Hybrid Inexact BCD for Coupled Structured Matrix Factorization in Hyperspectral Super-Resolution

TL;DR

This paper introduces a hybrid inexact block coordinate descent method combining FPG and FW updates for efficient coupled structured matrix factorization in hyperspectral super-resolution, demonstrating superior computational performance.

Contribution

The paper proposes a novel hybrid optimization scheme (HiBCD) that leverages the strengths of FPG and FW methods for CoSMF problems, with proven convergence to stationarity.

Findings

HiBCD is more computationally efficient than existing methods.

The scheme guarantees convergence to stationary points.

Numerical experiments validate improved performance in hyperspectral super-resolution tasks.

Abstract

This paper develops a first-order optimization method for coupled structured matrix factorization (CoSMF) problems that arise in the context of hyperspectral super-resolution (HSR) in remote sensing. To best leverage the problem structures for computational efficiency, we introduce a hybrid inexact block coordinate descent (HiBCD) scheme wherein one coordinate is updated via the fast proximal gradient (FPG) method, while another via the Frank-Wolfe (FW) method. The FPG-type methods are known to take less number of iterations to converge, by numerical experience, while the FW-type methods can offer lower per-iteration complexity in certain cases; and we wish to take the best of both. We show that the limit points of this HiBCD scheme are stationary. Our proof treats HiBCD as an optimization framework for a class of multi-block structured optimization problems, and our stationarity claim is applicable not only to CoSMF but also to many other problems. Previous optimization research showed the same stationarity result for inexact block coordinate descent with either FPG or FW updates only. Numerical results indicate that the proposed HiBCD scheme is computationally much more efficient than the state-of-the-art CoSMF schemes in HSR.