# Given local responses by a bank of equally spaced (log-)Gabor filters, how can we estimate the response of an intermediate-scale filter?

Consider a grayscale image convolved with a bank of 2D wavelet quadrature pairs – in my case, log-Gabor filters. I have eight filters. For simplicity, let's say they are all vertically oriented, and an octave apart in frequency.

At some image location $$(x, y)$$ I now get 16 response values (one for each even and odd filter at eight different frequencies):

I would now like to estimate the response at an intermediate frequency, say, at three-and-a-half octaves. Can that be done?

Intuitively, I would expect the local distribution of even and odd frequencies to be something to which I can (within obvious sampling limits) fit a function, allowing me to estimate intermediate responses. Is this correct? Can such an expression be derived from the filter kernel itself?