Reproducing Kernel Hilbert Space Pruning for Sparse Hyperspectral Abundance Prediction

TL;DR

This paper introduces a novel Hilbert space-based pruning method for sparse hyperspectral abundance prediction, significantly improving accuracy and convergence speed over traditional and neural network approaches.

Contribution

It proposes a new transformation into Hilbert spaces for pruning and constructing sparse representations, enhancing spectral reconstruction and compression efficiency.

Findings

Hilbert space pruning reduces error by up to 40% compared to standard methods

The proposed method converges faster than matching pursuit algorithms

Outperforms neural network autoencoders in spectral reconstruction accuracy

Abstract

Hyperspectral measurements from long range sensors can give a detailed picture of the items, materials, and chemicals in a scene but analysis can be difficult, slow, and expensive due to high spatial and spectral resolutions of state-of-the-art sensors. As such, sparsity is important to enable the future of spectral compression and analytics. It has been observed that environmental and atmospheric effects, including scattering, can produce nonlinear effects posing challenges for existing source separation and compression methods. We present a novel transformation into Hilbert spaces for pruning and constructing sparse representations via non-negative least squares minimization. Then we introduce max likelihood compression vectors to decrease information loss. Our approach is benchmarked against standard pruning and least squares as well as deep learning methods. Our methods are evaluated in terms of overall spectral reconstruction error and compression rate using real and synthetic data. We find that pruning least squares methods converge quickly unlike matching pursuit methods. We find that Hilbert space pruning can reduce error by as much as 40% of the error of standard pruning and also outperform neural network autoencoders.