Enhancing hyperspectral image unmixing with spatial correlations

TL;DR

This paper introduces a Bayesian algorithm for hyperspectral image unmixing that leverages spatial correlations via Markov random fields, improving accuracy by modeling class-based homogeneity and spatial dependencies.

Contribution

It presents a novel Bayesian framework incorporating Markov random fields to exploit spatial correlations in hyperspectral unmixing, which was not addressed in prior methods.

Findings

Improved unmixing accuracy on synthetic data

Effective classification of pixel regions

Robust parameter estimation using MCMC methods

Abstract

This paper describes a new algorithm for hyperspectral image unmixing. Most of the unmixing algorithms proposed in the literature do not take into account the possible spatial correlations between the pixels. In this work, a Bayesian model is introduced to exploit these correlations. The image to be unmixed is assumed to be partitioned into regions (or classes) where the statistical properties of the abundance coefficients are homogeneous. A Markov random field is then proposed to model the spatial dependency of the pixels within any class. Conditionally upon a given class, each pixel is modeled by using the classical linear mixing model with additive white Gaussian noise. This strategy is investigated the well known linear mixing model. For this model, the posterior distributions of the unknown parameters and hyperparameters allow ones to infer the parameters of interest. These parameters include the abundances for each pixel, the means and variances of the abundances for each class, as well as a classification map indicating the classes of all pixels in the image. To overcome the complexity of the posterior distribution of interest, we consider Markov chain Monte Carlo methods that generate samples distributed according to the posterior of interest. The generated samples are then used for parameter and hyperparameter estimation. The accuracy of the proposed algorithms is illustrated on synthetic and real data.