# Help with deconvolving photon reads distributed across neighboring pixels

I'm building a radiation detector that collects photons in CCD pixels and we can relate the energy of the photon from the intensity of the pixel. To test the detector, I took the following spectrum of Iron 55, which is expected to have a single peak at 6 keV:

The tail at lower values of the energy is interesting because it's not supposed to be there. Taking a closer look at pixels in this range, I see that they are clustered next to each other, with what seems to be energies from a single photon distributed into multiple neighboring pixels.

I am intrigued by the possibility of getting a cleaner spectrum by collecting these pixels together. I could try manually going through and clustering at each pixel, but I thought a more elegant way would be to deconvolve the image using a simple point spread function. In the result of this deconvolution I need 2 things to be true:

1. the energy of the system should be conserved, so the sum of the pixels (the $L_1$ norm) should be conserved.
2. there should be no negative pixel intensities, since those are unphysical.

I did that, using a Gaussian PSF with a half-pixel standard deviation. However, I find that I either need to violate condition 1 of my requirements, or condition 2 of my requirements. Just using the gaussian PSF with $L_1$ norm 1, which conserves the energy, gives me a plot like this:

The white pixels are negative, unphysical values. At this point I'm stumped, but also obsessed with this problem, because it seems like it should have a clean solution. Any advice?

• How are you doing the deconvolution? Possible issues: a Gaussian PSF is a good assumption, but it might not be exact enough; the estimated size of the PSF might be off; there is noise in the system that throws off trivial deconvolution methods. Take a look at iterative solvers, and add a non-negativity constraint. There are lots of things to try, but it's hard to give advice without knowing what you've tried. – Cris Luengo Apr 27 '18 at 1:56
• Do you always have a single blob like this? Or multiple ones but nicely separated? If so, try fitting a Gaussian to the data, instead of deconvolving. – Cris Luengo Apr 27 '18 at 1:57
• Without knowing the experimental set up its hard to understand why the extra photons are where they are, but would not a better /complimentary solution be to look at your experiment and eliminate them at source? – porphyrin May 1 '18 at 8:27
• @porphyrin they're not extra photons, they are a single photon being read by multiple pixels either via some process on the CCD chip whether that is imperfect absorption/scattering or voltage leaking across pixels. Would be hard to eliminate without designing very specialized equipment which could be a multi-year project by itself – Mike Flynn May 1 '18 at 22:57
• Do you mean that as the photon is so energetic that some energy is removed by absorption at a ccd pixel then the remaining energy (as a photon ?) is scattered in some way and detected again but now with lower energy. This would be consistent with your spectrum. – porphyrin May 2 '18 at 6:43