Efficient Data Processing for Coded Aperture Snapshot Spectral Imager Systems

Snapshot Spectral Imaging enables the acquisition of hyperspectral images (HSI) from 2D projected measurements employing specialized optical systems, such as the Coded Aperture Snapshot Spectral Imager (CASSI). Specifically, the CASSI system performs spatio-spectral codification of light obtaining 2D projected measurements. These measurements are then processed by algorithms to obtain the desired spectral images. Most traditional algorithms must compute an inverse matrix through decomposition, factorization, or block-operating a matrix related to the sensing protocol. However, since HSIs often have a high spatial or spectral resolution, the computation of an inverse matrix has a high computational cost. In this work, we propose an algebraic framework for computing the inverse matrix based on the nature of the codification protocol, accelerating its computation, in a tensorial form. Performed experiments from our proposed framework against some comparison methods based on linear algebra decomposition, factorization or block operations, show that the proposed framework is between 3 to 15 times faster than the best competing method, where the latter factor occurs when the matrices become bigger, which usually corresponds to realistic HSI sizes for spectral imaging applications.