Hessian Free Convolutional Dictionary Learning for Hyperspectral Imagery With Application to Compressive Chromo-Tomography

Convolutional dictionary learning (CDL) is an unsupervised learning method to seek a translation-invariant sparse representation for signals, and has gained a lot of interest in various image processing and computer vision applications. However, 3D hyperspectral images pose unique challenges due to their high dimensionality and complex structures, making optimization of the dictionary and its application to inverse problems difficult. This paper proposes an efficient CDL algorithm that neither explicit evaluation of the Hessians nor their inversion is required in the optimization process, which leads to substantial acceleration and memory savings. Furthermore, we exploit the learned kernels as the convolutional sparse coding (CSC) image prior for the compressive chromo-tomographic (CCT) reconstruction problem, and examine the usability and performances of the proposed method for CCT reconstruction. Numerical experiments show that, for CCT, 1) the proposed CSC can provide an efficient representation for HSI by using several tens of 3D filters; 2) the learned convolutional dictionary has reliable generalization capability; and 3) the proposed CSC-based method outperforms the classical reconstruction method using an analytic sparsifying basis.