Phantom and clinical evaluation of Block Sequential Regularized Expectation Maximization (BSREM) reconstruction algorithm in 68Ga-PSMA PET-CT studies

In this study, we aimed to examine the effect of varying β-values in the block sequential regularized expectation maximization (BSREM) algorithm under differing lesion sizes to determine an optimal penalty factor for clinical application. The National Electrical Manufacturers Association phantom and 15 prostate cancer patients were injected with 68Ga-PSMA and scanned using a GE Discovery IQ PET/CT scanner. Images were reconstructed using ordered subset expectation maximization (OSEM) and BSREM with different β-values. Then, the background variability (BV), contrast recovery, signal-to-noise ratio, and lung residual error were measured from the phantom data, and the signal-to-background ratio (SBR) and contrast from the clinical data. The increment of BV using a β-value of 100 was 120.0%, and the decrement of BV using a β-value of 1000 was 40.5% compared to OSEM. As β decreased from 1000 to 100, the SUVmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${SUV}_{max}$$\end{document} increased by 59.0% for a sphere with a diameter of 10 mm and 26.4% for a sphere with a diameter of 37 mm. Conversely, ΔSNR100-1000\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta } {SNR}_{100-1000}$$\end{document} increased by 140.5% and 29.0% in the smallest and largest spheres, respectively. Furthermore, the ΔLEOSEM-100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${LE}_{OSEM-100}$$\end{document} and ΔLEOSEM-1000\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${LE}_{OSEM-1000}$$\end{document} were − 41.1% and − 36.7%, respectively. In the clinical study, OSEM exhibited the lowest SBR and contrast. When the β-value was reduced from 500 to 100, the SBR and contrast increased by 69.7% and 71.8% in small and 35.6% and 33.0%, respectively, in large lesions. Moreover, the optimal β-value decreased as lesion size decreased. In conclusion, a β-value of 400 is optimal for small lesion reconstruction, while β-values of 600 and 500 are optimal for large lesions in phantom and clinical studies, respectively.


Introduction
Today, PET-CT today is one of the standard imaging options for oncology diagnosis and for assessing treatment response [1]. In PET imaging, the choice of image reconstruction algorithm significantly affects the accuracy and reproducibility of quantitative measurements [2]. Compared to previously used analytic techniques, iterative reconstruction techniques such as ordered subset expectation maximization (OSEM) improve overall image quality and signal-to-noise ratio (SNR). However, OSEM reconstruction has a significant limitation: image noise is proportional to the number of iterations. Therefore, as the number of iterations increases, image noise intensifies, limiting the ability to detect small lesions [3]. An earlier terminating iteration (typically 2 or 4) and post-filtering help reduce image noise; however, incomplete convergence and quantification inaccuracy result from lower iterations, including underestimating smaller lesion SUVs [4].
With the continued development of iterative reconstruction methods, the block sequential regularized expectation maximization (BSREM) algorithm was developed [5]. The BSREM algorithm employs modeling of the point spread function (PSF) and a penalty term that enables high iterations without degrading image quality [6]. The user can monitor the trade-off between spatial resolution and image noise by adjusting the global smoothing parameter. Therefore, β acts as a penalization factor that suppresses excessive image noise at high iteration numbers, where full convergence of each voxel can improve the accuracy of quantitative measurements such as precise SUVs in smaller lesions.
Nuclear medicine employs a variety of radiopharmaceuticals for specific diseases based on their properties. The parameter β depends on the positron range, as the positron range influences image noise and quality [7]. Therefore, extensive studies are required for each radiopharmaceutical to determine the image quality and quantification performance of the BSREM reconstruction algorithm.
The efficacy of BSREM on 18 F-FDG PET imaging, the most commonly used radiopharmaceutical for cancer diagnosis, has been extensively investigated in prior researchs. For example, Liberini et al. investigated the BSREM using a β-value of 450 in 18 F-FDG PET-CT scans of patients with in-transit metastases of malignant melanoma. In comparison to OSEM, BSREM demonstrated greater lesion detectability, higher SUV max , and a better target-to-background ratio (TBR) (39.0%, 76.5%, and 77.0%, respectively) [8].
