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Suppose you have a set of $n$ sensors with overlapping sensitivities--like the cone cells of an animal retina, which is in fact the sort of system I am trying to model. Given the frequency-response curves for each sensor, how can I calculate a matrix transformation that will a new set of $n-1$ maximally-decorrelated dimensions, and one weighted-sum dimension? I.e., it may not always be possible to do this perfectly, but in the ideal transformed space, we should be able to select any given dimension from the decorrelated set, and find an impulse that will increase/decrease the value of that dimension without affecting any others.

For reference, this is exactly what human retinal ganglia do to convert RGB cone signals into luminance, red-green opponence, and blue-yellow opponence signals. I would like to be able to calculate the equivalent opponence signals for an arbitrary set of possible "cone cells" with different sensitivities. If it helps simplify things, it is an acceptable loss of fidelity to model each sensor response curve as a gaussian.

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I am not sure about the model, but if you can simulate the sensor by its frequency response, a vector, then you could use the Principal Component Analysis (PCA) to create a linear combination of new responses which are decorrelated.

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  • $\begingroup$ Apparently, all the components of the first eigenvector of a covariance matrix are always of like sign, and thus correspond to the luminance component, which is really convenient. That requires calculating the covariance matrix though, and while I can use simulation for that, I was really hoping there would be a way to do it directly. $\endgroup$ Commented May 1, 2023 at 23:05

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