Andrew J. Reader

List-mode-based reconstruction for respiratory motion correction in PET using non-rigid body transformations

Respiratory motion in emission tomography leads to reduced image quality. Developed correction methodology has been concentrating on the use of respiratory synchronized acquisitions leading to gated frames. Such frames, however, are of low signal-to-noise ratio as a result of containing reduced statistics. In this work, we describe the implementation of an elastic transformation within a list-mode-based reconstruction for the correction of respiratory motion over the thorax, allowing the use of all data available throughout a respiratory motion average acquisition. The developed algorithm was evaluated using datasets of the NCAT phantom generated at different points throughout the respiratory cycle. List-mode-data-based PET-simulated frames were subsequently produced by combining the NCAT datasets with Monte Carlo simulation. A non-rigid registration algorithm based on B-spline basis functions was employed to derive transformation parameters accounting for the respiratory motion using the NCAT dynamic CT images. The displacement matrices derived were subsequently applied during the image reconstruction of the original emission list mode data. Two different implementations for the incorporation of the elastic transformations within the one-pass list mode EM (OPL-EM) algorithm were developed and evaluated. The corrected images were compared with those produced using an affine transformation of list mode data prior to reconstruction, as well as with uncorrected respiratory motion average images. Results demonstrate that although both correction techniques considered lead to significant improvements in accounting for respiratory motion artefacts in the lung fields, the elastic-transformation-based correction leads to a more uniform improvement across the lungs for different lesion sizes and locations.

Impact of Image-Space Resolution Modeling for Studies with the High-Resolution Research Tomograph

Brain PET in small structures is challenged by low resolution inducing bias in the activity measurements. Improved spatial resolution may be obtained by using dedicated tomographs and more comprehensive modeling of the acquisition system during reconstruction. In this study, we assess the impact of resolution modeling (RM) during reconstruction on image quality and on the estimates of biologic parameters in a clinical study performed on a high-resolution research tomograph. Methods: An accelerated list-mode ordinary Poisson ordered-subset expectation maximization (OP-OSEM) algorithm, including sinogram-based corrections and an experimental stationary model of resolution, has been designed. Experimental phantom studies are used to assess contrast and noise characteristics of the reconstructed images. The binding potential of a selective tracer of the dopamine transporter is also assessed in anatomic volumes of interest in a 5-patient study. Results: In the phantom experiment, a slower convergence and a higher contrast recovery are observed for RM-OP-OSEM than for OP-OSEM for the same level of statistical noise. RM-OP-OSEM yields contrast recovery levels that could not be reached without RM as well as better visual recovery of the smallest spheres and better delineation of the structures in the reconstructed images. Statistical noise has lower variance at the voxel level with RM than without at matched resolution. In a uniform activity region, RM induces higher positive and lower negative correlations with neighboring voxels, leading to lower spatial variance. Clinical images reconstructed with RM demonstrate better delineation of cortical and subcortical structures in both time-averaged and parametric images. The binding potential in the striatum is also increased, a result similar to the one observed in the phantom study. Conclusion: In high-resolution PET, RM during reconstruction improves quantitative accuracy by reducing the partial-volume effects.

One-pass list-mode EM algorithm for high-resolution 3-D PET image reconstruction into large arrays

High-resolution three-dimensional (3-D) positron emission tomography (PET) scanners with high count rate performance, such as the quad-high density avalanche chamber (HIDAC), place new demands on image reconstruction algorithms due to the large quantities of high-precision list-mode data which are produced. Therefore, a reconstruction algorithm is required which can, in a practical time frame, reconstruct into very large image arrays (submillimeter voxels, which range over a large field of view) whilst preferably retaining the precision of the data. This work presents an algorithm which meets these demands: one-pass list-mode expectation maximization (OPL-EM) algorithm. The algorithm operates directly on list-mode data, passes through the data once only, accounts for finite resolution effects in the system model, and can also include regularization. The algorithm performs multiple image updates during its single pass through the list-mode data, corresponding to the number of subsets that the data have been split into. The algorithm has been assessed using list-mode data from a quad-HIDAC and is compared to the analytic reconstruction method 3-D reprojection (RP) with 3-D filtered backprojection.

Fast accurate iterative reconstruction for low-statistics positron volume imaging

A fast accurate iterative reconstruction (FAIR) method suitable for low-statistics positron volume imaging has been developed. The method, based on the expectation maximization-maximum likelihood (EM-ML) technique, operates on list-mode data rather than histogrammed projection data and can, in just one pass through the data, generate images with the same characteristics as several ML iterations. Use of list-mode data preserves maximum sampling accuracy and implicitly ignores lines of response (LORs) in which no counts were recorded. The method is particularly suited to systems where sampling accuracy can be lost by histogramming events into coarse LOR bins, and also to sparse data situations such as fast whole-body and dynamic imaging where sampling accuracy may be compromised by storage requirements and where reconstruction time can be wasted by including LORs with no counts. The technique can be accelerated by operating on subsets of list-mode data which also allows scope for simultaneous data acquisition and iterative reconstruction. The method is compared with a standard implementation of the EM-ML technique and is shown to offer improved resolution, contrast and noise properties as a direct result of using improved spatial sampling, limited only by hardware specifications.