Caribe et al. also performed phantom and clinical scans to evaluate BSREM in 18 F-FDG PET-CT examinations. Similar to other studies, they observed that BSREM led to a higher contrast recovery (CR) and contrast-to-noise ratio (CNR) while simultaneously reducing noise [9]. In our study, we evaluated the performance of BSREM in PET-CT imaging of 68Ga-PSMA. The 68Ga has a distinct distribution pattern compared to other tracers, and its use in nuclear medicine imaging for prostate cancer diagnosis represents a significant recent advancement [10]. Certain subcentimetersized pelvic lymph nodes are infiltrated by the tumor, and an underestimation of SUV max results in false negative reports. Numerous previous studies have investigated the performance of BSREM in improvement of 68Ga-PSMA imaging on PET scanners with lutetium yttrium oxyorthosilicate (LYSO) crystals utilizing time-of-flight (TOF) technology. To our knowledge, however, the lesion size performance of BSREM on images acquired with bismuth germanium oxide (BGO) crystals has not been evaluated.
For example, Jonmarker et al. studied 61 prostate cancer patients scanned with LYSO crystals on a GE Discovery MI scanner with LYSO crystals. Images were reconstructed with OSEM and BSREM (both algorithms consist of TOF and PSF techniques). A β-value of 700 was utilized to reconstruct the images with BSREM. The researchers concluded that BSREM detected fewer ambiguous lesions than OSEM (175 vs. 187 lesions, respectively) [11].
Lindström et al. analyzed data of patients with recurrent prostate cancer and also scanned them with a GE Discovery MI and reconstructed images with TOF OSEM vs. TOF BSREM with β-values ranging from 100 to 1300 at 100point intervals. The OSEM method produced images with 15.0% noise. Compared to OSEM, noise was significantly lower in BSREM images with β-values greater than 300 (36.0% in BSREM 100 and 8.0% in BSREM 1300 ), and the SNR increased by 25.0% in BSREM 200 and 66.0% in BSREM 1300 [12]. Our research involved the injection of 68Ga-PSMA and the use of a non-TOF PET-CT scanner with BGO crystals to acquire data. In the context of gallium radiopharmaceutical studies, the lesion-to-background ratio is a critical parameter to consider. In 68Ga-PSMA imaging typically high lesionto-background ratios was used, thereby creating a strong contrast. However, it is essential to evaluate tumors with low radiopharmaceutical uptake, resulting in lower contrast. To address this, we analyzed the low LBR 4:1 in a phantom study, enabling us to effectively assess tumors with reduced uptake. In addition, we investigated the effect of lesion size on the BSREM algorithm's output.
Therefore, this study aimed to investigate the effect of various noise penalization factor strengths on 68Ga-PSMA imaging with a BGO scanner for clinical use in prostate cancer patients. We analyzed phantom and clinical data under varying lesion sizes to determine the optimal penalty factor by considering the quantitative and qualitative image evaluation parameters.

PET-CT system and reconstruction algorithm
All data were collected utilizing a digital GE Discovery IQ PET-CT scanner (GE Healthcare, Waukesha, WI, USA) with a 5-ring setup installed at the Nuclear Medicine Department of The University Hospital, Tehran University of Medical Sciences. BGO detectors were utilized through a non-TOF scanner. Each ring with a diameter of 74 cm was comprised of 36 detector blocks that offered a trans-axial and axial field of view (FOV) of 70 cm and 26 cm, respectively. The scanner comprised 79 image planes, a plane spacing of 3.27 mm, and a 10-24% bed overlap. In addition, it possesses 720 photomultipliers with a coincidence window of 9.5 ns. A 16-slice CT scanner with a full rotation degree accompanied the PET system for attenuation and scatter correction [13]. The acquired raw data were reconstructed using OSEM methodology with four iterations and 12 subsets and postprocessed with a 4.8 mm Gaussian filter, per the manufacturer's recommendation for standard clinical image reconstruction. Similarly, per manufacturer specifications, BSREM with 25 iterations and four subsets was utilized without post-filtering. We utilized β-values ranging from 100 to 500 for clinical data and 100 to 1000 for phantom data, with a 100-point interval between each value.

