A universal sensing model for compressed hyperspectral image analysis

Hyperspectral imaging (HSI) systems have found success in a variety of applications and are continuing to grow into new applications placing an emphasis on developing more affordable systems. Compressive sensing (CS) is an enabling technology for applications requiring low cost, size, weight, and power (SWAP) HSI sensors. A typical compressed sensing system includes both sparse sampling (encoding) and sparse recovery (decoding); however, recent work has investigated the design of algorithms capable of operating directly in the compressed domain and have shown great success. Many of these works are based on a random sampling mathematical framework that explicitly models both the sparse representation basis and the sampling basis. Such a model requires the selection of a sparsifying representation basis that is seldom proven to be optimal for hyperspectral images and typically left as an open-ended question for future research. In this work, a brief review of the compressive sensing framework for Hyperspectral pixel vectors is provided and the concept of Universality is exploited to simplify the model, removing the need to specify the sparsifying basis entirely for CS applications where sparse recovery is not required. A simple experiment is constructed to demonstrate Universality in sparse reconstruction and to better illustrate the concept. The results to this experiment clearly show, that with a random sampling framework, knowledge of the sparsifying basis is only required during sparse recovery.