Sparsity Based Spectral Super-Resolution and Applications to Ocean Water Color

Hyperspectral imagery (HSI) is an important imaging modality for remote sensing applications in many fields, including oceanic and atmospheric sciences [1], agriculture [2], defense, and space exploration [3]. Despite the richer potential of HSI sensors for scientific studies and applications, engineering tradeoffs, such as memory and communication bandwidth constraints, typically favor multispectral (MSI) sensor designs. We outline here continuing work which utilizes the statistical structure of HSI in order to extrapolate HSI-resolution spectra from more limited multi-spectral measurements. Accurate spectral super-resolution can substantially extend the utility of current and legacy MSI sensors, as well as open up the engineering design space of future missions. Ideally, both high spatial and high spectral resolution can be obtained with a combination of heritage optical design and sparse signal processing. While previous works on this topic demonstrate success on resolving MSI data simulated by artificially blurring real HSI images [4, 5], we demonstrate the utility of our methods on resolving real MSI data and validating the results by comparing to HSI images of the same scene. Specifically, we take geographically co-located oceanic water-color images taken by the VIIRS MSI imager [6] and the HICO HSI imager [7] and demonstrate that the proposed methodology can extrapolate HICO-resolution spectra from the more limited VIIRS measurements. Our proposed methodology is based on recent advances in sparsity-based signal processing. Sparsity-based techniques seek to describe data via a parsimonious representation in a large ambient space. In particular, given a large dictionary of feature vectors, sparse methods attempt to recover the smallest number of these features which explain the observation. Sparsity-based signal processing has proven invaluable in obtaining state-of-the-art solution to many linear inverse problems [8], and recent work demonstrates the applicability of sparsity based methods to HSI data. In fact both spatial and spectral sparsity has been used in the HSI literature for spectral unmixing [9, 10], classification [11], spectral dictionary learning [12, 4], and spatial super-resolution [13].