An Automated Spectral Deconvolution Algorithm: Application to Thermal Infrared Studies of Earth and Mars

Introduction: The linear mixing of thermal infrared (TIR) emission spectra in multi-mineralic mixtures has been proven, and its limits and applicability have been quantitatively investigated [1,2]. Limiting factors in the accuracy of any linear retrieval (spectral deconvolution) algorithm include the spectral precision of the instrumentation as well as the fact that the number of end-members must be ≤ the number of spectral bands in the TIR [1]. Because of this end-member constraint, there is no way to examine a multispectral TIR image using a large, spectral endmember library [3]. A possible solution is the implementation of an automated, blind end-member algorithm to analyze all possible subsets (of arbitrary size k) of minerals present in the mixture from within a mineral library (of size n). For example, in the only such study to employ this technique, the Kelso Dunes, California were examined using 375 unique combinations (k4) of the most likely (n=) 15 minerals present in the dunes [4]. The deconvolution model results were analyzed for their “goodness of fit” to laboratory spectra of collected sand samples. This investigation proved highly successful, further supporting the capabilities of linear retrieval in the TIR [4]. However, the process was computationally intensive because it was entirely manual. The development of an automated algorithm to accomplish this task would decrease the amount of time required for such an investigation by many orders of magnitude. From a remote sensing perspective, an automated blind end-member spectral deconvolution algorithm could be useful to determine mineral abundance for any mixture (or pixel-by-pixel in a TIR image) using a large emissivity library of minerals as input. This approach is particularly timely as there multispectral TIR mapping instruments now orbiting Earth and Mars.