Reduction of random noise from multiband image data using phase relationships among their Fourier coefficients

The problem of reducing the random noise from multiband image data is examined, taking a nine-band image data set of a terrestrial scene and adding a significant amount of noise to the original pixel value of each band. For each of these data sets, data of three nearby bands generally exhibit a high correlation among them. Selected data for several sets of three nearby bands are transformed from the spatial domain to the frequency domain to study phase relationships (i.e., coherency) among their Fourier coefficients of various frequencies. It is shown that, in general, the addition of random noise results in the rapid change, with frequency, of a quantity called the coherency measure. (This is a quantitative measure of the phase agreement among the phases of various Fourier coefficients at a given frequency.) The coherency measure vs. frequency curve for a given data line is then used to attenuate various Fourier coefficients of the corresponding nearby bands of that line. It is then shown that the inverse transformation of such modified Fourier coefficients results in a statistically significant reduction of noise from the data of single lines, or from those data of some finite areas of the image. Results of a supervised boxcar multispectral classification with the original as well as various modified data sets of the selected image are also presented to provide additional guidance in the use of such a sophisticated analytic procedure in image processing.