Phantom study
In this study, a set of National Electrical Manufacturers Association (NEMA) image-quality (IQ) phantoms were evaluated (GE HealthCare, Germany) [14]. The NEMA phantom with a volume of 9780 mL comprised six fillable spheres with inner diameters of 10 mm, 13 mm, 17 mm, 22 mm, 28 mm, and 37 mm, as well as a lung insert with a diameter of 44.5 mm [15,16]. The background volume of the phantom was filled with 5 kBq/ml of the radiopharmaceutical 68Ga-PSMA. The spheres were then filled with a four-to-one lesion-to-background ratio (LBR = 4:1) to simulate the uptake of clinical tumors. Furthermore, the lung insert was filled with water and Styrofoam to simulate human lung tissue better. The phantom was positioned in the center of the FOV and scanned according to NEMA procedures [14]. All phantom scans with varying β-values were acquired with a 2 min acquisition time per each bed position.
Using the NEMA analysis tool, the background variability (BV) and quantitative features in spheres, including the SUV max , CR, SNR, recovery coefficient (RC), and lung residual error (LE) in the lung insert, were measured [17]. To compute the BV, 60 regions of interest (ROIs) with a 5 mm diameter were drawn on the background of five central slices of spheres (each slice consisting of 12 ROIs). BV was calculated as standard deviation of those 60 ROIs divided by the mean background ROI counts. To include spheres, the volume of interest (VOI) was placed in the central slice of spheres with individual diameters proportional to sphere diameters. The CR of each sphere size was computed through Eq. (1) [18]: where C H and C B denote the mean counts of each VOI and the mean counts of 60 ROIs in the background, respectively, and a H a B represents the activity ratio in hot lesions to the background equal to the LBR. The SNR measurement was defined as the mean voxel count of each VOI divided by the standard deviation of the activity of the background ROIs. In addition, the RC was defined as the ratio of detected activity to the actual activity of individual inserts. Moreover, the LE was computed by dividing the mean lung insert activity by the mean background activity.

Clinical study
This study analyzed clinical data from three-dimensional whole-body 68Ga-PSMA PET-CT scans of 15 patients. Patients with prostate cancer and metastases of varying sizes throughout the body who had been scanned between September 2021, and February 2022 were retrospectively selected. The patient's weights ranged from 55 to 98 kg, and their average height and age were 168 ± 23 cm and 68 ± 9.5 years, respectively. Patients were intravenously injected with 68Ga-PSMA at the clinically recommended activity of 1.85 MBq per kilogram of body weight (0.05 mCi/kg), and data acquisition began almost 60 min after injection. All clinical scans were acquired using a 2 min acquisition duration for each bed position, and patients were scanned from the vertex to the thigh.
For image evaluation, we surrounded lesions with VOI to encompass them. We observed a total of 50 lesions in 15 patients, which were separated into two size groups: lesions with diameters ≤ 15 mm (n = 27) and lesions with diameters > 15 mm (n = 20). We analyzed clinical data based on image noise, SUV max , SNR, signal to background ratio (SBR), and contrast. In addition, nine ROIs with a 3 mm diameter were positioned in a homogeneous area of the liver to calculate image noise (each slice consisting of 3 ROIs and avoiding vessels and portal vein) in the largest slice of the right lobe of the liver and a slice before and after. The clinical data noise was defined as the ratio of SD to the mean activity of nine ROIs in the liver (similar to the equation of BV in the phantom data). The SNR of each lesion was determined by dividing the individual lesion's SUV max by noise. As a liver reference, a single ROI with a diameter of 10 mm was identified in a homogeneous area of the liver. SBR was defined as follows [18]: The contrast was calculated by dividing the maximum activity of the lesion by the mean activity of the nine ROIs in the liver.

