Wenli Wang

Systematic and Distributed Time-of-Flight List Mode PET Reconstruction

Philips has recently released the time-of-flight (TOF) PET/CT GEMINI-TF scanner. It uses 4 times 4 times 22 mm3 LYSO crystals, which has 600 ps timing resolution, 12% energy resolution and 4.8 mm spatial resolution. This paper describes the system design and general approach of TOF reconstruction in Philips GEMINI-TF scanner. A relaxed list mode ordered subset expectation maximization (LMOSEM) algorithm is used in the reconstruction, with chronologically ordered subsets. The sensitivity and emission object in LMOSEM are computed in the spherically symmetric basis function (blob) space. The multiplicative correction factors of detector normalization, isotope decay, system dead-time and crystal timing are pre-corrected for each list mode event. Attenuation, scatter and randoms are corrected in the reconstruction system matrix. A TOF-dependent single scatter simulation (SSS) is implemented for TOF scatter estimation. To accelerate reconstruction, the sensitivity calculation and list mode reconstruction are distributed to multiple processors, using a dynamic load balancing scheme. For this paper, a uniform cylinder phantom with cold and hot cylinder inserts, a NEMA body IEC phantom and a patient study are reconstructed with both TOF and non-TOF reconstructions. We have demonstrated that TOF reconstruction converges faster than non-TOF, and controls noise well than non-TOF. It has better contrast-noise trade-offs than non-TOF for cold regions and small hot lesions.

3D RBI-EM reconstruction with spherically-symmetric basis function for SPECT rotating slat collimator

A single photon emission computed tomography (SPECT) rotating slat collimator with strip detector acquires distance-weighted plane integral data, along with the attenuation factor and distance-dependent detector response. In order to image a 3D object, the slat collimator device has first to spin around its axis and then rotate around the object to produce 3D projection measurements. Compared to the slice-by-slice 2D reconstruction for the parallel-hole collimator and line integral data, a more complex 3D reconstruction is needed for the slat collimator and plane integral data. In this paper, we propose a 3D RBI-EM reconstruction algorithm with spherically-symmetric basis function, also called blobs, for the slat collimator. It has a closed and spherically symmetric analytical expression for the 3D Radon transform, which makes it easier to compute the plane integral than the voxel. It is completely localized in the spatial domain and nearly band-limited in the frequency domain. Its size and shape can be controlled by several parameters to have desired reconstructed image quality. A mathematical lesion phantom study has demonstrated that the blob reconstruction can achieve better contrast-noise trade-offs than the voxel reconstruction without greatly degrading the image resolution. A real lesion phantom study further confirmed this and showed that a slat collimator with CZT detector has better image quality than the conventional parallel-hole collimator with NaI detector. The improvement might be due to both the slat collimation and the better energy resolution of the CZT detector.

An LOR-based fully-3D PET image reconstruction using a blob-basis function

Conventional reconstruction in Positron Emission Tomography (PET) imaging involves a line-of-response (LOR) preprocessing step where the raw LOR data are interpolated to evenly spaced sinogram data. The LOR-based reconstruction eliminates this interpolation step and thus gives rise to better spatial resolution and image quality. In the Philips PET/CT product, Gemini GXL, this approach is combined with a blob basis function that leads not only to substantial suppression of the image noise but also to preservation of the resolution. When projecting along the raw LORs, however, the computational advantage associated with projecting an evenly spaced sinogram is lost. In addition, using blobs to represent an object results in more image elements to trace in the projection because an LOR intersects more blobs than voxels for equivalent image quality. Therefore, the combined use of LOR-based reconstruction and a blob basis function requires significantly more computation time and represents a reconstruction performance challenge. In the Gemini GXL software we have used a system-matrix lookup table. Both multiplicative and additive corrections are modeled in the system matrix but not included in the lookup table. By making use of the scanner symmetry, and, more importantly, by aligning the blob matrix with the axial crystal rings, the lookup table is reduced in size by a factor of more than 100. The reconstruction performance is optimized by continuous memory access and block looping techniques in a hybrid-projection method. Compared to a calculate-on-the-fly approach, it is ~3 times faster on a Xeon 3.06 GHz dual-processor computer, which allows GXL to achieve excellent clinical performance.

