Hamiltonian dynamics for stochastic reconstruction in emission tomography
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.