Practical implementation of tetrahedral mesh reconstruction in emission tomography

Anatomy-guided multi-resolution image reconstruction in PET

Objective. In this paper, we propose positron emission tomography image reconstruction using a multi-resolution triangular mesh. The mesh can be adapted based on patient specific anatomical information that can be in the form of a computed tomography or magnetic resonance imaging image in the hybrid imaging systems. The triangular mesh can be adapted to high resolution in localized anatomical regions of interest (ROI) and made coarser in other regions, leading to an imaging model with high resolution in the ROI with clearly reduced number of degrees of freedom compared to a conventional uniformly dense imaging model.Approach.We compare maximum likelihood expectation maximization reconstructions with the multi-resolution model to reconstructions using a uniformly dense mesh, a sparse mesh and regular rectangular pixel mesh. Two simulated cases are used in the comparison, with the first one using the NEMA image quality phantom and the second the XCAT human phantom.Main results.When compared to the results with the uniform imaging models, the locally refined multi-resolution mesh retains the accuracy of the dense mesh reconstruction in the ROI while being faster to compute than the reconstructions with the uniformly dense mesh. The locally dense multi-resolution model leads also to more accurate reconstruction than the pixel-based mesh or the sparse triangular mesh.Significance.The findings suggest that triangular multi-resolution mesh, which can be made patient and application specific, is a potential alternative for pixel-based reconstruction.

Reconstruction of positron emission tomography images using adaptive sliced remeshing strategy

Purpose: The reconstruction of positron emission tomography images is a computationally intensive task which benefits from the use of increasingly complex physical models. Aiming to reduce the computational burden by means of a reduced system matrix, we present a list mode reconstruction approach based on maximum likelihood-expectation maximization and a sliced mesh support. Approach: The reconstruction strategy uses a fully 3D projection along series of 2D meshes arranged in the axial plane of the scanner. These series of meshes describe the continuous volumetric activity using a piece-wise linear function interpolated from the mesh elements. The mesh support is automatically adapted to the underlying structure of the activity by means of a remeshing process. This process finds a high-quality compact mesh representation constrained to a controlled interpolation error. Results: The method is tested using a Monte Carlo simulation of a Hoffman brain phantom and a National Electrical Manufacturers Association image quality phantom acquisition, using different sets of statistics. The reconstructions are compared against a voxelized reconstruction under different conditions, achieving similar or superior results. The number of parameters needed to reconstruct the image in voxel and mesh support is also compared, and the mesh reconstruction permits to reduce the number of nodes used to represent a complex image. Conclusions: The proposed reconstruction strategy reduces the number of parameters needed to describe the activity distribution by more than one order of magnitude for similar voxel size and with similar accuracy than state-of-the-art methods.

Statistical content-adapted sampling (SCAS) for 3D Computed Tomography

In this paper, a framework to create a statistical content-adapted sampling (SCAS) for 3D X-ray Computed Tomography (CT) is introduced. SCAS aims at providing an accurate but light reconstruction volume. Based on decision theory, the 3D reconstruction space is sampled from the raw projection data in three steps to directly fit the sample. To do so, the structural information is first extracted from the projections by edge detection. This information is then merged in the reconstruction space, providing a pointcloud which accurately delineates the 3D interfaces of the specimen. From this pointcloud, a 3D mesh, closely fitting the shape of the studied object, is finally built via constrained Delaunay tetrahedralization. To assess the potential of the proposed SCAS for CT imaging, an iterative reconstruction was performed by classical Ordered Subset Simultaneous Algebraic Reconstruction Technique (OS-SART) - with fitting projection operator. The SCAS was evaluated on both numerical and experimental data. Results show that the use of statistical testing enabled the design of a robust, automated and fast method to build accurate pointclouds from a limited number of projections. The 3D meshes generated from these pointclouds are composed of few cells when compared to the regular voxel representation, leading to a downsize in computational cost and achieving up to 90% of memory footprint reduction. Simulations showed that performed reconstruction on such meshes provide accurate description of the object due to the finer sampling at interfaces.

List-mode image reconstruction for positron emission tomography using tetrahedral voxels

Image space decomposition based on tetrahedral voxels are interesting candidates for use in emission tomography. Tetrahedral voxels provide many of the advantages of point clouds with irregular spacing, such as being intrinsically multi-resolution, yet they also serve as a volumetric partition of the image space and so are comparable to more standard cubic voxels. Additionally, non-rigid displacement fields can be applied to the tetrahedral mesh in a straight-forward manner. So far studies incorporating tetrahedral decomposition of the image space have concentrated on pre-calculated, node-based, system matrix elements which reduces the flexibility of the tetrahedral approach and the capacity to accurately define regions of interest. Here, a list-mode on-the-fly calculation of the system matrix elements is described using a tetrahedral decomposition of the image space and volumetric elements-voxels. The algorithm is demonstrated in the context of awake animal PET which may require both rigid and non-rigid motion compensation, as well as quantification within small regions of the brain. This approach allows accurate, event based, motion compensation including non-rigid deformations.

Image reconstruction in higher dimensions: myocardial perfusion imaging of tracer dynamics with cardiac motion due to deformation and respiration

Myocardial perfusion imaging (MPI) using slow rotating large field of view cameras requires spatiotemporal reconstruction of dynamically acquired data to capture the time variation of the radiotracer concentration. In vivo, MPI contains additional degrees of freedom involving unavoidable motion of the heart due to quasiperiodic beating and the effects of respiration, which can severely degrade the quality of the images. This work develops a technique for a single photon emission computed tomography (SPECT) that reconstructs the distribution of the radiotracer concentration in the myocardium using a tensor product of different sets of basis functions that approximately describe the spatiotemporal variation of the radiotracer concentration and the motion of the heart. In this study the temporal B-spline basis functions are chosen to reflect the dynamics of the radiotracer, while the intrinsic deformation and the extrinsic motion of the heart are described by a product of a discrete set of Gaussian basis functions. Reconstruction results are presented showing the dynamics of the tracer in the myocardium as it deforms due to cardiac beating, and is displaced due to respiratory motion. These results are compared with the conventional 4D-spatiotemporal reconstruction method that models only the temporal changes of the tracer activity. The higher dimensional reconstruction method proposed here improves bias, yet the signal-to-noise ratio (SNR) decreases slightly due to redistribution of the counts over the cardiac-respiratory gates. Additionally, there is a trade-off between the number of gates and the number of projections per gate to achieve high contrast images.

Reconstruction of 4-D dynamic SPECT images from inconsistent projections using a Spline initialized FADS algorithm (SIFADS)

In this paper, we propose and validate an algorithm of extracting voxel-by-voxel time activity curves directly from inconsistent projections applied in dynamic cardiac SPECT. The algorithm was derived based on factor analysis of dynamic structures (FADS) approach and imposes prior information by applying several regularization functions with adaptively changing relative weighting. The anatomical information of the imaged subject was used to apply the proposed regularization functions adaptively in the spatial domain. The algorithm performance is validated by reconstructing dynamic datasets simulated using the NCAT phantom with a range of different input tissue time-activity curves. The results are compared to the spline-based and FADS methods. The validated algorithm is then applied to reconstruct pre-clinical cardiac SPECT data from canine and murine subjects. Images, generated from both simulated and experimentally acquired data confirm the ability of the new algorithm to solve the inverse problem of dynamic SPECT with slow gantry rotation.