EM algorithm system modeling by image-space techniques for PET reconstruction

Methodology for PET system modeling using image-space techniques in the expectation maximization (EM) algorithm is presented. The approach, applicable to both list-mode data and projection data, is of particular significance to EM algorithm implementations which otherwise only use basic system models (such as those which calculate the system matrix elements on the fly). A basic version of the proposed technique can be implemented using image-space convolution, in order to include resolution effects into the system matrix, so that the EM algorithm gradually recovers the modeled resolution with each update. The improved system modeling (achieved by inclusion of two convolutions per iteration) results in both enhanced resolution and lower noise, and there is often no need for regularization-other than to limit the number of iterations. Tests have been performed with simulated list-mode data and also with measured projection data from a GE Advance PET scanner, for both [/sup 18/F]-FDG and [/sup 124/I]-NaI. The method demonstrates improved image quality in all cases when compared to the conventional FBP and EM methods presently used for clinical data (which do not include resolution modeling). The benefits of this approach for /sup 124/I (which has a low positron yield and a large positron range, usually resulting in noisier and poorer resolution images) are particularly noticeable.

Respiratory motion correction for PET oncology applications using affine transformation of list mode data

Respiratory motion is a source of artefacts and reduced image quality in PET. Proposed methodology for correction of respiratory effects involves the use of gated frames, which are however of low signal-to-noise ratio. Therefore a method accounting for respiratory motion effects without affecting the statistical quality of the reconstructed images is necessary. We have implemented an affine transformation of list mode data for the correction of respiratory motion over the thorax. The study was performed using datasets of the NCAT phantom at different points throughout the respiratory cycle. List mode data based PET simulated frames were produced by combining the NCAT datasets with a Monte Carlo simulation. Transformation parameters accounting for respiratory motion were estimated according to an affine registration and were subsequently applied on the original list mode data. The corrected and uncorrected list mode datasets were subsequently reconstructed using the one-pass list mode EM (OPL-EM) algorithm. Comparison of corrected and uncorrected respiratory motion average frames suggests that an affine transformation in the list mode data prior to reconstruction can produce significant improvements in accounting for respiratory motion artefacts in the lungs and heart. However, the application of a common set of transformation parameters across the imaging field of view does not significantly correct the respiratory effects on organs such as the stomach, liver or spleen.

Statistical list-mode image reconstruction for the high resolution research tomograph

We have investigated statistical list-mode reconstruction applicable to a depth-encoding high resolution research tomograph. An image non-negativity constraint has been employed in the reconstructions and is shown to effectively remove the overestimation bias introduced by the sinogram non-negativity constraint. We have furthermore implemented a convergent subsetized (CS) list-mode reconstruction algorithm, based on previous work (Hsiao et al 2002 Conf. Rec. SPIE Med. Imaging 4684 10-19; Hsiao et al 2002 Conf. Rec. IEEE Int. Symp. Biomed. Imaging 409-12) on convergent histogram OSEM reconstruction. We have demonstrated that the first step of the convergent algorithm is exactly equivalent (unlike the histogram-mode case) to the regular subsetized list-mode EM algorithm, while the second and final step takes the form of additive updates in image space. We have shown that in terms of contrast, noise as well as FWHM width behaviour, the CS algorithm is robust and does not result in limit cycles. A hybrid algorithm based on the ordinary and the convergent algorithms is also proposed, and is shown to combine the advantages of the two algorithms (i.e. it is able to reach a higher image quality in fewer iterations while maintaining the convergent behaviour), making the hybrid approach a good alternative to the ordinary subsetized list-mode EM algorithm.

Joint estimation of dynamic PET images and temporal basis functions using fully 4D ML-EM

A fully 4D joint-estimation approach to reconstruction of temporal sequences of 3D positron emission tomography (PET) images is proposed. The method estimates both a set of temporal basis functions and the corresponding coefficient for each basis function at each spatial location within the image. The joint estimation is performed through a fully 4D version of the maximum likelihood expectation maximization (ML-EM) algorithm in conjunction with two different models of the mean of the Poisson measured data. The first model regards the coefficients of the temporal basis functions as the unknown parameters to be estimated and the second model regards the temporal basis functions themselves as the unknown parameters. The fully 4D methodology is compared to the conventional frame-by-frame independent reconstruction approach (3D ML-EM) for varying levels of both spatial and temporal post-reconstruction smoothing. It is found that using a set of temporally extensive basis functions (estimated from the data by 4D ML-EM) significantly reduces the spatial noise when compared to the independent method for a given level of image resolution. In addition to spatial image quality advantages, for smaller regions of interest (where statistical quality is often limited) the reconstructed time-activity curves show a lower level of bias and a lower level of noise compared to the independent reconstruction approach. Finally, the method is demonstrated on clinical 4D PET data.

Regularized one-pass list-mode EM algorithm for high resolution 3D PET image reconstruction into large arrays

High resolution 3D PET scanners with high count rate performance, such as the quad-HIDAC, place new demands on image reconstruction algorithms due to the large quantities of high precision list-mode data which are produced. Therefore a reconstruction algorithm is required which can, in a practical time frame, reconstruct into very large image arrays (submillimetre voxels, which range over a large field of view) whilst preferably retaining the precision of the data. This work presents an algorithm which meets these demands: Regularized One-Pass List-mode EM (ROPLE). The algorithm operates directly on list-mode data, passes through the data once only, accounts for finite resolution effects in the system model and also includes regularization. The algorithm performs multiple image updates during its single pass through the list-mode data, corresponding to the number of subsets that the data have been split into. The algorithm has been assessed using list-mode data from a quad-HIDAC, and is compared to the analytic reconstruction method 3D RP.

Advances in PET Image Reconstruction

Until recently, the most widely used methods for image reconstruction were direct analytic techniques. Iterative techniques, although computationally much more intensive, produce improved images (principally arising from more accurate modeling of the acquired projection data), enabling these techniques to replace analytic techniques not only in research settings but also in the clinic. This article offers an overview of image reconstruction theory and algorithms for PET, with a particular emphasis on statistical iterative reconstruction techniques. Future directions for image reconstruction in PET are considered, which concern mainly improving the modeling of the data acquisition process and task-specific specification of the parameters to be estimated in image reconstruction.