Tech Report: A Fast Multiscale Spatial Regularization for Sparse Hyperspectral Unmixing

TL;DR

This paper introduces a fast multiscale spatial regularization method for sparse hyperspectral unmixing, effectively improving solution quality while maintaining computational efficiency.

Contribution

A novel multiscale spatial regularization approach using superpixels that decomposes the unmixing problem for faster, more accurate solutions.

Findings

Outperforms state-of-the-art Total Variation algorithms

Reduces computational time significantly

Effective on both synthetic and real data

Abstract

Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit from spatial regularization strategies. While existing spatial regularization methods improve the problem conditioning and promote piecewise smooth solutions, they lead to large nonsmooth optimization problems. Thus, efficiently introducing spatial context in the unmixing problem remains a challenge, and a necessity for many real world applications. In this paper, a novel multiscale spatial regularization approach for sparse unmixing is proposed. The method uses a signal-adaptive spatial multiscale decomposition based on superpixels to decompose the unmixing problem into two simpler problems, one in the approximation domain and another in the original domain. Simulation results using both synthetic and real data indicate that the proposed method can outperform state-of-the-art Total Variation-based algorithms with a computation time comparable to that of their unregularized counterparts.