Scalable low dimensional manifold model in the reconstruction of noisy and incomplete hyperspectral images

TL;DR

This paper introduces a scalable low-dimensional manifold model that effectively reconstructs noisy and incomplete hyperspectral images by leveraging the low-dimensional structure of spatial-spectral blocks, resulting in improved speed and accuracy.

Contribution

The paper proposes a novel scalable manifold-based reconstruction method that shares similarity matrices across spectral bands, enhancing efficiency for hyperspectral images.

Findings

Outperforms existing methods in speed and accuracy.

Effectively reconstructs images from sparse and noisy data.

Utilizes shared similarity matrices for scalability.

Abstract

We present a scalable low dimensional manifold model for the reconstruction of noisy and incomplete hyperspectral images. The model is based on the observation that the spatial-spectral blocks of a hyperspectral image typically lie close to a collection of low dimensional manifolds. To emphasize this, the dimension of the manifold is directly used as a regularizer in a variational functional, which is solved efficiently by alternating direction of minimization and weighted nonlocal Laplacian. Unlike general 3D images, the same similarity matrix can be shared across all spectral bands for a hyperspectral image, therefore the resulting algorithm is much more scalable than that for general 3D data. Numerical experiments on the reconstruction of hyperspectral images from sparse and noisy sampling demonstrate the superiority of our proposed algorithm in terms of both speed and accuracy.