Hamiltonian dynamics for stochastic reconstruction in emission tomography - Theodoros Leontiou; Anna Frixou; Elena Ttofi; Charalambos Chrysostomou; Yiannis Parpottas; Konstantinos Michael; Savvas Frangos; Efstathios Stiliaris; Costas N Papanicolas (Physics in Medicine & Biology, 2026)
Abstract Objective. To develop a practical stochastic reconstruction framework for emission
tomography that generates ensembles of data-compatible images and enables
uncertainty quantification and assessment of forward-model adequacy. Approach.
The framework combines stochastic-gradient descent initialization with
Hamiltonian Monte Carlo (HMC) sampling directly in high-dimensional voxel
space. Beyond point reconstruction, we introduce a spatially resolved
operator-weighted diagnostic, the sampled data-visible variance, which
quantifies how image fluctuations propagate through the imaging operator
and thereby probes the local conditioning of the inverse problem under
realistic acquisition physics. The methodology is evaluated using
controlled software phantoms, experimental anthropomorphic phantom
measurements, and a clinical DATSCAN SPECT acquisition. Main results.
Under ideal conditions, the HMC ensemble mean provides point-estimate
accuracy comparable to deterministic reconstruction methods, while the
sampled ensemble provides additional physically interpretable information.
The ensemble analysis helps distinguish uncertainty associated with the
intrinsic ill-posedness of the inverse problem from variability linked to
forward-model inadequacy. The clinical example demonstrates applicability
under realistic acquisition statistics rather than diagnostic performance.
Significance. The proposed stochastic reconstruction framework provides a practical
ensemble-based approach for emission tomography that extends conventional
point reconstruction with model-conditioned uncertainty estimates and
spatially resolved diagnostics of forward-model adequacy.