A New Component Approach to Efficiency Normalization for 3D PET

Efficiency normalization is to correct the non-uniform response of the 3D PET detector due to the scanners geometry, crystal non-uniformity, and gain variation in the photo-multiply-tubes. In the literature, most of the component approach detector efficiency normalization is applied to block-design ring scanner. In this paper, we propose a new component normalization method for Philips non-block design ring scanner, where the normalization is mainly consists of two components, the crystal efficiency and the detector geometry. The derivation is based on the measured datas physics model, along with an assumption, so that the crystal efficiency can be separated from the model and both terms can be estimated independently. The crystal efficiency is calibrated using a uniform cylinder phantom. A minimum-least-square estimation method is used to smooth the noisy crystal efficiency. The detector geometry is calibrated using a stationary uniform plane phantom since it is independent of the projection rays azimuthal angle. The result is then applied with a radial solid angle correction to compensate for the plane sources unusual geometry. This technique is finally validated with a uniform cylinder phantom reconstruction along with scatter and attenuation correction

Local tomography property of residual minimization reconstruction with planar integral data

Residual minimization with the well-known conjugate gradient (CG) algorithm has been applied to medical image reconstruction for years. The main advantage of this method is its fast convergence rate. In this paper, we point out that this method has another property-local tomography, when this image reconstruction method is applied to planar integral projections. By local tomography we mean the following: The object is relatively large, the entire object is not sufficiently measured, and the projections are truncated due to a small detector size. However, a small region-of-interest (ROI) is sufficiently measured. The small ROI is able to be exactly reconstructed. This local tomographic property is found for planar integral data only and is not found for line-integral measurements. Iterative local tomography has been applied to cos/spl alpha//r weighted planar integral data through computer simulations and phantom experiments. An efficient projector that models the cos/spl alpha//r weighting factor is also developed.

Dynamic Load Balancing on Distributed Listmode Time-of-Flight Image Reconstruction

A major obstacle in performing listmode reconstruction in PET imaging is the increased computation time compared to a conventional frame or histogrammed reconstruction. To overcome this challenge in a clinical setting, it is desirable to distribute the reconstruction task to multiple nodes. A previous work investigated the impact of high performance communication networks and focused mainly on static distribution. In practice, optimal static load balancing is difficult. Therefore we have developed a dynamic load balancing approach, which is flexible and can easily be adapted to a varying number of nodes, and the performance of which is not constrained by variation of the load levels of nodes needed for other tasks or by asymmetric network. In this approach, one of the nodes is designated as the distributor, whose task is to partition the events into small chunks and then distribute those chunks to other nodes for processing. Other nodes, which do the actual data processing, are called workers. Each worker requests a new chunk of data to process upon completion of an old one. In case of the OSEM algorithm, when all chunks have been processed in a subset, the workers are synchronized and the image is updated. This image forms the basis for the next subset. This system has been deployed in the Philips GEMINI-TF PET/CT system. For a whole-body patient scan of 150M events, the event processing time with 8 Xeon 3.6GHz dual-processor computers amounts to approximately 9 minutes for 3 iterations.

Noise weighting with an exponent for transmission CT

It is widely believed that the correct weighting function is the reciprocal of the noise variance of the associated measurement. Many researchers are making great efforts to find the accurate variance for the measurements for imaging systems so that they can hopefully achieve an optimal reconstruction. An optimal solution in the context of this paper is referred to as the image that reaches optimum according to a criterion or criteria among a group of candidates, regardless how the images in the group are obtained. This optimal solution is not a theoretical concept, but is simply the best of the bunch. The goal of the paper is to investigate how the weighting function affects the image noise when the image contrast is pre-specified in an iterative algorithm for x-ray CT. This paper makes some interesting observations: there is no universal optimal weighting function. The noise weighting function can introduce artifacts. The optimal noise weighting varies with the object to be reconstructed and targeted image contrast in an iterative image reconstruction algorithm and in a filtered backprojection algorithm that incorporates the projection noise. It is suggested that an exponent be used in the weighting function so that the artifacts caused by the weighting function can be reduced.

Does Noise Weighting Matter in CT Iterative Reconstruction

This paper uses a computer simulation to investigate whether a more accurate noise model always results in less noisy images in CT iterative reconstruction. We start with a hypothetic non-realistic noise model for the CT measurements, by assuming that the attenuation coefficient is energy independent and there is no scattering. A variance formula for this model is derived and presented. Based on this model, computer simulations are conducted with 12 different ad hoc noise weighting methods, and their results are compared. The simple Poisson noise model performs better than other more accurate models, when the projection data are generated with the hypothetical noise model. A more accurate noise model does not necessarily produce a less-noisy image. In this counter example, modeling the system’s electronic noise during reconstruction does not help reducing the image noise. A simpler noise model sometimes can outperform the complicated and more accurate noise model.