Hyperspectral Remote Sensing has the potential to be used as an effective coral monitoring system from either space or airborne sensors. The problems to be addressed in hyperspectral imagery of coastal waters are related to the medium, which presents high scattering and absorption, and the object to be detected. The object to be detected, in this case coral reefs or different types of ocean floor, has a weak signal as a consequence of its interaction with the medium. The retrieval of information about these targets 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 that does not use labeled samples to detect coral reefs under coastal shallow waters. Synthetic data was generated to simulate data gathered using a high resolution imaging spectrometer (hyperspectral) sensor. A semi-analytic 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 as a starting point in order to arrive at an inverse formulation that incorporates a priori information about the target. This expression will be used in an inversion process on a pixel by pixel basis to estimate the ocean floor signal. The a priori information is in the form of previously measured spectral signatures of objects of interest, such as sand, corals, and sea grass.