Inversion of data from diffraction-limited multiwavelength remote sensors. I - Linear case

The remote sensing inverse problem is considered in which the sensor does not necessarily view the same area on the earth at each wavelength, and spatial correlations of the geophysical parameters may be present. Under the conditions of linearity and stationary statistics, the minimum mean-square error solution to the problem of inverting such data is a spatial filter of the Wiener-Kolmogorov class. The resulting remote-sensing system can be characterized by an impulse response matrix in ordinary space or by a transfer matrix in frequency space. A signal-to-noise matrix for the geophysical parameters to be sensed is also defined; this matrix depends on the postulated a priori statistics and on the characteristics of the remote-sensing instrument. The system transfer matrix and the signal-to-noise matrix are simultaneously diagonalizable. The optimum transfer matrix filters out of the estimate vector those eigenparameters for which eigenvalues of the signal-to-noise matrix are less than unity.