EUROPT 2025
Abstract Submission

537. A Strongly Convex Framework for Image Reconstruction Using Generic Smoothing Filters

Invited abstract in session MB-2: Optimization and applications, stream Nonsmooth and nonconvex optimization.

Monday, 10:30-12:30
Room: B100/7011

Authors (first author is the speaker)

1. Arghya Sinha
Computational and Data Sciences, Indian Institute of Science
2. Kunal N. Chaudhury
Department of Electrical Engineering, Indian Institute of Science

Abstract

We study a class of regularized optimization problems related to image reconstruction, which are implicitly parametrized by a denoiser. We show that, with a specific class of linear denoisers, the associated objective functions exhibit strong convexity. Generally, strong convexity arises when either the loss function or the regularizer is strongly convex. We show these denoisers are proximable in a suitable inner product space and correspond to a nonsmooth, convex regularizer. Furthermore, even if neither the loss function nor the regularizer is strongly convex, we develop a sufficient condition that ensures their sum is strongly convex. However, to make nonsymmetric denoisers proximable, we must either symmetrize or alter the inner product space, which can increase time complexity and reduce reconstruction quality. To address this issue, we use sufficient conditions similar to those before to consider an alternative optimization problem that achieves better reconstructions in a shorter time frame without requiring the denoiser to be proximable. Specifically, we demonstrate that the inherent properties of nonnegativity and stochasticity can be used to create a strongly convex optimization framework that can be efficiently solved using conjugate gradient methods. In practice, this approach is significantly faster—by an order of magnitude—than splitting algorithms that use the same denoisers, and it produces improved reconstructions when nonsymmetric denoisers are applied.

Keywords

Status: accepted

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