Log-Likelihood Method of Reducing Noise in CRISM Along-Track Oversampled Hyperspectral Images

Abstract:

The Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) began taking Along-Track Oversampled (ATO) observations in 2010 to obtain super-resolution hyperspectral images, with spatial resolutions in the along-track direction of as small as ~5 m/pixel. We present a new method to both process and reduce noise in the ATOs. We developed a log-likelihood algorithm to determine the most likely estimate of the actual Martian surface given the CRISM spectral radiance measurements and spatial and spectral transfer functions (TF). We assume the spatial TF is given by a 2D Gaussian and use the asymmetric Gaussian spectral TF given in the CRISM documentation. The log-likelihood method reduces Poisson noise in the spectrum for a given hyperspectral pixel, allowing for identification of subtle spectral absorptions otherwise lost in noise. We assume that the data are Poisson distributed and that the mean μ is given by a blurred version of the actual scene c. The CRISM ATO is this blurred version. It is more efficient to maximize the log of a function rather than the function itself, so we compute the image c that maximizes the log-likelihood function for the data. We begin with an initial guess for the projected, estimated scene c and have the freedom to choose any reasonable output pixel size. To forward project, we convolve the spatial TF with c and then convolve the spectral TF with the output. The result is a simulation of the measured ATO. We divide the CRISM ATO by this simulated scene to obtain the error, and then we backproject the error into dimensions of c by applying transposes of the TFs. Finally, we update our guess for the actual scene by multiplying c by the backprojected error. We iterate until convergence. We focus our analysis on recent ATOs of Gale Crater to illustrate the advantages of the method. We will also present a combined Poisson and Gaussian noise iterative approach with regularization and results for reducing noise in CRISM data.