Dynamic Row-action Maximum Likelihood Algorithm Research Articles

Organ-Specific Positron Emission Tomography Scanners for Breast Imaging: Comparison between the Performances of Prior and Novel Models.

The performances of photomultiplier tube (PMT)-based dedicated breast positron emission tomography (PET) and silicon photomultiplier tube (SiPM)-based time-of-flight (TOF) PET, which is applicable not only to breast imaging but also to head imaging, were compared using a phantom study. A cylindrical phantom containing four spheres (3-10 mm in diameter) filled with 18F-FDG at two signal-to-background ratios (SBRs), 4:1 and 8:1, was scanned. The phantom images, which were reconstructed using three-dimensional list-mode dynamic row-action maximum likelihood algorithm with various β-values and post-smoothing filters, were visually and quantitatively compared. Visual evaluation showed that the 3 mm sphere was more clearly visualized with higher β and smaller post-filters, while the background was noisier; SiPM-based TOF-PET was superior to PMT-based dbPET in sharpness, smoothness, and detectability, although the background was noisier at the SBR of 8:1. Quantitative evaluation revealed that the detection index (DI) and recovery coefficient (CRC) of SiPM-based TOF-PET images were higher than those of PMT-based PET images, despite a higher background coefficient of variation (CVBG). The two organ-specific PET systems showed that a 3 mm lesion in the breast could be visualized at the center of the detector, and there was less noise in the SiPM-based TOF-PET image.

Dr. Eiichi Tanaka's Achievement in the Research of Image Reconstruction

In memoriam of Dr. Eiichi Tanaka who passed away on August 21, 2021, I review his achievement in the research of tomographic image reconstruction. Tomographic image reconstruction is an important research area which has wide applications including X-ray CT, nuclear medicine imaging such as PET and SPECT, and electron microscopy. Since 1970's, Dr. Tanaka has worked on numerous important topics in tomographic reconstruction fields aiming at using them in image reconstruction for PET and SPECT. Among them, in this paper, I will introduce his research on Filtered BackProjection (FBP) method, analytical attenuation correction in SPECT, image reconstruction in Time-of-Flight PET, image reconstruction for 3-D PET imaging, and iterative image reconstruction method called Dynamic Row-Action Maximum Likelihood Algorithm (DRAMA).

Optimal relaxation parameters of dynamic row-action maximum likelihood algorithm and post-smoothing filter for image reconstruction of dedicated breast PET.

This study aimed to determine the optimal β value of the relaxation control parameter and the post-smoothing filter in the list-mode dynamic row-action maximum likelihood algorithm (LM-DRAMA) to detect early stage breast cancer with high-resolution dedicated breast positron emission tomography (dbPET) in phantom and clinical studies. A breast phantom containing four spheres (5, 7.5, 10, and 16mm in diameter) was filled with 18F-fluorodeoxyglucose solution (sphere-to-background ratio, 8:1) and scanned on a dbPET scanner. The images were reconstructed using LM-DRAMA with different β values (5, 20, or 100) and Gaussian post-filters (0, 0.78, 1.17, 1.56, 1.95, or 2.34mm). Other conditions were according to those routinely used (1 iteration and 128 subsets including attenuation and scatter correction). Image quality was evaluated visually and by computing the coefficient of variation of the background (CVBG), detectability index (DI), and contrast recovery coefficient. Parameters optimized in these phantom studies were applied to 25 clinical data sets. Variabilities for different reconstruction methods in visual scores, the maximum standardized uptake value of breast cancer, and the tumor-to-background uptake ratio were estimated. The reconstruction images of the phantom with higher β values and smaller post-filters yielded higher visual scores for detectability and DI and lower smoothness and CVBG scores. Based on the phantom study, the β values and post-filter were optimized for clinical dbPET images except for β5 and 2.34mm post-filter. Applying the other reconstructions to clinical studies showed that β100 provided higher quantitative parameter values. The detectability of lesions was similar for β100 and β20 and decreased with larger post-filters. The lesion detection rate was similar for β100 and β20 and decreased with larger post-filter. The relaxation coefficient factor β20 and a 0.78- or 1.17-mm post-filter were optimal for dbPET image reconstruction with balanced spatial resolution and noise. However, they should be selected according to the impact on the dbPET image and the purpose of the examination.

