Fast Semisupervised Unmixing Using Nonconvex Optimization

TL;DR

This paper presents a new nonconvex optimization-based semisupervised unmixing model that effectively handles library mismatch and enforces abundance sum-to-one constraints, demonstrating superior accuracy and efficiency over traditional methods.

Contribution

The paper introduces a novel nonconvex model for semisupervised unmixing that incorporates library mismatch considerations and enforces the sum-to-one constraint, solved efficiently with ADMM.

Findings

Convexity constraint outperforms sparsity prior in unmixing accuracy.

Proposed algorithms are significantly faster than traditional sparse unmixing methods.

Validated on simulated and real datasets, showing improved performance.

Abstract

In this paper, we introduce a novel linear model tailored for semisupervised/library-based unmixing. Our model incorporates considerations for library mismatch while enabling the enforcement of the abundance sum-to-one constraint (ASC). Unlike conventional sparse unmixing methods, this model involves nonconvex optimization, presenting significant computational challenges. We demonstrate the efficacy of Alternating Methods of Multipliers (ADMM) in cyclically solving these intricate problems. We propose two semisupervised unmixing approaches, each relying on distinct priors applied to the new model in addition to the ASC: sparsity prior and convexity constraint. Our experimental results validate that enforcing the convexity constraint outperforms the sparsity prior for the endmember library. These results are corroborated across three simulated datasets (accounting for spectral variability and varying pixel purity levels) and the Cuprite dataset. Additionally, our comparison with conventional sparse unmixing methods showcases considerable advantages of our proposed model, which entails nonconvex optimization. Notably, our implementations of the proposed algorithms-fast semisupervised unmixing (FaSUn) and sparse unmixing using soft-shrinkage (SUnS)-prove considerably more efficient than traditional sparse unmixing methods. SUnS and FaSUn were implemented using PyTorch and provided in a dedicated Python package called Fast Semisupervised Unmixing (FUnmix), which is open-source and available at https://github.com/BehnoodRasti/FUnmix