Introduction of spatial smoothness constraints via linear diffusion for optimization‐based hyperspectral coastal ocean remote‐sensing inversion

An optimization‐based, shallow water remote‐sensing inversion algorithm was recently developed by Lee et al. (1999) that simultaneously derives bottom depth and water column inherent optical properties. Only measured remote‐sensing reflectance is required as input, which is a noted advantage; however, the algorithm is sensitive to noise. Given the observation that bottom depth and optical properties generally change slowly over the spatial domain, we applied a smoothness assumption by modifying the Lee algorithm to accommodate a spatial smoothness constraint. Spatial constraints were introduced through a linear diffusion process. The new spatial constraint model retrievals were compared with those from the original Lee model, as well as from the original model plus smoothing performed as postprocessing. Synthetic and real field data experiments were performed. For the synthetic experiments the Lee method was the most sensitive to noise and posted the largest absolute and standard errors. For the field experiments, Portable Hyperspectral Imager for Low Light Spectroscopy Sensor (PHILLS) imagery was acquired over optically shallow water. An in situ acoustic sensor mounted on a towed Hyperspectral Tethered Spectral Radiometer Buoy (HTSRB) provided measured bottom depth transects, and remote‐sensing reflectance was HTSRB derived. Bathymetry estimates were validated in this research. Lee method bottom depth retrievals were more erratic than those generated via the other methods. Unlike postsmoothing the spatial constraint method corrected large deviations of the Lee method spanning several transect points. Overall, our spatial constraint method yielded the most accurate estimates and represents a significant improvement upon the Lee method. Mean absolute estimation errors for the Lee, postprocessing, and spatial constraint methods were 0.412, 0.389, and 0.335 m, respectively.