A Modified Lyzenga’s Model for Multispectral Bathymetry Using Tikhonov Regularization

The derivation of shallow-water bathymetry from multispectral satellite images has become a highly active field of research in recent years. Nowadays, as satellite images become more and more freely available worldwide and easily accessible, this type of technique is a cost-effective surrogate for the derivation of bathymetric information, even about the most remote areas. In fact, traditional bathymetric methods, such as acoustic and LIght Detection And Ranging (LIDAR) systems, are still very expensive and difficult to operate. Among all the models that have been presented in literature for multispectral bathymetry, the log-linear inversion model proposed by Lyzenga is still the most popular model, which is due to its simplicity and physically intuitive nature. However, it is well known that it has relatively low accuracy and that the optical uniformity assumption is unrealistic. We propose a modified Lyzenga's model that can account for spatial heterogeneity. This is particularly important when the imaged area corresponds to heterogeneous bottom types and varying water quality. The estimation of the bathymetric parameters is performed by solving an inverse problem with a Tikhonov-like regularization term. We test the proposed model with satellite Landsat 8 multispectral images and in-situ depth measurements of a shallow-water site. The results obtained indicate that the new model is more accurate, with negligible extra complexity.