Exploiting Structural Complexity for Robust and Rapid Hyperspectral Imaging

TL;DR

This paper introduces novel spectral de-noising and hypercube reconstruction techniques for hyperspectral imaging, leveraging low-rank and sparse structures to improve robustness and speed without prior noise knowledge.

Contribution

It presents a new method for simultaneous spectral de-noising and noise band estimation using low-rank and sparse minimization, applicable to hyperspectral imaging and CT systems.

Findings

Effective spectral de-noising without prior noise band knowledge

Improved hyperspectral imaging under limited angle tomography

Utilization of low-rank matrix completion techniques

Abstract

This paper presents several strategies for spectral de-noising of hyperspectral images and hypercube reconstruction from a limited number of tomographic measurements. In particular we show that the non-noisy spectral data, when stacked across the spectral dimension, exhibits low-rank. On the other hand, under the same representation, the spectral noise exhibits a banded structure. Motivated by this we show that the de-noised spectral data and the unknown spectral noise and the respective bands can be simultaneously estimated through the use of a low-rank and simultaneous sparse minimization operation without prior knowledge of the noisy bands. This result is novel for for hyperspectral imaging applications. In addition, we show that imaging for the Computed Tomography Imaging Systems (CTIS) can be improved under limited angle tomography by using low-rank penalization. For both of these cases we exploit the recent results in the theory of low-rank matrix completion using nuclear norm minimization.