Compressive Source Separation: Theory and Methods for Hyperspectral Imaging

TL;DR

This paper introduces novel compressive sampling methods for hyperspectral imaging that leverage source models and inter-channel correlations, significantly reducing measurements and computational effort for signal reconstruction.

Contribution

It proposes new sampling schemes based on source mixture models for hyperspectral images, with theoretical bounds and algorithms demonstrating improved efficiency over classical CS methods.

Findings

Reduces the number of measurements needed for hyperspectral image recovery.

Provides theoretical bounds on measurement requirements.

Demonstrates superior performance in experiments compared to traditional CS.

Abstract

With the development of numbers of high resolution data acquisition systems and the global requirement to lower the energy consumption, the development of efficient sensing techniques becomes critical. Recently, Compressed Sampling (CS) techniques, which exploit the sparsity of signals, have allowed to reconstruct signal and images with less measurements than the traditional Nyquist sensing approach. However, multichannel signals like Hyperspectral images (HSI) have additional structures, like inter-channel correlations, that are not taken into account in the classical CS scheme. In this paper we exploit the linear mixture of sources model, that is the assumption that the multichannel signal is composed of a linear combination of sources, each of them having its own spectral signature, and propose new sampling schemes exploiting this model to considerably decrease the number of measurements needed for the acquisition and source separation. Moreover, we give theoretical lower bounds on the number of measurements required to perform reconstruction of both the multichannel signal and its sources. We also proposed optimization algorithms and extensive experimentation on our target application which is HSI, and show that our approach recovers HSI with far less measurements and computational effort than traditional CS approaches.