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 i n many remote sensing studies. To this end, linear regression analysis is generally employed. Given two matrices of paired noise-infected me asurements, classical linear regression is usually employed to find op timal parameters of a model calibration function which fits the observ ed readings best, in the minimal least squares sense. The squared coef ficient of determination R=(variation due to the model)/(total variati on) is a common quality measure of the chosen model, while the varianc e S-r of the 'residuals' is a measure of the information that the chos en calibration function is unable to explain. The basic premise of reg ression analysis requires that the reference ground data must be preci se and noiseless. Since in most remote sensing studies this condition is not met, classical regression is not an efficient tool for discover ing the true functional relation between remotely-sensed data and grou nd observations. A new calibration method is proposed whereby the leas t-squares minimization is conducted on the amplitude matrices of the r eadings via the FFT. For a given model, R is always increased beyond t he value obtained by conventional regression at the expense of a sligh t 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, bel ow the value obtained by conventional regression. The new calibration method is a radical departure from classical statistics and has the po tential of significantly improving statistical inference in remote sen sing. The line taken is illustrated by numerical examples which compar e the new calibration method to the classical regression technique. It is demonstrated, that the new method can discover better the true fun ctional relation between satellite images or between ground based sens or arrays and satellite images, which may be occluded by noise.