Statistical analysis
At this stage, a sample t-test with a p value < 0.05 was employed to evaluate the results of BSREM reconstructions with OSEM or the differences between the results of two β-values. In addition, we assessed the significance of the differences between multiple reconstructions using analysis of variance (ANOVA). All statistical analyses in this study were conducted using SPSS software (v. 23, IBM Corporation, Armonk, NY, USA).
This research determined the optimal β-value for various lesion sizes based on all image evaluation parameters. First, β-values were selected to have an appropriate BV level and to achieve an RC value as close to 1 as possible, indicating that SUV changes were appropriate (increasing or decreasing). Then, among the β-values that satisfied these conditions, the β-value with the highest SNR or CR and SUV max according to lesion size was deemed the optimal value. Moreover, given that OSEM is the most popular reconstruction method in clinical applications and that clinicians use it to diagnose and evaluate patient images, the results of BSREM and OSEM reconstruction were contrasted.
To compare the effect of different β-values, each evaluation parameter's relative increase or decrease at equal β-value intervals was compared. To this end, the relative difference between the old reconstruction (a) and the new reconstruction (b) was calculated as follows: Figure 1 depicts the results of SUV max in different lesion sizes and BV. The BV decreased as the β-value increased. No consistent decrease in BV was observed as β-values increased; however, as β increased from 100 to 200, BV

NEMA phantom
decreased by 29.4%, and once it increased from 900 to 1000, BV decreased by 3.4%. The BV variation became more uniform above BSREM 700 ; as β increased from 700 to 800, then from 800 to 900, and finally from 900 to 1000, the BV decreased by 5.5%, 4.6%, and 3.9%, respectively. The increase in BV for a β-value of 100 was 120.0%, while the decreases in BV for β-values of 500 and 1000 were 3.9% and 40.5%, respectively, compared to OSEM. All plots of SUV max for various lesion sizes in BSREM reconstruction exhibited a similar inversed trend, demonstrating an increase in SUV max with a decreasing β-value. As β decreased from 1000 to 100, the SUV max increased by 59.0% for the smallest sphere (10 mm), 27.1% for the sphere with a diameter of 22 mm, and 26.4% for the largest sphere (37 mm). However, there was no significant difference in SUV max behavior at higher β-values. Using BSREM 800 , BSREM 900 , and BSREM 1000 , the SUV max was 4.8, 4.7, and 4.6 for the smallest sphere, 10.9, 10.5, and 10.1 for the 22 mm sphere, and 15.8, 15.7, and 15.7 for the 37 mm sphere. Figure 2 depicts the central slice of BSREM 100−1000 and OSEM phantom data. The figure shows insufficient noise suppression in BSREM with a lower β-value and a higher BV, which is undesirable for clinical applications because it degrades image quality. On the other hand, the potential of high values for background smoothing and contrast enhancement resulted in improved lesion detection and overall image quality. Table 1 summarizes the relative differences in CR for various sphere diameters. All sphere sizes exhibited a negative correlation between the β-value and CR. Consequently, as the β-value increased, the CR decreased, such   that BSREM with a β-value of 100 had the highest CR. The relative difference of CR by increasing the β-value from 100 to 1000 (ΔCR 100−1000 ) was − 61.7%, − 23.2%, and − 11.2% in spheres with diameters of 10 mm, 22 mm, and 37 mm, respectively. In the smallest sphere (10 mm), β-values equal to or greater than 500 resulted in a lower CR than OSEM, whereas in the largest sphere (37 mm), regardless of the β-value, the CR of BSREM was greater than the CR of OSEM. The Δ CR OSEM−100 , Δ CR OSEM−500 , Δ CR OSEM−1000 were 80.3%, − 1.9%, and − 3.2% in the smallest sphere (10 mm), 22.7%, 7.4%, and 0.2% in the sphere with a 22 mm diameter, and 12.9%, 5.2%, and 5.9% in the largest sphere (37 mm), respectively. Figure 3 depicts the SNR and RC of six hot spheres (10 mm, 13 mm, 17 mm, 22 mm, 28 mm, and 37 mm in diameter) that were reconstructed using various algorithms. In BSREM images, a decrease in β-value led to a rise in RC. The RC of small lesions (10 mm, 13 mm, and 17 mm) caused by BSREM with all β-values was