Image reconstruction and subsurface detection by the application of Tikhonov regularization to inverse problems in hyperspectral images

Hyperspectral Remote Sensing has the potential to be used as an effective coral monitoring system from space. The problems to be addressed in hyperspectral imagery of coastal waters are related to the medium, clutter, and the object to be detected. In coastal waters the variability due to the interaction between the coast and the sea can bring significant disparity in the optical properties of the water column and the sea bottom. In terms of the medium, there is high scattering and absorption. Related to clutter we have the ocean floor, dissolved salt and gases, and dissolved organic matter. The object to be detected, in this case the coral reefs, has a weak signal, with temporal and spatial variation. In real scenarios the absorption and backscattering coefficients have spatial variation due to different sources of variability (river discharge, different depths of shallow waters, water currents) and temporal fluctuations. The retrieval of information about an object beneath some medium with high scattering and absorption properties requires the development of mathematical models and processing tools in the area of inversion, image reconstruction and detection. This paper presents the development of algorithms for retrieving information and its application to the recognition and classification of coral reefs under water with particles that provide high absorption and scattering. The data was gathered using a high resolution imaging spectrometer (hyperspectral) sensor. A mathematical model that simplifies the radiative transfer equation was used to quantify the interaction between the object of interest, the medium and the sensor. Tikhonov method of regularization was used in the inversion process to estimate the bottom albedo, ρ, of the ocean floor using a priori information. The a priori information is in the form of measured spectral signatures of objects of interest, such as sand, corals, and sea grass.