Snapshot interferometric multispectral imaging using deconvolution and colorimetric fit

Multispectral imaging techniques provide spatial and spectral information about a scene. Among them, the spatial Fourier transform interferometric approach is popular, because it does not use moving parts and has the signal advantage. But the inherent antagonism between the recording of spectral and spatial frequencies in such techniques is truly bypassed only in remote sensing by using the relative motion between the scene and the imager as a substitute for the scanning device. Snapshot techniques, which do not use any sort of scanning, were also developed, but at the price of sacrificing the overall spatial-spectral resolution. They use mapping, multiplexing, and filtering to spread the spatial and the spectral information over a large sensor array. Here, a snapshot interferometric multispectral imaging technique is presented, that does not sacrifice resolution. The whole spectral and spatial information is obtained from a small quantity of input data; this was made possible by the use of deconvolution in the Fourier spatial spectrum and colorimetric fit, which puts our technique in the vicinity of the compressive sensing approach. A severe limitation is that the technique can be applied only to scenes that can be divided into subscenes in which the dependencies of the light intensity on the spectral and the spatial variables respectively are separable, i.e. the input data has high sparsity. This shifts the burden of creating complex hardware capable of performing snapshot spectral analysis to finding algorithms for dividing the scene in spectrally uniform subscenes. Another difficulty is the fact that the subscenes need to be smooth enough so that the Fourier spectrum due to interference does not overlap the Fourier spectrum of the non-interfered subscene. However, solutions to these problems exist or they are in development. For instance, we propose a test of high probability for separability. The use of deconvolution and colorimetric fit eliminates the need for calibrated dispersive elements in the spectral analysis and may be separated from other considerations and construed as a contribution to spectral analysis.