Reconstruction of Compressive Multispectral Sensing Data Using a Multi-layered Conditional Random Field Approach

The prevalence of compressive sensing is continually growing in all facets of imaging science. Compressive sensing allows for the capture and reconstruction of an entire signal from a sparse (under-sampled), yet sufficient, set of measurements that is representative of the target being observed. This compressive sensing strategy reduces the duration of the data capture, the size of the acquired data, and the cost of the imaging hardware as well as complexity while preserving the necessary underlying information. Compressive sensing systems require the accompaniment of advanced reconstruction algorithms to reconstruct complete signals from the sparse measurements made. Here, a new reconstruction algorithm is introduced specifically for the reconstruction of compressive multispectral sensing data that allows for high-quality reconstruction from acquisitions at sub-Nyquist rates. We propose a multi-layered conditional random field (MCRF) model, which extends upon the CRF model by incorporating two joint layers of certainty and estimated states. The proposed algorithm treats the reconstruction of each spectral channel as a MCRF given the sparse multispectral measurements. Since the observations are incomplete, the MCRF incorporates an extra layer determining the certainty of the measurements. The proposed MCRF approach was evaluated using compressive multispectral data acquisitions, and is shown to enable fast acquisition of multispectral sensing data with reduced imaging hardware cost and complexity.