Inclusion Criteria:  Pathologically proven prostate cancer Rising prostate-specific antigen (PSA) after definitive therapy with prostatectomy or radiation therapy (external beam or brachytherapy) Karnofsky performance status (KPS) >= 50 (Eastern Cooperative Oncology Group [ECOG]/World Health Organization [WHO] 0, 1, or 2) Ability to understand and willingness to provide informed consent Participants with known metastatic prostate cancer planned to undergo active systemic treatment  Exclusion Criteria:  Unable to lie flat, still, or tolerate a PET or MRI scan Contraindication to optional furosemide administration including prior allergy or adverse reaction to furosemide or sulfa drugs. This exclusion criteria can be removed if furosemide is omitted as part of the PET imaging protocol if a second-generation scatter correction - (defined as either Ga-68 specific prompt gamma correction or multiple scatter model) is available for the used PET device