET) reconstruction is a challenging inverse problem due to severe degradations arising from Poisson noise, photon scarcity, and attenuation correction errors. Existing deep learning methods typically…
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…
The phase retrieval problem is a fundamental problem in many fields, which is appealing for investigation. It is to recover the signal vector $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots,…
In this work, we propose an optimization algorithm which we call norm-adapted gradient descent. This algorithm is similar to other gradient-based optimization algorithms like Adam or Adagrad in that it adapts the learning rate of stochastic…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
A systematic procedure for optimising the friction coefficient in underdamped Langevin dynamics as a sampling tool is given by taking the gradient of the associated asymptotic variance with respect to friction. We give an expression for…
We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…
The phase retrieval from multi-frequency intensity (power) observations is considered. The object to be reconstructed is complex-valued. A novel algorithm is presented that accomplishes both the object phase (absolute phase) retrieval and…
The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex…
Poisson distribution is used for modeling noise in photon-limited imaging. While canonical examples include relatively exotic types of sensing like spectral imaging or astronomy, the problem is relevant to regular photography now more than…
Imaging systems' performance at low light intensity is affected by shot noise, which becomes increasingly strong as the power of the light source decreases. In this paper we experimentally demonstrate the use of deep neural networks to…
The aim of this paper is to provide a variational interpretation of the nonlinear filter in continuous time. A time-stepping procedure is introduced, consisting of successive minimization problems in the space of probability densities. The…
Gradient descent optimization algorithms, while increasingly popular, are often used as black-box optimizers, as practical explanations of their strengths and weaknesses are hard to come by. This article aims to provide the reader with…
We give a extensive account of a recent new way of applying the Dirichlet form theory to random Poisson measures. The main application is to obtain existence of density for thelaws of random functionals of L\'evy processes or solutions of…
We study the distributed stochastic compositional optimization problems over directed communication networks in which agents privately own a stochastic compositional objective function and collaborate to minimize the sum of all objective…
Coded distributed computation has become common practice for performing gradient descent on large datasets to mitigate stragglers and other faults. This paper proposes a novel algorithm that encodes the partial derivatives themselves and…