## 1 Introduction  
Coral reefs are among the most biologically diverse and productive ecosystems [1] and provide a variety of goods and services to many tropical and sub-tropical coastal nations [2; 3]. Coral reef health and economic value are on the decline worldwide in response to direct human impacts and global changes in climate [4] and this trend is expected to continue [5; 6; 7]. Within human-dominated environments, rapid and potentially irrecoverable changes in the state of coral reef ecosystems have been described as regime shifts [8; 9], the most notable cause of which is the systematic removal of herbivores that prevent algae from overgrowing live coral [10]. Thus, the benthic cover offers a key metric to describe changes in coral reef health and is typically characterized optically as three primary endmembers; healthy corals and associated organisms, minimal coral cover dominated by fleshy macroalgae overgrowth, and uncolonized calcareous sand and dead coral rubble [11; 12]. Coral reef benthic components, both fauna and flora, are highly diverse in appearance. [PERSON] et al. [13] analyzed over 13,000 reflectance spectra of benthic coral reef components and identified 12 characteristic spectra representing algae, soft and hard coral, and sediments. Subtle differences in benthic reflectance can be detected in the above-water light field. Airborne imaging spectrometers providing continuous, high resolution sampling across the visible and near-infrared spectrum have been shown to yield more accurate discrimination between shallow water benthic types compared to multispectral systems that provide data at a small number of broad spectral bands [14; 15; 16; 17; 18]. [PERSON] and [PERSON] [19] examined the detailed spectral reflectance of various coral species and reported that spectral unmixing approaches, such as derivative analysis, are potentially effective discrimination techniques. [PERSON] et al. [20] used radiative transfer simulations to investigate the effect of spectral sampling to discriminate between coral endmembers and concluded that increasing spectral sampling and resolution increased the depth from 2 m to 6 m, at which primary reef features can be identified within clear coastal water. As a result of these and other similar findings, remote sensing methods operating within the visible and near infrared portions of the light spectrum are rapidly becoming incorporated into coral reef monitoring efforts [21]. In addition to high spectral fidelity, coral reef scientists desire high spatial resolution, expressed as ground sampling distance (\(GSD\)), of less than a few tens of meters in order to limit sub-pixel variability and provide meaningful ecological information [22]. Building upon the lessons of modeling and in situ spectrometry and the positive applications of airborne imaging spectrometers with high spatial resolution, future satellite sensors are under development that will strive to provide similar data on a global scale. The NASA Surface Biology and Geology sensor, formerly the Hyperspectral Infrared Imager, for example, is envisioned as an imaging spectrometer that will provide continuous spectra between 380 and 2500 nm with 10 nm channels and a spatial resolution of 30 m [23]. Remote sensing of coral reefs is a challenging problem from environmental and engineering perspectives. In order to retrieve meaningful benthic and water column signals the confounding effects associated with environmental variability, e.g., atmospheric conditions and glint from the water surface must either be removed from the data or avoided. Uncertainty associated with such corrections is often referred to as environmental noise. From an engineering perspective, the sensor must be designed to collect as much light per pixel as possible in order to minimize signal variability associated with system electronics and random variations in light intensity. This variability is commonly referred to as sensor noise and expressed as the ratio of signal to noise (\(SNR\)).