Regularized estimation of bathymetry and water quality using hyperspectral remote sensing

Abstract

ABSTRACTCoastal water mapping from remote-sensing hyperspectral data suffers from poor retrieval performance when the targeted parameters have little effect on subsurface reflectance, especially due to the ill-posed nature of the inversion problem. For example, depth cannot accurately be retrieved for deep water, where the bottom influence is negligible. Similarly, for very shallow water it is difficult to estimate the water quality because the subsurface reflectance is affected more by the bottom than by optically active water components.Most methods based on radiative transfer model inversion do not consider the distribution of targeted parameters within the inversion process, thereby implicitly assuming that any parameter value in the estimation range has the same probability. In order to improve the estimation accuracy for the above limiting cases, we propose to regularize the objective functions of two estimation methods (maximum likelihood or ML, and hyperspectral optimization process exemplar, or HOPE) by introducing local prior knowledge on the parameters of interest. To do so, loss functions are introduced into ML and HOPE objective functions in order to reduce the range of parameter estimation. These loss functions can be characterized either by using prior or expert knowledge, or by inferring this knowledge from the data (thus avoiding the use of additional information).This approach was tested both on simulated and real hyperspectral remote-sensing data. We show that the regularized objective functions are more peaked than their non-regularized counterparts when the parameter of interest has little effect on subsurface reflectance. As a result, the estimation accuracy of regularized methods is higher for these depth ranges. In particular, when evaluated on real data, these methods were able to estimate depths up to 20 m, while corresponding non-regularized methods were accurate only up to 13 m on average for the same data.This approach thus provides a solution to deal with such difficult estimation conditions. Furthermore, because no specific framework is needed, it can be extended to any estimation method that is based on iterative optimization.