Hybrid Norm Pursuit Method for Hyperspectral Image Reconstruction

Abstract

This paper proposes a hybrid $l_{0}$ and $l_{1}$ norm pursuit (HNP) method for reconstructing hyperspectral image with high speed and high fidelity. The HNP method provides an approximate result by a simple and fast $l_{0}$ norm algorithm [such as the orthogonal matching pursuit (OMP)] first and then regulates it to an accurate result by a good but slow $l_{1}$ norm algorithm [such as the gradient projection for sparse reconstruction (GPSR)]. We build a mathematic model for the HNP method and formulate it to be a constraint optimization problem. How to choose the best switch point is investigated to ensure that the HNP method is able to provide the best reconstruction performance. Experimental results demonstrate that the HNP method is fast and offers high accuracy for hyperspectral image reconstruction and classification.