Low dimensional manifold model in hyperspectral image reconstruction

Abstract

In this chapter, we present a low dimensional manifold model (LDMM) for hyperspectral image reconstruction. This model is based on the observation that the spatial–spectral blocks of hyperspectral images typically lie close to a collection of low dimensional manifolds. To emphasize this, we directly use the dimension of the manifold as a regularization term in a variational functional, which can be solved efficiently by alternating direction of minimization and advanced numerical discretization. Experiments on the reconstruction of hyperspectral images from sparse and noisy sampling demonstrate the superiority of LDMM in terms of both speed and accuracy.