less than one, such that in lesions with a diameter of 10 and 13 mm, the RC obtained from β-values of 100 was equal to 0.7 and 0.8, respectively. In contrast, the obtained RC from lower β-values was greater than 1 in large lesions (β-values of 100, 200, and 300 in lesion sizes of 22 mm, 28 mm, and 37 mm and β-values of 400 and 500 in lesion sizes of 37 mm). In addition, excessive smoothing at higher β-values resulted in insufficient RC. The SNR results demonstrated that an increase in β-value led to an increase in SNR, whereas the lower β-values (100 and 200) exhibited insufficient SNR due to their excessive noise levels. The SNR of BSREM 100 was 12.0, 52.8, and 83.8 for spheres with a diameter of 10 mm, 22 mm, and 37 mm, respectively, while the SNR of OSEM reconstruction was 22.2, 70.8, and 100.2. Sphere size determined the relative differences in SNR. As the β-value rose from 100 to 1000, the SNR increased by 140.5%, 37.6%, and 29.0% in the smallest, medium, and largest spheres, respectively. BSREM 500 and above produced a higher SNR than OSEM, except for the largest sphere. Only β-values 100 and 200 in the largest sphere had a lower SNR than OSEM. The Δ SNR OSEM−700 was 19.9% and 6.7% in the smallest and largest spheres, respectively.
The calculated LE from BSREM reconstruction revealed that different β-values led to nearly identical LE, so the maximum relative difference of LE between different β-values was 12.9%. Using all examined β-values, BSREM produced a lower LE than OSEM. The Δ LE OSEM−100 and Δ LE OSEM−1000 values were − 41.1% and − 36.7%, respectively.

Clinical study
A total of 15 patients with 47 lesions (27 small lesions and 20 large lesions) who were referred for prostate cancer staging with 68Ga-PSMA PET/CT were included in the study. Figure 4 shows coronal slices of a patient reconstructed with BSREM using various β-values and OSEM. The arrows indicate focal 68Ga-PSMA uptake, and the noise level of each reconstruction is indicated. Figure 4 depicts a positive relationship between the β-value and image quality. Lower β-values (100-200) suffer from high noise levels while Fig. 3 The RC (a) and SNR (b) measurements for 10 mm, 13 mm, 17 mm, 22 mm, 28 mm, and 37 mm hot spheres in the NEMA image quality phantom study with various reconstructions: BSREM employ-ing β-values between 100 and 1000 and the OSEM algorithm. The dashed line represented the optimal RC level, which is equal to 1 improving lesion uptake. Higher β-values (400-500) provide adequate lesion conspicuity and image homogeneity, allowing small lesions to be detected as well as large lesions. Figure 5 depicts the outcomes of clinical evaluations, including SUV max , SNR, SBR, contrast, and noise for two lesion sizes and multiple reconstruction datasets. BSREM with β-values less than 400 produced more noise than OSEM. Furthermore, changes in reconstruction from OSEM to β-values of 100, 200, and 300 resulted in relative noise differences of 123.2%, 51.0%, and 15.9%, respectively. BSREM using a β-value of 500 as the lowest noise reconstruction, exhibited 12.4% less noise than OSEM. Moreover, as β increased, SUV max decreased for all lesions.
Reducing the β-value from 500 to 100 resulted in a 73.2% and 37.4% increase in SUV max for small and large lesions, respectively. The mean SUV max values for small and large lesion size groups were 12.1 ± 2.4 and 25.0 ± 8.1 for BSREM 500 and 7.9 ± 3.2 and 21.8 ± 8.2 for OSEM, respectively. SBR and contrast increased as the β-value decreased, while an increase in β-value increased SNR. Regardless   Fig. 5 a The mean SUV max , b SNR, c SBR, d contrast, and e noise in the homogeneous area of the liver for two lesion size groups (small and large) in a clinical study with 68Ga-PSMA. OSEM and BSREM were employed for reconstruction, with β-values ranging from 100 to 500 at 100-step intervals. Dashed lines connect the median val-ues. Note that the asterisks in the diagrams represent the p-values obtained from the paired t test between the two reconstruction methods, with * representing p < 0.01, ** representing p < 0.001, *** representing p < 0.0001, and **** representing p < 0.00001 of lesion size and β-value, the lowest SBR and contrast were correlated with the OSEM. The Δ SBR OSEM−100 and Δ SBR OSEM−500 were 159.9% and 53.1% for small lesions, and 54.3 and 13.8 for large lesions, respectively.
