Solvability and Speed Improvement in Iterative Processing with Deterministic Pseudo-Inversions

摘要

Tomographic spectral imagers owe much of their development to sophisticated numerical processing. In order to reduce system size and complexity, mechanical detail has often been replaced with ever-increasing algorithm sophistication. In developing the Field Multiplexed Dispersive Imaging Spectrometer (FMDIS), the processing has been broken down into two steps; one which deconvolves the solution spatially and a second which deconvolves the solution spectrally. The first step is characterized by large inversion matrices of a few iterations (typically less than 10), while the second requires small matrices and a large number of iterations (hundreds to millions). Iterative processing has been employed due to the physical nature of the data. Inversions must be robust to moderate amounts of noise and calibration uncertainty. In this paper we present a deterministic pseudo inversion technique to replace the second iterative processing step in FMDIS datacube generation. It is shown to be within required limits of accuracy and can speed up processing by an order of magnitude or more. While not intended to replace the iterative solution technique, it provides a fast means of processing data when speed is more important than accuracy. Implementation of the solution algorithm is discussed relative to the over-all solvability of the under determined system of equations. Several results are shown from a visible instrument with 33 colors which contrast the two techniques.