Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case

Abstract

In blind hyperspectral unmixing (HU), the pure-pixel assumption is well-known to be powerful in enabling simple and effective blind HU solutions. However, the pure-pixel assumption is not always satisfied in an exact sense, especially for scenarios where pixels are heavily mixed. In the no pure-pixel case, a good blind HU approach to consider is the minimum volume enclosing simplex (MVES). Empirical experience has suggested that MVES algorithms can perform well without pure pixels, although it was not totally clear why this is true from a theoretical viewpoint. This paper aims to address the latter issue. We develop an analysis framework wherein the perfect endmember identifiability of MVES is studied under the noiseless case. We prove that MVES is indeed robust against lack of pure pixels, as long as the pixels do not get too heavily mixed and too asymmetrically spread. The theoretical results are verified by numerical simulations.

References in corpus (1)

• Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization

Cited by in corpus (25)

• Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications
• Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clustering
• On Identifiability of Nonnegative Matrix Factorization
• Blind Audio Source Separation with Minimum-Volume Beta-Divergence NMF
• A Fast Hyperplane-Based Minimum-Volume Enclosing Simplex Algorithm for Blind Hyperspectral Unmixing
• Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package
• Spectral Variability Aware Blind Hyperspectral Image Unmixing Based on Convex Geometry
• Penalty Dual Decomposition Method For Nonsmooth Nonconvex Optimization
• Generalized Separable Nonnegative Matrix Factorization
• Quaternion Non-negative Matrix Factorization: definition, uniqueness and algorithm
• Simplex-Structured Matrix Factorization: Sparsity-based Identifiability and Provably Correct Algorithms
• Transformer-Driven Inverse Problem Transform for Fast Blind Hyperspectral Image Dehazing
• Hybrid Inexact BCD for Coupled Structured Matrix Factorization in Hyperspectral Super-Resolution
• Probabilistic Simplex Component Analysis
• Polytopic Matrix Factorization: Determinant Maximization Based Criterion and Identifiability
• Learning Nonlinear Mixtures: Identifiability and Algorithm
• Near-Convex Archetypal Analysis
• Maximum Volume Inscribed Ellipsoid: A New Simplex-Structured Matrix Factorization Framework via Facet Enumeration and Convex Optimization
• Smoothed Separable Nonnegative Matrix Factorization
• Bounded Simplex-Structured Matrix Factorization: Algorithms, Identifiability and Applications
• Global Mapping of Surface Composition on an Exo-Earth Using Sparse Modeling
• Dual Simplex Volume Maximization for Simplex-Structured Matrix Factorization
• Block Majorization Minimization with Extrapolation and Application to $\beta$-NMF
• Checking the Sufficiently Scattered Condition using a Global Non-Convex Optimization Software
• On Hyperspectral Unmixing