Identical results were observed in contrast so that Δ contrast OSEM−100 and Δ contrast OSEM−500 were 169.3% and 56.7% for small lesions and 55.6 and 16.3 for large lesions, respectively. In the BSREM algorithm, lesion size had a greater effect on the relative difference of SBR and contrast; as lesion size decreased, the relative difference of SBR and contrast increased. When β-values decreased from 500 to 100, the SBR and contrast increased by 69.7% and 71.8% in small lesions and by 35.6% and 33.0% in large lesions, respectively. The lowest SNR was attributed to OSEM in more than 78.0% of small lesions, while it was attributed to BSREM 100 in all large lesions. In addition, the average Δ SNR OSEM−100 was 17.2% in small lesions and − 33.6% in large lesions. In the latter case, β-values greater than 200 resulted in a higher SNR than OSEM. The average increase in SNR for large lesions with β-values of 400 and 500 was 32.4% and 53.2%, while the increase for small lesions was 82.0% and 94.6%, respectively, relative to OSEM.

Discussion
The BSREM reconstruction algorithm, which employs a penalization factor, has been studied extensively on TOF LYSO PET/CT scanners utilizing 18-F-FDG but less so on non-TOF BGO PET/CT systems, especially for 68Ga-PSMA with a focus on small-sized lesions. Consequently, the current study evaluated the optimal regularization parameter for the BSREM algorithm and compared the results to those of the conventional OSEM algorithm. To this end, comprehensive quantitative evaluations were performed using a NEMA phantom with LBR 4:1 and prostate cancer patients receiving 68Ga-PSMA injections for PET/CT imaging.
The potential of applying BSREM reconstruction in suppressing excessive noise enables the use of high iterations (approximately 25 for BSREM versus four for conventional OSEM) in a feasible manner. In BSREM, the excess noise level is dampened by a penalization factor [11]. The phantom evaluations in the current study revealed that decreasing the β-value increased SUV max at the expense of an increase in BV, which is undesirable in oncological studies (Fig. 1). Comparing BSREM and OSEM in terms of BV indicated that BSREM with β-values over 400 resulted in a lower BV than OSEM. In the most extreme case, disregarding SUV max and employing BSREM 1000 produced images with a BV of 4.2, which is significantly lower than OSEM's BV of 5.9 (Fig. 1), further proving this point.
The results of the clinical part of this study corroborated our phantom findings. As previously mentioned, multiple studies have highlighted the effect of β-values on image noise. Using 18 F-FDG injection, Liberini et al. analyzed different β-values (100-700, in increments of 100) to detect brain metastases in 40 patients with lung cancer. They reported that the BSREM 100 setting is less accurate due to the degradation of image quality caused by noise [19]. In both phantom and clinical data, the noise of BSREM 400 reconstruction was comparable to that of OSEM.
In the phantom study, BV 400 and BV OSEM were 6.2% and 6.0%, respectively, whereas in the clinical study, they were 8.2% and 8.4%, respectively. This result is also evidenced in another study by Lindström et al., where they assessed a NEMA phantom that was filled with 68Ga-DOTATOC with LBR 4.3:1 and 4:1. BSREM with β-values of 133, 267, 400, and 533 and OSEM were used for image reconstruction. For image reconstruction, BSREM with β-values of 133, 267, 400, and 533 and OSEM were used. According to their findings, BSREM 400 can produce noise levels comparable to OSEM [7]. At this equivalent noise level, the evaluation parameters of BSREM 400 outperformed OSEM for all sphere sizes. In the phantom study, the SUV max , CR, and SNR of BSREM 400 spheres were greater or comparable to those of OSEM.
