correct TOF start/end ranges and normalize TOF kernel - Githubissues

gschramm / parallelproj

code for parallel TOF and NONTOF projections

MIT License

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correct TOF start/end ranges and normalize TOF kernel #69

Closed gschramm closed 3 months ago

gschramm commented 3 months ago

right now we calculate relevant TOF bins (sino mode) and start and stop positions (listmode) based on "n * sigma_tof"
this is not correct if the tofbin width >> sigma tof
TOF kernel is also not normalized (because it is truncated)

proposed fix

use "effective sigma" when calculating start and stop ranges -> sqrt(sig_tof^2 + (binwidth^2) / 12)
calculate missing part of Gaussian integral due to truncation: truncated_int = erf((num_sig sig_eff + 0.5 binwidth) / (sqrt(2) sig_eff)) or truncated_int = erf((num_sig sig_eff) / (sqrt(2) * sig_eff)) = erf(num_sig/sqrt(2))

proposed new tests

fwd project point in non-tof and tof sinomode + check wether sum over tofbins is non-tof