Unknown filter

Equation (1) solves Y=XF for X. This is called the deconvolution problem with a known wavelet F. An opposite interpretation of Y=XF is that the filter F is unknown, but the input X and output Y are given. Here stabilization is less likely to be needed, but it would be if the input and output do not fill the frequency band. Performing derivatives as above, but with respect to F instead of X gives again equation (1) with X and F interchanged.  

$$F(\omega) {=} { \overline{X(\omega)} \ Y(\omega) \over \overline{X(\omega)} X(\omega) \ +\ \epsilon^2}$$ (6)