The relative difference in SUV max , CR and SNR for the largest sphere (37 mm) between OSEM and BSREM 400 was 1.1%, 7.3%, and 6.0%, respectively (Figs. 1 and 3, and Table 1). Similar results were observed in our clinical investigation. For the patient data at comparable noise levels, the average SUV max , SNR, SBR, and contrast of lesions were 38.0%, 49.3%, 36.5%, and 40.9% higher than OSEM (Fig. 5). Caribé et al. demonstrated that BSREM has a superior tumor SUV mean , SUV max , and contrast compared to OSEM at equivalent noise levels [9].
The expanded number of iterations in BSREM allows each image voxel to reach full convergence, avoiding problems of insufficient iteration arising from the partial convergence of single voxels. Namely, the full convergence translates into improved quantification accuracy of focal uptakes, which can be pivotal in clinical diagnosis. For almost all lesion sizes in our phantom study, we reported higher SUV max in BSREM with β-values less than 700 and lower SUV max with β-values more than 700 when compared to OSEM.
In the present clinical study, all BSREM reconstructions resulted in a greater SUV max than OSEM reconstructions for both small and large lesion size groups (Fig. 5). The relative difference of SUV max between OSEM and BSREM 100 for small and large lesion size groups was 164.0% and 57.6%, respectively (Fig. 5). Voert et al. examined 25 patients who underwent 68Ga-PSMA PET/MR; the TOF images were reconstructed using OSEM and BSREM with β-values ranging from 150 to 1200. In lesions with low activity, they 1 3 found that BSREM with β-values greater than 600 led to a lower SUV max than OSEM [20].
The results of Lohaus et al. in the detection of pulmonary nodules with 18-F-FDG PET/CT also demonstrated that the SUV max of nodules was significantly higher in BSREM than in OSEM (the mean SUV max of nodules in BSREM 450 and OSEM was 5.4 and 3.6, respectively) [21].
When BSREM was utilized with high β-values, the quantitative parameters of our PET images appeared to stabilize with minimal variation. For lower βs at or below 200, however, a significant increase was observed in SUV max , BV and CR when reducing the β-value (the ΔSUV max200−100 and the ΔCR 200−100 for a lesion size of 10 mm was 17.8% and 24.4%, respectively), whereas a negligible gain in quantitative parameters was observed when reducing the β-value from 1000 to 900 ( Fig. 1; Table 1, The ΔSUV max1000−900 and the ΔCR 1000−900 for lesion size of 10 mm was 1.3% and 5.9%, respectively). Trägårdh et al. evaluated BSREM reconstructions on silicon photomultiplier PET-CT scanners in 25 patients referred for 18 F-FDG imaging. For image reconstruction, they used BSREM with β-values ranging from 100 to 700 and found that the lesion SUV max varied significantly in BSREM reconstructions with lower β values [22].
A closer examination of the various lesion sizes revealed that BSREM had a greater effect on smaller lesions in the current study. This is essential for the detection of abnormal pelvic lymphadenopathies of small size. In the phantom study, the relative difference of lesion uptake and CR from β-values of 1000 to 100 increased by 59.0-161.0% for the smallest sphere (10 mm) and by 26.4-12.6% for the largest sphere (37 mm) ( Table 1). In addition, the ΔSNR 1000−100 decreased by 58.4% for the smallest sphere and 20.5% for the largest sphere. The present clinical study involving various lesion size groups confirmed these results.
According to Fig. 3, lesions with smaller diameters were more affected by the fluctuating β-values. The percentage difference of SUV max , SBR and contrast in BSREM with β-values between 500 and 100 was 73.2%, 69.7%, and 71.8% for small lesions and 37.4%, 35.6%, and 33.0% for large lesions (Fig. 5). Thus, the findings of Lindström et al.'s research were consistent with the current study. Comparing BSREM and OSEM, they observed that the relative difference of SUV max decreased as lesion volume increased. In addition, they found no significant difference in SUV max for lesions with a volume greater than 3 mL as lesion size increased [23]. Lesions smaller than 2 cm were significantly different in terms of SUV mean , SUV max , and SBR in BSREM with a β-value of 570 compared to OSEM, whereas lesions larger than or equal to 2 cm were unaffected by these reconstructions [24].
