高光谱超分辨率中耦合结构矩阵分解的混合非精确BCD算法
Hybrid Inexact BCD for Coupled Structured Matrix Factorization in Hyperspectral Super-Resolution
摘要：
针对遥感高光谱超分辨率（HSR）中的耦合结构矩阵分解（CoSMF）问题，提出了一种一阶优化方法。为了最好地利用计算效率的问题结构，我们引入了一个混合不精确块坐标下降（HiBCD）计划，其中一个坐标是通过快速邻近梯度（FPG）方法更新，而另一个通过弗兰克-沃尔夫（FW）方法。根据数值经验，已知FPGA型方法需要较少的迭代次数来收敛，而FW型方法在某些情况下可以提供较低的每次迭代复杂度;我们希望两者都能发挥最大作用。我们证明了这个HiBCD方案的极限点是平稳的。我们的证明将HiBCD作为一类多块结构优化问题的优化框架，我们的平稳性要求不仅适用于CoSMF，而且适用于许多其他问题。先前的优化研究表明，对于仅使用FPG或FW更新的不精确块坐标下降，具有相同的平稳性结果。数值结果表明，所提出的HiBCD方案在计算效率上比HSR中最先进的CoSMF方案高得多。
英文摘要：
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.
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