Inclusion Criteria  Signed informed consent must be obtained prior to participation in the study Biopsy proven prostate adenocarcinoma. Biochemical recurrence following initial definitive therapy (with either RP or curative intent radiation therapy) as defined:  by AUA criteria (Cookson et al 2007) for patients who have undergone RP: Initial serum PSA of ≥0.2 ng/ml measured at least 6 weeks after RP with a second confirmatory persistent PSA level of >0.2 ng/ml, or by ASTRO-Phoenix criteria (Roach et al 2006) for patients who have undergone curative-intent radiation therapy (RT): Rise of serum PSA measurement of 2 or more ng/mL above the nadir PSA observed post RT.  ECOG performance status 0-2 Participants must be adults ≥ 18 years of age  Exclusion Criteria:  Inability to complete the needed investigational and standard-of-care imaging examinations due to any reason (severe claustrophobia, inability to lie still for the entire imaging time, etc.) Any additional medical condition, serious intercurrent illness, concomitant cancer or other extenuating circumstance that, in the opinion of the Investigator, would indicate a significant risk to safety or impair study participation, including, but not limited to, current severe urinary incontinence, hydronephrosis, severe voiding dysfunction, need of indwelling/condom catheters, New York Heart Association class III or IV congestive heart failure, history of congenital prolonged QT syndrome, uncontrolled infection, active hepatitis B or C, and COVID-19 Prior major surgery undergone less than 12 weeks prior to screening (with the exception of any surgery related to prostatic cancer) Known allergy, hypersensitivity, or intolerance to [18F]CTT1057, [68Ga]Ga-PSMA-11, or to CT contrast Prior and current use of PSMA targeted therapies Prior ADT (first or second generation), including LHRH analogues (agonists or antagonists), within 9 months before screening Any 5-alpha reductase inhibitors within 30 days before screening Use of other investigational drugs within 30 days before screening Castration-resistant patients Patient with small cell or neuroendocrine PCa in more than 50% of biopsy tissue Prior salvage surgery or salvage radiation therapy