Single-photon emission computed tomography (SPECT) is widely used for imaging radiotracer distribution in vivo. In several SPECT applications, patients are administered a significant amount of radiation dose and thus, it is desirable to reduce the dose level. However, reducing the dose level results in low-count data, which leads to a decrease in image quality in terms of the performance on clinical tasks. Moreover, SPECT in applications such as alpha-particle radiopharmaceutical therapies (α-RPT) is inherently count limited. Methods to improve the image quality in low-dose/low-count settings for SPECT images are thus much needed. The goal of this dissertation is to develop computational methods to fulfill this need and to objectively evaluate such methods on clinical estimation and detection tasks. To compensate for image-degrading processes of attenuation and scatter of photons in SPECT, a separate CT scan is often performed. However, CT-based compensation method leads to higher dose and possibility of misalignment between CT and SPECT scans. Thus, investigation towards quantifying the information content present in SPECT emission data for jointly estimating the attenuation and activity map is of significant importance. For this purpose, we developed a Fisher information analysis framework to quantify the information content in list-mode (LM) SPECT data. We demonstrated that LM SPECT emission data contains information for the joint estimation task. In applications such as α-RPT, SPECT provides an opportunity to quantify absorbed dose, but this task is challenged by the low number of detected counts. Thus, developing methods to reconstruct SPECT images that extracts maximal possible information from detected photons are required. Toward this goal, we developed a LM reconstruction method that uses data from multiple energy windows and includes energy attributes of detected photons. The proposed method yielded improved quantification performance compared to a conventional method that uses data from a single energy window and incorporates data in binned-mode format. The next part of this dissertation focuses on developing methods to improve image quality in the context of low-dose/low-count myocardial perfusion imaging (MPI) SPECT. In MPI SPECT, which is a widely used imaging modality, an important clinical task is the detection of perfusion defects. There is an important need for methods to process/acquire MPI SPECT images in low-dose settings. Toward this goal, we first developed a deep learning-based task-specific denoising method, DEMIST. We demonstrated that the DEMIST method significantly outperformed low-dose images and the conventional deep learning-based denoising methods on the task of detecting perfusion defects. A second approach to improve image quality is to optimize the image acquisition protocol in low-dose setting. In such low-dose settings, we observed that current clinical acquisition protocols yield sub-optimal image quality when applied to patients displaying outlier anatomical characteristics, such as those with large body habitus, or female patients with large breasts. To address this issue, we developed a detection-task-specific protocol optimization method based on the anatomical characteristics of each patient. We demonstrated that an optimized protocol for each patient yielded significant improvement compared to the clinical protocol on the task of detecting perfusion defects. Overall, this dissertation demonstrates that development of new computational methods can assist with improving performance on clinical tasks in SPECT in low dose and low-count settings