The effect of a low penalizing parameter (β-value ≤ 300) on increasing noise can result in false positive enhancement of lesion uptake estimation or false positive detection of noise instead of lesions. On the other hand, excessive smoothing in BSREM with higher β-values (≥ 700) can result in lower SUV max , RC values less than 1, and thus false-negative interpretations. Consequently, based on our phantom results, a BSREM technique employing β-values in the range of 400 to 600 is recommended for image evaluations, where accurate SUV and greater contrast recovery were obtained while maintaining image quality.
The clinical evaluations in the current study supported the above conclusion, where for optimal reconstruction in clinical examinations with 68Ga-PSMA, BSREM with β-values between 400 and 500 appears to be the recommended method. Thus, from both a phantom and clinical standpoint, BSREM with a β-value of 400 could be deemed suitable for small lesions with low activity, as it increases lesion uptake and contrast while maintaining appropriate image noise, thereby increasing the detectability of small lesions. Due to the high activity of large lesions, increasing their absorption by applying low values is not required. In phantom and clinical studies, therefore, values of 500 and 600 may be optimal for reconstructing large lesions, thereby enhancing SNR and image conspicuity. This result is comparable to Voert et al., who reported an optimal value for β-values between 400 and 550 determined by BSREM reconstruction [20].
The selection of a non-TOF study and the relevant BGO vs. LSO-based system employed in the present investigation also warrants a brief mention. The coincidence window that can be used with BGO systems must be relatively larger and used with lower activity; as a result, it cannot be commonly used in TOF reconstruction mode. Thus, even though LSO/LYSO detectors continue to be the detector of choice in commercial TOF systems due to their higher light yield and faster decay times, BGO scanners retain certain advantages and require reconstruction improvement procedures, such as a higher effective atomic number (hence improved detection efficiency at 511 keV), lower intrinsic radiation, and lower production costs [25].
Patients in the current study were limited to a smaller number than desired. In addition, the analysis was limited by the small range of lesion sizes; as a result, larger observations are required to confirm the findings of the present study.
It can be hypothesized that a larger and more diverse cohort population analysis could have yielded better results, e.g., concerning SUV lesion volume dependences. Thus, assessing the effect of Body Mass Index (BMI) on β-factor optimization in larger patients remained beyond the scope of this study. In addition, previous studies with 18 F-FDG, such as those conducted by Jonmarker et al., indicate that BSREM optimization may depend on the injected dose. Due to the failure to evaluate various scan durations and injected doses, the performance of BSREM under the conditions above is unknown. Moreover, the BSREM algorithm is based on a convex relative difference penalty term modulated by two parameters: the parameter β (which we discussed in this study) and a second parameter γ that controls the level of edge preservation [26]. The latter parameter was not investigated. In PET/CT imaging with 68Ga-PSMA injection, the high absorption in the bladder and kidneys relative to the surrounding soft tissue can result in halo artifacts [27]. Thus, the effect of this artifact was excluded from the current investigation. Moreover, this BSREM analysis necessitates additional research to determine and clarify the diagnostic efficacy of 68Ga-PSMA PET imaging.

Conclusion
In conclusion, BSREM improves quantitative accuracies such as SUV max , CR, and SNR by a fully convergent image voxel by applying a penalization factor to control image noise. In the present clinical study, achieving higher SNR, SBR, and contrast at similar liver homogeneity to OSEM was possible. In small lesions, differences in quantitative parameters between β-values were more pronounced than in large lesions, and the optimal β-value for subcentimetric lesions is suggested to be 400. Moreover, lesion size significantly impacted BSREM optimization; the optimum β-value also decreased as lesion size reduced.

Conflict of interest
The authors declare that they have no conflict of interest.
Informed consent No informed consent was required due to the anonymized patient's data were used.