  Single-photon emission computed tomography (SPECT) provides a mechanism to
estimate regional isotope uptake in lesions and at-risk organs after
administration of {\alpha}-particle-emitting radiopharmaceutical therapies
({\alpha}-RPTs). However, this estimation task is challenging due to the
complex emission spectra, the very low number of detected counts, the impact of
stray-radiation-related noise at these low counts, and the multiple
image-degrading processes in SPECT. The conventional reconstruction-based
quantification methods are observed to be erroneous for {\alpha}-RPT SPECT. To
address these challenges, we developed a low-count quantitative SPECT
(LC-QSPECT) method that directly estimates the regional activity uptake from
the projection data, compensates for stray-radiation-related noise, and for the
radioisotope and SPECT physics. The method was validated in the context of
three-dimensional SPECT with 223 Ra. Validation was performed using both
realistic simulation studies, including a virtual clinical trial, and synthetic
and anthropomorphic physical-phantom studies. Across all studies, the LC-QSPECT
method yielded reliable regional-uptake estimates and outperformed the
conventional ordered subset expectation maximization (OSEM)-based
reconstruction and geometric transfer matrix (GTM)-based post-reconstruction
partial-volume compensation methods. Further, the method yielded reliable
uptake across different lesion sizes, contrasts, and different levels of
intra-lesion heterogeneity. Additionally, the variance of the estimated uptake
approached the Cram\'e-Rao bound-defined theoretical limit.