Qualitative and Quantitative Assessment of Nonlocal Means Reconstruction Algorithm in a Flexible PET Scanner.

OBJECTIVE. Flexible PET (fxPET) was designed to fit existing MRI systems. The newly modified nonlocal means (NLM) algorithm is combined with the 3D dynamic row-action maximum likelihood algorithm (DRAMA). We investigated qualitative and quantitative acceptability of fxPET images reconstructed by modified NLM compared with whole-body (WB) PET/CT images and conventional 3D DRAMA reconstruction alone. MATERIALS AND METHODS. Fifty-nine patients with known or suspected malignancies underwent WB PET/CT scanning approximately 1 hour after the injection of 18F-FDG, after which they underwent fxPET scanning. Two readers rated the quality of fxPET images by consensus. Detection rate (the proportion of lesions found on PET), maximal standardized uptake value (SUVmax), metabolic tumor volume (MTV), total lesion glycolysis (TLG), tumor-to-normal liver ratio (TNR), and background liver signal-to-noise ratio (SNR) were compared among the three datasets. RESULTS. Higher image quality was obtained by modified NLM reconstruction than by conventional reconstruction without statistical significance. The detection rate was comparable among three datasets. SUVmax was significantly higher, and MTV and TLG were significantly lower in the modified NLM dataset (p < 0.002) than in the other two datasets, with significantly positive correlations (p < 0.001; Spearman rank correlation coefficient, 0.87-0.99). The TNRs in modified NLM images were significantly larger than in the other datasets (p < 0.05). The background SNRs in modified NLM images were comparable with those in WB PET/CT images, and significantly higher than in the conventional fxPET images (p < 0.005). CONCLUSION. The modified NLM algorithm was clinically acceptable, yielding higher TNR and background SNR compared with conventional reconstruction. Image quality and the lesion detection rate were comparable in this population.

Accuracy of Resolution Recovery in PSF-based Fully-3D PET Image Reconstruction: Simulation and Phantom Study in Multicenter Trial

Recently, the quality of positron emission tomography (PET) images has rapidly improved using resolution recovery algorithm with point spread function (PSF). The aim of this study was to investigate the accuracy of the resolution recovery algorithm using three different PET systems. Three PET scanner models, the GE Discovery 600 M (D600M), SIEMENS Biograph mCT (mCT), and SHIMADZU SET-3000GCT/X (3000GCT) were used in this study. The radial dependences of spatial resolution (full width at half maximum: FWHM) were obtained by point source measurements (0.9 mmφ). All PET data were acquired in three-dimensional (3D) mode and reconstructed using the filtered back projection (FBP) , 3D-ordered subsets expectation maximization (3D-OSEM or dynamic row-action maximum likelihood algorithm) , and 3D-OSEM+PSF (PSF) algorithms. Two indicators, aspect ratio (ASR) and resolution recovery ratio (RRR), were calculated from measured FWHMs and compared among the three PET scanners. In D600 and 3000GCT, distortions of the radial direction were slightly increased at circumference of field of view (FOV). On the other hand, random distortions were occurred in both radial and tangential direction in mCT. ASRs calculated from 3D-OSEM images at circumference of FOV were 2.06, 1.22, and 2.04 on D600M, mCT, and 3000GCT, respectively. ASR improved with PSF in all PET scanners. On the other hand, RRR with PSF were calculated 57.6%, 61.4%, and 31.6%, respectively. Our results suggest that the spatial resolutions of PET images could be improved with PSF algorithm in all PET systems; however, effect of PSF was different depending on PET systems. Furthermore, PSF algorithm could not completely improve spatial resolutions in circumference of FOV.

