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The nonconvex optimization method has attracted increasing attention due to its excellent ability of promoting sparsity in signal processing, image restoration, and machine learning. In this paper, we consider a new minimization method L1 -ß Lq ((ß, q)-[0, 1]×[1, 8)\(1, 1)) and its applications in signal recovery and image reconstruction because L1 -ß Lq minimization provides an effective way to solve the q-ratio sparsity minimization model. Our main contributions are to establish a convex hull decomposition for L1 -ß Lq and investigate RIP-based conditions for stable signal recovery and image reconstruction by L1 -ß Lq minimization. For one-dimensional signal recovery, our derived RIP condition extends existing results. For two-dimensional image recovery under L1 -ß Lq minimization of image gradients, we provide the error estimate of the resulting optimal solutions in terms of sparsity and noise level, which is missing in the literature. Numerical results of the limited angle problem in computed tomography imaging and image deblurring are presented to validate the efficiency and superiority of the proposed minimization method among the state-of-art image recovery methods. [ABSTRACT FROM AUTHOR]

Objectives: To assess the correlation of pathological radical prostatectomy (RP) specimen features and prostate‐specific antigen (PSA) characteristics to imaging findings on subsequent 18F‐DCFPyL positron emission tomography/computed tomography (PET/CT) in patients with biochemical failure (BF). Patients and Methods: Retrospective analysis of combined 18F‐DCFPyL PET/CT database of patients from centres in Australia and New Zealand was performed. A total of 205 patients presenting with BF after RP were included in this study. Imaging findings on 18F‐DCFPyL PET/CT were recorded and correlated with the PSA characteristics at BF and pathological features of the original tumour. Results: Of the 205 patients, 120 (58.5%) had evidence of abnormal prostate‐specific membrane antigen (PSMA) expression compatible with recurrent prostate cancer. Increasing PSA velocity (P = 0.01), International Society of Urological Pathology (ISUP) Grade Group (P = 0.02), lymphovascular invasion (P = 0.05) and nodal positivity (P = 0.02) at the time of RP were more likely to demonstrate PSMA positivity. Multivariable logistic regression revealed a higher PSA level prior to PSMA PET/CT (P < 0.01), adjuvant radiotherapy (P = 0.09), Gleason score ≥8 (P < 0.01) and nodal positivity (P = 0.05) were all predictive of PSMA positivity. Conclusion: 18F‐DCFPyL PET/CT positivity, both generally and site specific, correlates with PSA and RP pathological factors. Our results echo cohorts focussing on post‐RP patients, those imaged with 68Ga‐PSMA and those concerning biochemical persistence. Nomograms that include risk factors for 'PSMA‐positive recurrence' in the BF population may increase the catchment of patients with disease confined to the prostate bed or pelvis who have a greater probability of prolonged disease‐free survival. [ABSTRACT FROM AUTHOR]

Purpose: Prostate-specific membrane antigen (PSMA) PET/CT is increasingly used in patients with biochemical recurrence post prostatectomy to detect local recurrence and metastatic disease at low PSA levels. The aim of this study was to assess patterns of disease detection, predictive factors and safety using [18F]DCFPyL PET/CT versus diagnostic CT in patients being considered for salvage radiotherapy with biochemical recurrence post prostatectomy. Methods: We conducted a prospective trial recruiting 100 patients with detectable PSA post prostatectomy (PSA 0.2–2.0 ng/mL) and referred for salvage radiotherapy from August 2018 to July 2020. All patients underwent a PSMA PET/CT using the [18F]DCFPyL tracer and a diagnostic CT. The detection rates of [18F]DCFPyL PET/CT vs diagnostic CT were compared and patterns of disease are reported. Clinical patient and tumour characteristics were analysed for predictive utility. Thirty-day post-scan safety is reported. Results: Of 100 patients recruited, 98 were suitable for analysis with a median PSA of 0.32 ng/mL. [18F]DCFPyL PET/CT was positive 46.4% and equivocal 5.2%, compared to 15.5% positivity for diagnostic CT. Local recurrence was detected on [18F]DCFPyL PET/CT in 28.5%, nodal disease in 27.5% and bony metastases in 6.1% of patients. Both ISUP grade group (p < 0.001) and pre-scan PSA (p = 0.029) were significant predictors of [18F]DCFPyL PET/CT positivity, and logistic regression generated probabilities combining the two showed improved prediction rates. No significant safety events were reported post [18F]DCFPyL administration. Conclusions: [18F]DCFPyL PET/CT increases detection of disease in patients with biochemical recurrence post prostatectomy compared to diagnostic CT. Patients being considered for salvage radiotherapy with a PSA >0.2 ng/mL should be considered for [18F]DCFPyL PET/CT scan. Trial registration: Australian New Zealand Clinical Trials Registry Number: ACTRN12618001530213 (http://www.anzctr.org.au/Trial/Registration/TrialReview.aspx?id=375932&isReview=true) [ABSTRACT FROM AUTHOR]