3D reconstruction for a multi-ring PET scanner by single-slice rebinning and axial deconvolution

TOPAS-imaging: extensions to the TOPAS simulation toolkit for medical imaging systems

Objective. The TOol for PArticle Simulation (TOPAS) is a Geant4-based Monte Carlo software application that has been used for both research and clinical studies in medical physics. So far, most users of TOPAS have focused on radiotherapy-related studies, such as modeling radiation therapy delivery systems or patient dose calculation. Here, we present the first set of TOPAS extensions to make it easier for TOPAS users to model medical imaging systems.Approach. We used the extension system of TOPAS to implement pre-built, user-configurable geometry components such as detectors (e.g. flat-panel and multi-planar detectors) for various imaging modalities and pre-built, user-configurable scorers for medical imaging systems (e.g. digitizer chain).Main results. We developed a flexible set of extensions that can be adapted to solve research questions for a variety of imaging modalities. We then utilized these extensions to model specific examples of cone-beam CT (CBCT), positron emission tomography (PET), and prompt gamma (PG) systems. The first of these new geometry components, the FlatImager, was used to model example CBCT and PG systems. Detected signals were accumulated in each detector pixel to obtain the intensity of x-rays penetrating objects or prompt gammas from proton-nuclear interaction. The second of these new geometry components, the RingImager, was used to model an example PET system. Positron-electron annihilation signals were recorded in crystals of the RingImager and coincidences were detected. The simulated data were processed using corresponding post-processing algorithms for each modality and obtained results in good agreement with the expected true signals or experimental measurement.Significance. The newly developed extension is a first step to making it easier for TOPAS users to build and simulate medical imaging systems. Together with existing TOPAS tools, this extension can help integrate medical imaging systems with radiotherapy simulations for image-guided radiotherapy.

GapFill-Recon Net: A Cascade Network for simultaneously PET Gap Filling and Image Reconstruction

PET image reconstruction from incomplete data, such as the gap between adjacent detector blocks generally introduces partial projection data loss, is an important and challenging problem in medical imaging. This work proposes an efficient convolutional neural network (CNN) framework, called GapFill-Recon Net, that jointly reconstructs PET images and their associated sinogram data. GapFill-Recon Net including two blocks: the Gap-Filling block first address the sinogram gap and the Image-Recon block maps the filled sinogram onto the final image directly. A total of 43,660 pairs of synthetic 2D PET sinograms with gaps and images generated from the MOBY phantom are utilized for network training, testing and validation. Whole-body mouse Monte Carlo (MC) simulated data are also used for evaluation. The experimental results show that the reconstructed image quality of GapFill-Recon Net outperforms filtered back-projection (FBP) and maximum likelihood expectation maximization (MLEM) in terms of the structural similarity index metric (SSIM), relative root mean squared error (rRMSE), and peak signal-to-noise ratio (PSNR). Moreover, the reconstruction speed is equivalent to that of FBP and was nearly 83 times faster than that of MLEM. In conclusion, compared with the traditional reconstruction algorithm, GapFill-Recon Net achieves relatively optimal performance in image quality and reconstruction speed, which effectively achieves a balance between efficiency and performance.

Real-Time 3D PET Image with Pseudoinverse Reconstruction

Real-time positron emission tomography (PET) may provide information from first-shot images, enable PET-guided biopsies, and allow awake animal studies. Fully-3D iterative reconstructions yield the best images in PET, but they are too slow for real-time imaging. Analytical methods such as Fourier back projection (FBP) are very fast, but yield images of poor quality with artifacts due to noise or data incompleteness. In this work, an image reconstruction based on the pseudoinverse of the system response matrix (SRM) is presented. w. To implement the pseudoinverse method, the reconstruction problem is separated into two stages. First, the axial part of the SRM is pseudo-inverted (PINV) to rebin the 3D data into 2D datasets. Then, the resulting 2D slices can be reconstructed with analytical methods or by applying the pseudoinverse algorithm again. The proposed two-step PINV reconstruction yielded good-quality images at a rate of several frames per second, compatible with real time applications. Furthermore, extremely fast direct PINV reconstruction of projections of the 3D image collapsed along specific directions can be implemented.

Real-Time 3D PET Image with Pseudoinverse Reconstruction

Real-time positron emission tomography (PET) may provide information from first-shot images, enable PET-guided biopsies, and allow awake animal studies. Fully-3D iterative reconstructions yield the best images in PET, but they are too slow for real-time imaging. Analytical methods such as Fourier back projection (FBP) are very fast, but yield images of poor quality with artifacts due to noise or data incompleteness. In this work, an image reconstruction based on the pseudoinverse of the system response matrix (SRM) is presented. w. To implement the pseudoinverse method, the reconstruction problem is separated into two stages. First, the axial part of the SRM is pseudo-inverted (PINV) to rebin the 3D data into 2D datasets. Then, the resulting 2D slices can be reconstructed with analytical methods or by applying the pseudoinverse algorithm again. The proposed two-step PINV reconstruction yielded good-quality images at a rate of several frames per second, compatible with real time applications. Furthermore, extremely fast direct PINV reconstruction of projections of the 3D image collapsed along specific directions can be implemented.