Bootstrap methods for estimating PET image noise: experimental validation and an application to evaluation of image reconstruction algorithms

Accurate and validated methods for estimating regional PET image noise are helpful for optimizing image processing. The bootstrap is a data-based simulation method for statistical inference, which can be used to estimate the PET image noise without repeated measurements. The aim of this study was to experimentally validate bootstrap-based methods as a tool for estimating PET image noise and demonstrate its usefulness for evaluating image reconstruction algorithms. Two bootstrap-based method, the list-mode data bootstrap (LMBS) and the sinogram bootstrap (SNBS), were implemented on a clinical PET scanner. A uniform cylindrical phantom filled with (18)F solution was scanned using list-mode acquisition. A reference standard deviation (SD) map was calculated from 60 statistically independent measured list-mode data. Using one of the 60 list-mode data, 60 bootstrap replicates were generated and used to calculate bootstrap SD maps. Brain (18)F-FDG data from a healthy volunteer were also processed as an example of the bootstrap application. Three reconstruction algorithms, FBP 2D and both 2D and 3D versions of dynamic row-action maximum likelihood algorithm (DRAMA), were assessed. For all the reconstruction algorithms used, the bootstrap SD maps agreed well with the reference SD map, confirming the validity of the bootstrap methods for assessing image noise. The two bootstrap methods were equivalent with respect to the performance of image noise estimation. The bootstrap analysis of the FDG data showed the better contrast-noise relation curve for DRAMA 3D compared to DRAMA 2D and FBP 2D. The bootstrap methods provide the estimates of image noise for various reconstruction algorithms with reasonable accuracy, require only a single measurement, not repeated measures, and are, therefore, applicable for a human PET study.

GPU-Based PET Image Reconstruction Using an Accurate Geometrical System Model

In positron emission tomography (PET), 3D iterative image reconstruction methods have a huge computational burden. In this paper, we developed a list-mode image reconstruction method using graphics processing units (GPUs). Efficiency of acceleration for GPU implementation largely depends on the method chosen, where a reduced number of conditional statements and a reduced memory size are required. On the other hand, accurate system models are required to improve the quality of reconstructed images. Various accurate system models for conventional CPU implementation have been proposed, but these models basically require many conditional statements and huge memory size. Therefore, we developed a new system model which matches GPU implementation better. In this model, the detector response functions, which vary depending on each line of response (LOR), are pre-computed in CPUs and modeled by sixth-order polynomial functions in order to reduce the memory size occupied in GPUs. Each element of a system matrix is obtained on-the-fly in GPUs by calculating the distance between an LOR and a voxel. Therefore the developed system model enables efficient GPU implementation of the accurate system modeling with a reduced number of conditional statements and a reduced memory size. We applied the developed method to a small OpenPET prototype, in which 4-layered depth-of-interaction (DOI) detectors were used. For image reconstruction, we used the dynamic row-action maximum likelihood algorithm (DRAMA). Compared with a conventional model for GPU implementation, in which DRFs are given as a Gaussian function of fixed width, we saw no remarkable difference for DOI data, but for non-DOI data the proposed model outperformed the conventional at the peripheral region of the field-of-view. The proposed model had almost the same calculation time as the conventional model did. For further acceleration, we tried parallel GPU implementation, and we obtained 3.8-fold acceleration by using 4 GPUs.

Real-Time Imaging System for the OpenPET

The OpenPET and its real-time imaging capability have great potential for real-time tumor tracking in medical procedures such as biopsy and radiation therapy. For the real-time imaging system, we intend to use the one-pass list-mode dynamic row-action maximum likelihood algorithm (DRAMA) and implement it using general-purpose computing on graphics processing units (GPGPU) techniques. However, it is difficult to make consistent reconstructions in real-time because the amount of list-mode data acquired in PET scans may be large depending on the level of radioactivity, and the reconstruction speed depends on the amount of the list-mode data. In this study, we developed a system to control the data used in the reconstruction step while retaining quantitative performance. In the proposed system, the data transfer control system limits the event counts to be used in the reconstruction step according to the reconstruction speed, and the reconstructed images are properly intensified by using the ratio of the used counts to the total counts. We implemented the system on a small OpenPET prototype system and evaluated the performance in terms of the real-time tracking ability by displaying reconstructed images in which the intensity was compensated. The intensity of the displayed images correlated properly with the original count rate and a frame rate of 2 frames per second was achieved with average delay time of 2.1 s.

