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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):

example plot of even and odd responses

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?

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I have since found this paper, which provides a nice framework for how to think about this problem.

Inl

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