Exact and approximate Fourier rebinning algorithms for the solution of the data truncation problem in 3-D PET

This paper presents an extended 3-D exact rebinning formula in the Fourier space that leads to an iterative reprojection algorithm (iterative FOREPROJ), which enables the estimation of unmeasured oblique projection data on the basis of the whole set of measured data. In first approximation, this analytical formula also leads to an extended Fourier rebinning equation that is the basis for an approximate reprojection algorithm (extended FORE). These algorithms were evaluated on numerically simulated 3-D positron emission tomography (PET) data for the solution of the truncation problem, i.e., the estimation of the missing portions in the oblique projection data, before the application of algorithms that require complete projection data such as some rebinning methods (FOREX) or 3-D reconstruction algorithms (3DRP or direct Fourier methods). By taking advantage of all the 3-D data statistics, the iterative FOREPROJ reprojection provides a reliable alternative to the classical FOREPROJ method, which only exploits the low-statistics nonoblique data. It significantly improves the quality of the external reconstructed slices without loss of spatial resolution. As for the approximate extended FORE algorithm, it clearly exhibits limitations due to axial interpolations, but will require clinical studies with more realistic measured data in order to decide on its pertinence.

Exact rebinning methods for three-dimensional PET

The high computational cost of data processing in volume PET imaging is still hindering the routine application of this successful technique, especially in the case of dynamic studies. This paper describes two new algorithms based on an exact rebinning equation, which can be applied to accelerate the processing of three-dimensional (3-D) PET data. The first algorithm, FOREPROJ, is a fast-forward projection algorithm that allows calculation of the 3-D attenuation correction factors (ACF's) directly from a two-dimensional (2-D) transmission scan, without first reconstructing the attenuation map and then performing a 3-D forward projection. The use of FOREPROJ speeds up the estimation of the 3-D ACF's by more than a factor five. The second algorithm, FOREX, is a rebinning algorithm that is also more than five times faster, compared to the standard reprojection algorithm (3DRP) and does not suffer from the image distortions generated by the even faster approximate Fourier rebinning (FORE) method at large axial apertures. However, FOREX is probably not required by most existing scanners, as the axial apertures are not large enough to show improvements over FORE with clinical data. Both algorithms have been implemented and applied to data simulated for a scanner with a large axial aperture (30 degrees), and also to data acquired with the ECAT HR and the ECAT HR+ scanners. Results demonstrate the excellent accuracy achieved by these algorithms and the important speedup when the sinogram sizes are powers of two.

Performance of the Fourier rebinning algorithm for PET with large acceptance angles

The recently proposed Fourier rebinning (FORE) technique of 3D PET reconstruction is investigated over a wide range of axial acceptance angles. In this study we evaluate the performance of the FORE technique using spatial resolution, contrast and noise figures of merit and compare reconstruction performance of the FORE (followed by multislice 2D reconstruction) to the 3D-RP technique for large-acceptance-angle data (+/-26.25 degrees). Our results show that the FORE technique does not affect the transverse resolution. On the other hand the axial resolution using FORE deteriorates faster, compared with the 3D-RP, at large radii as the acceptance angle increases. Concerning the noise behaviour, we have found that filtering has better ability to suppress the noise in the FORE reconstruction, compared with the 3D-RP reconstruction, especially in the slices near the edge of the axial field of view. Overall, the combination of good performance and fast reconstruction time makes the FORE technique a practical choice for 3D PET applications.

Exact and approximate rebinning algorithms for 3-D PET data

This paper presents two new rebinning algorithms for the reconstruction of three-dimensional (3-D) positron emission tomography (PET) data. A rebinning algorithm is one that first sorts the 3-D data into an ordinary two-dimensional (2-D) data set containing one sinogram for each transaxial slice to be reconstructed; the 3-D image is then recovered by applying to each slice a 2-D reconstruction method such as filtered-backprojection. This approach allows a significant speedup of 3-D reconstruction, which is particularly useful for applications involving dynamic acquisitions or whole-body imaging. The first new algorithm is obtained by discretizing an exact analytical inversion formula. The second algorithm, called the Fourier rebinning algorithm (FORE), is approximate but allows an efficient implementation based on taking 2-D Fourier transforms of the data. This second algorithm was implemented and applied to data acquired with the new generation of PET systems and also to simulated data for a scanner with an 18 degrees axial aperture. The reconstructed images were compared to those obtained with the 3-D reprojection algorithm (3DRP) which is the standard "exact" 3-D filtered-backprojection method. Results demonstrate that FORE provides a reliable alternative to 3DRP, while at the same time achieving an order of magnitude reduction in processing time.