We discuss the DISORT-based radiative transfer pipeline (“CRISM_LambertAlb”) for atmospheric and thermal correction of MRO/CRISM data acquired in multispectral mapping mode ($ \sim$200 m/pixel, 72 spectral channels). Currently, in this phase-one version of the system, we use aerosol optical depths, surface temperatures, and lower atmospheric temperatures, all from climatology derived from Mars Global Surveyor Thermal Emission Spectrometer (MGS-TES) data and from surface altimetry derived from MGS Mars Orbiter Laser Altimeter (MOLA). The DISORT-based model takes the dust and ice aerosol optical depths (scaled to the CRISM wavelength range), the surface pressures (computed from MOLA altimetry, MGS-TES lower atmospheric thermometry, and Viking-based pressure climatology), the surface temperatures, the reconstructed instrumental photometric angles, and the measured$I/F$spectrum as inputs, and then a Lambertian albedo spectrum is computed as the output. The Lambertian albedo spectrum is valuable geologically because it allows the mineralogical composition to be estimated. Here,$I/F$is defined as the ratio of the radiance measured by CRISM to the solar irradiance at Mars divided by$\pi$; if there was no martian atmosphere,$I/F$divided by the cosine of the incidence angle would be equal to the Lambert albedo for a Lambertian surface. After discussing the capabilities and limitations of the pipeline software system, we demonstrate its application on several multispectral data cubes—particularly, the outer reaches of the northern ice cap of Mars, the Tyrrhena Terra area that is northeast of the Hellas basin, and an area near the landing site for the Phoenix mission in the northern plains. For the icy spectra near the northern polar cap, aerosols need to be included in order to properly correct for the$ \hbox{CO}_{2}$absorption in the$\hbox{H}_{2}\hbox{O}$ice bands at wavelengths near 2.0$\mu\hbox{m}$. In future phases of software development, we intend to use CRISM data directly in order to retrieve the spatiotemporal maps of aerosol optical depths, surface pressure, and surface temperature. This will allow a second level of refinement in the atmospheric and thermal correction of CRISM multispectral data.

The theoretical classification performance of a Hopfield neural network is presented. An important link between empirically based investigations of neural network classification models and the correct application of these models to AI-based systems is established. General expressions are derived relating the performance of the Hopfield model to the number and dimensionality of code vectors stored in memory. The average performance of the network is analyzed by randomizing the subsequent code vectors and examining classification relative to the output bit errors. An exact probabilistic description of the network is derived for the first iteration, and an approximate second-moment analysis generalizable to multiple iterations examines performance near a fixed point. Degradations generated by noisy or incomplete input data are analyzed. The results show that the Hopfield net has major limitations when applied to fixed pattern classification problems because of its sensitivity to the number of code vectors stored in memory and the signal-to-noise ratio of the input data.>