Gap compensation during PET image reconstruction by constrained, total variation minimization

Ahn, S.; Kim, Soo Mee; Son, Jungah; Lee, Dong Hoon; Lee, Jae Sung

doi:10.1118/1.3673775

Cited by 26 publications

(33 citation statements)

References 33 publications

(39 reference statements)

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“…1(a). The resultant sinograms were then reconstructed using our image recovery technique (WTV) as well as a simple TV reconstruction similar to the approach of Ahn et al 12 A block diagram of the recovery process is shown in Fig. 1(b).…”

Section: B1 Simulation Studymentioning

confidence: 99%

“…For the WTV approach, we used the partially sampled image reconstructed using MLEM (20 iterations) as the initialization point and iterated 150 times due to the complexity of the proposed cost function while using the steepest descent algorithm 12 to reach the global minimum. In this implementation, the α and β values were set to 0.24 and 0.63, respectively.…”

Section: B1 Simulation Studymentioning

confidence: 99%

“…Ahn et al 12 recently used the CS technique to fill the missing data in images from the high-resolution research tomograph (HRRT) PET scanner. In these scanners, the octagonal shape of the PET system introduces gaps among the detectors, creating undesired missing data in the sinogram that accounts to about 10% of the sinogram space.…”

Section: Introductionmentioning

confidence: 99%

“…In these scanners, the octagonal shape of the PET system introduces gaps among the detectors, creating undesired missing data in the sinogram that accounts to about 10% of the sinogram space. In their implementation, Ahn et al 12 used the GMD as a sparsifying domain and applied total variation minimization to find the sparsest coefficients. Although Ahn et al 12 showed that CS can recover the gaps inherent in the HRRT scanner design, their model relied on only minimizing the TV and they did not model the noise in their formulation.…”

Section: Introductionmentioning

confidence: 99%

“…More recently, compressive sensing (CS) techniques have been used as a third approach to recover a PET image from an incomplete dataset. 12 The general idea of CS is to reproduce the exact signal from fewer samples than is required (twice the maximum frequency exhibited by signal). This can be achieved by transforming the signal to a new domain (called sparsifying domain) such that the corresponding coefficients that represent the signal in the new domain are very sparse (few nonzero elements).…”

Section: Introductionmentioning

confidence: 99%

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Using compressive sensing to recover images from PET scanners with partial detector rings

2015

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Purpose: Most positron emission tomography/computed tomography (PET/CT) scanners consist of tightly packed discrete detector rings to improve scanner efficiency. The authors' aim was to use compressive sensing (CS) techniques in PET imaging to investigate the possibility of decreasing the number of detector elements per ring (introducing gaps) while maintaining image quality. Methods: A CS model based on a combination of gradient magnitude and wavelet domains (wavelet-TV) was developed to recover missing observations in PET data acquisition. The model was designed to minimize the total variation (TV) and L1-norm of wavelet coefficients while constrained by the partially observed data. The CS model also incorporated a Poisson noise term that modeled the observed noise while suppressing its contribution by penalizing the Poisson log likelihood function. Three experiments were performed to evaluate the proposed CS recovery algorithm: a simulation study, a phantom study, and six patient studies. The simulation dataset comprised six disks of various sizes in a uniform background with an activity concentration of 5:1. The simulated image was multiplied by the system matrix to obtain the corresponding sinogram and then Poisson noise was added. The resultant sinogram was masked to create the effect of partial detector removal and then the proposed CS algorithm was applied to recover the missing PET data. In addition, different levels of noise were simulated to assess the performance of the proposed algorithm. For the phantom study, an IEC phantom with six internal spheres each filled with F-18 at an activity-to-background ratio of 10:1 was used. The phantom was imaged twice on a RX PET/CT scanner: once with all detectors operational (baseline) and once with four detector blocks (11%) turned off at each of 0˚, 90˚, 180˚, and 270• (partially sampled). The partially acquired sinograms were then recovered using the proposed algorithm. For the third test, PET images from six patient studies were investigated using the same strategy of the phantom study. The recovered images using WTV and TV as well as the partially sampled images from all three experiments were then compared with the fully sampled images (the baseline). Comparisons were done by calculating the mean error (%bias), root mean square error (RMSE), contrast recovery (CR), and SNR of activity concentration in regions of interest drawn in the background as well as the disks, spheres, and lesions. Results: For the simulation study, the mean error, RMSE, and CR for the WTV (TV) recovered images were 0.26% (0.48%), 2.6% (2.9%), 97% (96%), respectively, when compared to baseline. For the partially sampled images, these results were 22.5%, 45.9%, and 64%, respectively. For the simulation study, the average SNR for the baseline was 41.7 while for WTV (TV), recovered image was 44.2 (44.0). The phantom study showed similar trends with 5.4% (18.2%), 15.6% (18.8%), and 78% (60%), respectively, for the WTV (TV) images and 33%, 34.3%, and 69% for the partially sampled images. ...

