Emission tomography reconstruction algorithms (sinogram data)

A tour of reconstruction algorithms for the (regularised) Poisson problem, all built on the data-fidelity and prior objects in parallelproj.functions. Start with the MLEM / OSEM / SVRG convergence comparison, then explore the stochastic-gradient variants, PDHG / SPDHG with edge-preserving priors, filtered back projection, De Pierro’s MAP-EM, the effect of TOF on variance, and out-of-core (memory-mapped) OSEM.

Convergence comparison: MLEM vs OSEM vs SVRG

Convergence comparison: MLEM vs OSEM vs SVRG

Convergence comparison: SGD vs SVRG with logcosh regularization

Convergence comparison: SGD vs SVRG with logcosh regularization

PDHG and SPDHG for PET reconstruction with a directional TV prior

PDHG and SPDHG for PET reconstruction with a directional TV prior

2D non-TOF filtered back projection (FBP) of Poisson data

2D non-TOF filtered back projection (FBP) of Poisson data

DePierro’s algorithm to optimize the Poisson logL with quadratic intensity prior

DePierro's algorithm to optimize the Poisson logL with quadratic intensity prior

TOF vs non-TOF: variance reduction in a uniform cylinder

TOF vs non-TOF: variance reduction in a uniform cylinder

RAM-efficient OSEM with disk-backed TOF sinograms

RAM-efficient OSEM with disk-backed TOF sinograms

Exact vs. “safe epsilon” mode of the negative Poisson log-likelihood

Exact vs. "safe epsilon" mode of the negative Poisson log-likelihood