Hyper-Spectral Image Analysis with Partially-Latent Regression and Spatial Markov Dependencies

TL;DR

This paper introduces a novel spatially-constrained partially-latent regression model for hyper-spectral image analysis, effectively estimating physical parameters from high-dimensional spectral data with spatial dependencies, demonstrated on Mars data.

Contribution

It combines GLLiM with a partially-latent response model and incorporates MRF priors to handle unobserved parameters and spatial structure in hyper-spectral data analysis.

Findings

Effective estimation of physical parameters from Mars hyper-spectral data.

Improved modeling of unobserved or artifact-affected parameters.

Demonstrated superior performance on planetary remote sensing data.

Abstract

Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between physical parameters and spectra has been established in a data-driven fashion, the learned relationship can be used to estimate physical parameters for new hyper-spectral observations. Within this framework, we propose a spatially-constrained and partially-latent regression method which maps high-dimensional inputs (hyper-spectral images) onto low-dimensional responses (physical parameters such as the local chemical composition of the soil). The proposed regression model comprises two key features. Firstly, it combines a Gaussian mixture of locally-linear mappings (GLLiM) with a partially-latent response model. While the former makes high-dimensional regression tractable, the latter enables to deal with physical parameters that cannot be observed or, more generally, with data contaminated by experimental artifacts that cannot be explained with noise models. Secondly, spatial constraints are introduced in the model through a Markov random field (MRF) prior which provides a spatial structure to the Gaussian-mixture hidden variables. Experiments conducted on a database composed of remotely sensed observations collected from the Mars planet by the Mars Express orbiter demonstrate the effectiveness of the proposed model.