ﻻ يوجد ملخص باللغة العربية
Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection (BP) based fidelity term as an alternative to the common least squares (LS), and demonstrated excellent results for popular inverse problems. These works have also empirically shown that using the BP term, rather than the LS term, requires fewer iterations of optimization algorithms. In this paper, we examine the convergence rate of the projected gradient descent (PGD) algorithm for the BP objective. Our analysis allows to identify an inherent source for its faster convergence compared to using the LS objective, while making only mild assumptions. We also analyze the more general proximal gradient method under a relaxed contraction condition on the proximal mapping of the prior. This analysis further highlights the advantage of BP when the linear measurement operator is badly conditioned. Numerical experiments with both $ell_1$-norm and GAN-based priors corroborate our theoretical results.
Communication has been seen as a significant bottleneck in industrial applications over large-scale networks. To alleviate the communication burden, sign-based optimization algorithms have gained popularity recently in both industrial and academic co
We establish a convergence theorem for a certain type of stochastic gradient descent, which leads to a convergent variant of the back-propagation algorithm
In this paper, we investigate the non-asymptotic stationary convergence behavior of Stochastic Mirror Descent (SMD) for nonconvex optimization. We focus on a general class of nonconvex nonsmooth stochastic optimization problems, in which the objectiv
A dynamical system is defined in terms of the gradient of a payoff function. Dynamical variables are of two types, ascent and descent. The ascent variables move in the direction of the gradient, while the descent variables move in the opposite direct
In this work, we analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes for non-convex optimization problems. Under generic assumptions, we prove that the algorithm iterate will almost s