A New Spectral Conjugate Subgradient Method with Application in Computed Tomography Image Reconstruction

TL;DR

This paper introduces a spectral conjugate subgradient method that effectively solves nonsmooth optimization problems and improves computed tomography image reconstruction quality.

Contribution

It combines spectral conjugate gradient and subgradient methods, offering a novel approach with enhanced performance in nonsmooth optimization and CT image reconstruction.

Findings

Spectral conjugate subgradient outperforms original spectral subgradient.

Polak-Ribiere formula yields the best performance.

Method effectively applies to CT image reconstruction with TV regularization.

Abstract

A new spectral conjugate subgradient method is presented to solve nonsmooth unconstrained optimization problems. The method combines the spectral conjugate gradient method for smooth problems with the spectral subgradient method for nonsmooth problems. We study the effect of two different choices of line search, as well as three formulas for determining the conjugate directions. In addition to numerical experiments with standard nonsmooth test problems, we also apply the method to several image reconstruction problems in computed tomography, using total variation regularization. Performance profiles are used to compare the performance of the algorithm using different line search strategies and conjugate directions to that of the original spectral subgradient method. Our results show that the spectral conjugate subgradient algorithm outperforms the original spectral subgradient method, and that the use of the Polak-Ribiere formula for conjugate directions provides the best and most robust performance.