My question concerns the Richardson–Lucy deconvolution algorithm, which is described in Richardson's original paper. I am interested in applying it in the context of a raw image converter for digital photography. The RawTherapee discussion that motivated this post can be found here.
By using a Poisson noise model, the original paper assumes the algorithm is being applied to the linear data recovered from the sensor, which in particular is not gamma corrected any does not have any additional nonlinear tone mapping applied. A Poisson random variable is no longer Poisson after a nonlinear transformation, so the model no longer applies to such data.
My understanding is that if we simply demosaic the data from the Bayer array on the sensor, then apply deconvolution to the resulting RGB data, we are in good shape because it is linear.
However, it seems traditional to apply the deconvolution only to the luminance data. (I'm not totally sure why, or whether it is advisable, so please consider this a sub-question.) RawTherapee does this, for example, by converting the image to a LAB color space and deconvolving the L channel.
But there's the issue. It doesn't seem like L is linear in the number of photons captured. I found some data that suggests reflectance percentages of (12.5, 25, 50, 100) correspond to L values of (42.4, 57.0, 75.8, 100). Possibly this conversion depends on the illuminant being used; I am not well-versed enough in color science to say. However, the point is that the mapping is definitely non-linear.
So, is there a practical way to apply the Richardson–Lucy algorithm to a "linearized" version of the luminance data? Is this even desirable? I am not sure what the best practices are here, so any references you could provide would be greatly appreciated. I could not find any mention of this issue in the references I looked at.