Evaluation of dynamic row-action maximum likelihood algorithm reconstruction for quantitative 15O brain PET

A modified version of row-action maximum likelihood algorithm (RAMLA) using a 'subset-dependent' relaxation parameter for noise suppression, or dynamic RAMLA (DRAMA), has been proposed. The aim of this study was to assess the capability of DRAMA reconstruction for quantitative (15)O brain positron emission tomography (PET). Seventeen healthy volunteers were studied using a 3D PET scanner. The PET study included 3 sequential PET scans for C(15)O, (15)O(2) and H (2) (15) O. First, the number of main iterations (N (it)) in DRAMA was optimized in relation to image convergence and statistical image noise. To estimate the statistical variance of reconstructed images on a pixel-by-pixel basis, a sinogram bootstrap method was applied using list-mode PET data. Once the optimal N (it) was determined, statistical image noise and quantitative parameters, i.e., cerebral blood flow (CBF), cerebral blood volume (CBV), cerebral metabolic rate of oxygen (CMRO(2)) and oxygen extraction fraction (OEF) were compared between DRAMA and conventional FBP. DRAMA images were post-filtered so that their spatial resolutions were matched with FBP images with a 6-mm FWHM Gaussian filter. Based on the count recovery data, N (it) = 3 was determined as an optimal parameter for (15)O PET data. The sinogram bootstrap analysis revealed that DRAMA reconstruction resulted in less statistical noise, especially in a low-activity region compared to FBP. Agreement of quantitative values between FBP and DRAMA was excellent. For DRAMA images, average gray matter values of CBF, CBV, CMRO(2) and OEF were 46.1 +/- 4.5 (mL/100 mL/min), 3.35 +/- 0.40 (mL/100 mL), 3.42 +/- 0.35 (mL/100 mL/min) and 42.1 +/- 3.8 (%), respectively. These values were comparable to corresponding values with FBP images: 46.6 +/- 4.6 (mL/100 mL/min), 3.34 +/- 0.39 (mL/100 mL), 3.48 +/- 0.34 (mL/100 mL/min) and 42.4 +/- 3.8 (%), respectively. DRAMA reconstruction is applicable to quantitative (15)O PET study and is superior to conventional FBP in terms of image quality.

Subset-dependent relaxation in block-iterative algorithms for image reconstruction in emission tomography

This paper presents a row-action maximum likelihood algorithm (RAMLA), in which the relaxation parameter is controlled in such a way that the noise propagation from projection data to the reconstructed image is substantially independent of the access order of the input data (subsets) in each cycle of the sub-iterations. The ‘subset-dependent’ relaxation parameter λk (q) is expressed as λk(q) = β0/(β0 + q + γkM), where M is the number of angular views, q (0 ≤ q ≤ M − 1) is the access order of the angular view, k is the iteration number and β0 and γ are constants. The constant β0 deals with the balance of the noise propagation and the constant γ controls the convergence of iterations. The value of β0 is determined from the geometrical correlation coefficients among lines of coincidence response. The proposed RAMLA using the subset-dependent (dynamic) relaxation ‘dynamic RAMLA (DRAMA)’ provides a reasonable signal-to-noise ratio with a satisfactory spatial resolution by a few iterations in the two-dimensional image reconstruction for PET. Dynamic OS-EM (DOSEM) has also been developed, which allows the use of a larger number of subsets (OS level) Msub without loss of signal-to-noise ratio as compared to the conventional OS-EM. DRAMA is a special case of DOSEM, where Msub = M, and it is no more profitable to use DOSEM with a smaller Msub (<M), because DRAMA provides similar performance with the fastest convergence and smallest computer burden. This paper describes the theory, algorithm and the results of the simulation studies on the performance of DRAMA and DOSEM.