Fast Fourier Transform based calibration in remote sensing

Quantification of the functional relation between remotely-sensed data and commensurable ground based observations is a basic prerequisite in many remote sensing studies. To this end, linear regression analysis is generally employed. Given two matrices of paired noise-infected measurements, classical linear regression is usually employed to find optimal parameters of a model calibration function which fits the observed readings best, in the minimal least squares sense. The squared coefficient of determination R=(variation due to the model)/(total variation) is a common quality measure of the chosen model, while the variance S-r of the 'residuals' is a measure of the information that the chosen calibration function is unable to explain. The basic premise of regression analysis requires that the reference ground data must be precise and noiseless. Since in most remote sensing studies this condition is not met, classical regression is not an efficient tool for discovering the true functional relation between remotely-sensed data and ground observations. A new calibration method is proposed whereby the least-squares minimization is conducted on the amplitude matrices of the readings via the FFT. For a given model, R is always increased beyond the value obtained by conventional regression at the expense of a slight increase in S-r. When one of the measurement sets may be considered noiseless, phase correction may be employed to reduce S-r as well, below the value obtained by conventional regression. The new calibration method is a radical departure from classical statistics and has the potential of significantly improving statistical inference in remote sensing. The line taken is illustrated by numerical examples which compare the new calibration method to the classical regression technique. It is demonstrated, that the new method can discover better the true functional relation between satellite images or between ground based sensor arrays and satellite images, which may be occluded by noise.