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Section: B1 Simulation Studymentioning

confidence: 99%

Section: B1 Simulation Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Using compressive sensing to recover images from PET scanners with partial detector rings

2015

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Proof‐of‐concept prototype time‐of‐flight PET system based on high‐quantum‐efficiency multianode PMTs

et al. 2017

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Simultaneous correction of sensitivity and spatial resolution in projection‐based magnetic particle imaging

Murase¹

2020

Medical Physics

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Purpose: The purpose of this study was to develop a method to simultaneously correct the spatial resolution and inhomogeneous sensitivity of a receiving coil in projection-based magnetic particle imagingand to investigate its efficacy through simulation and experimental studies. Methods: Magnetic particle imaging (MPI) images were reconstructed using the simultaneous algebraic reconstruction technique (SART), and simultaneous corrections to sensitivity and spatial resolution were performed by incorporating the sensitivity map of the receiving coil and the system function into the SART algorithm. After each SART update, the regularization methodwith total variation (TV) minimizationwas used to suppress noise amplification and artifact generation. For comparison, MPI images were also reconstructed using the filtered backprojection (FBP) method and the FBP-truncated singular value decomposition (TSVD) method, in which the system function was deconvolved from the projection data using TSVD. In simulation studies, the sensitivity map of a second-order, gradiometer-type receiving coil was generated using the Biot-Savart law, while the system function was obtained by calculating the MPI signals induced by magnetic nanoparticles at various distances from a field-free line (FFL), using a lock-in-amplifier model. The effects of a regularization parameter for TV minimization (a), number of iterations (N), and signal-to-noise ratio (SNR) of the MPI signals on the reconstructed MPI images of a numerical phantom were evaluated, using the image profiles and percent root mean square error (PRMSE). Experimental studies involved the calculation of the system function using a tube phantom. Projection data for an A-shaped phantom were acquired using our MPI scanner, and their MPI images were reconstructed from the projection data, as described above. Results: When both the sensitivity and spatial resolution were corrected (SART-SR), the quality of the reconstructed images was seen to have improved, compared to when the spatial resolution was not correctedor when the FBP and FBP-TSVD methods were used. When SNR was low (20), a larger a value yielded a better image. The minimum PRMSE occurred at N % 200-400 and increased with increasing N thereafter. When SNR was high (100), the image quality was generally not dependent on the a value within its studied range. The PRMSE decreased slowly with increasing N, and tended to converge to a constant value. The full width at half maximum (FWHM) of the profile was obtained from the A-shaped phantom, reconstructed using the SART-SR algorithm with a = 0.05 and N = 1000. The FWHM value of the tube (2 mm diameter) in the A-shaped phantom image was found to be 2.2 mm on average, whereas those calculated from the images obtained by the FBP and FBP-TSVD methods were 4.4 and 3.0 mm on average, respectively. Spatial resolution improved when using the FBP-TSVD method as compared to the FBP method but image distortion and artifacts were observed. Conclusions: Although further studies are necessary to opti...

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Gap compensation during PET image reconstruction by constrained, total variation minimization

Abstract: A TV minimization strategy incorporated into commonly used PET reconstruction algorithms was useful for reducing the occurrence of artifacts due to gaps between detector modules in small-diameter PET scanners.

Cited by 26 publications

References 33 publications

Using compressive sensing to recover images from PET scanners with partial detector rings

Using compressive sensing to recover images from PET scanners with partial detector rings

Proof‐of‐concept prototype time‐of‐flight PET system based on high‐quantum‐efficiency multianode PMTs

Simultaneous correction of sensitivity and spatial resolution in projection‐based magnetic particle imaging

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