Scatter modelling and compensation in emission tomography

In nuclear medicine, clinical assessment and diagnosis are generally based on qualitative assessment of the distribution pattern of radiotracers used. In addition, emission tomography (SPECT and PET) imaging methods offer the possibility of quantitative assessment of tracer concentration in vivo to quantify relevant parameters in clinical and research settings, provided accurate correction for the physical degrading factors (e.g. attenuation, scatter, partial volume effects) hampering their quantitative accuracy are applied. This review addresses the problem of Compton scattering as the dominant photon interaction phenomenon in emission tomography and discusses its impact on both the quality of reconstructed clinical images and the accuracy of quantitative analysis. After a general introduction, there is a section in which scatter modelling in uniform and non-uniform media is described in detail. This is followed by an overview of scatter compensation techniques and evaluation strategies used for the assessment of these correction methods. In the process, emphasis is placed on the clinical impact of image degradation due to Compton scattering. This, in turn, stresses the need for implementation of more accurate algorithms in software supplied by scanner manufacturers, although the choice of a general-purpose algorithm or algorithms may be difficul

Characterization and Compensation of Hysteretic Cardiac Respiratory Motion in Myocardial Perfusion Studies Through MRI Investigations

Respiratory motion causes artifacts and blurring of cardiac structures in reconstructed images of SPECT and PET cardiac studies. Hysteresis in respiratory motion causes the organs to move in distinct paths during inspiration and expiration. Current respiratory motion correction methods use a signal generated by tracking the motion of the abdomen during respiration to bin list- mode data as a function of the magnitude of this respiratory signal. They thereby fail to account for hysteretic motion. The goal of this research was to demonstrate the effects of hysteretic respiratory motion and the importance of its correction for different medical imaging techniques particularly SPECT and PET. This study describes a novel approach for detecting and correcting hysteresis in clinical SPECT and PET studies. From the combined use of MRI and a synchronized Visual Tracking System (VTS) in volunteers we developed hysteretic modeling using the Bouc-Wen model with inputs from measurements of both chest and abdomen respiratory motion. With the MRI determined heart motion as the truth in the volunteer studies we determined the Bouc Wen model could match the behavior over a range of hysteretic cycles. The proposed approach was validated through phantom simulations and applied to clinical SPECT studies

Nonlinear tube-fitting for the analysis of anatomical and functional structures

We are concerned with the estimation of the exterior surface and interior summaries of tube-shaped anatomical structures. This interest is motivated by two distinct scientific goals, one dealing with the distribution of HIV microbicide in the colon and the other with measuring degradation in white-matter tracts in the brain. Our problem is posed as the estimation of the support of a distribution in three dimensions from a sample from that distribution, possibly measured with error. We propose a novel tube-fitting algorithm to construct such estimators. Further, we conduct a simulation study to aid in the choice of a key parameter of the algorithm, and we test our algorithm with validation study tailored to the motivating data sets. Finally, we apply the tube-fitting algorithm to a colon image produced by single photon emission computed tomography (SPECT) and to a white-matter tract image produced using diffusion tensor imaging (DTI).Comment: Published in at http://dx.doi.org/10.1214/10-AOAS384 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Grouped-Coordinate Ascent Algorithms for Penalized-Likelihood Transmission Image Reconstruction

Presents a new class of algorithms for penalized-likelihood reconstruction of attenuation maps from low-count transmission scans. We derive the algorithms by applying to the transmission log-likelihood a version of the convexity technique developed by De Pierro for emission tomography. The new class includes the single-coordinate ascent (SCA) algorithm and Lange's convex algorithm for transmission tomography as special cases. The new grouped-coordinate ascent (GCA) algorithms in the class overcome several limitations associated with previous algorithms. (1) Fewer exponentiations are required than in the transmission maximum likelihood-expectation maximization (ML-EM) algorithm or in the SCA algorithm. (2) The algorithms intrinsically accommodate nonnegativity constraints, unlike many gradient-based methods. (3) The algorithms are easily parallelizable, unlike the SCA algorithm and perhaps line-search algorithms. We show that the GCA algorithms converge faster than the SCA algorithm, even on conventional workstations. An example from a low-count positron emission tomography (PET) transmission scan illustrates the method.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86021/1/Fessler93.pd

Mean and Variance of Implicitly Defined Biased Estimators (Such as Penalized Maximum Likelihood) : Applications to Tomography

Many estimators in signal processing problems are defined implicitly as the maximum of some objective function. Examples of implicitly defined estimators include maximum likelihood, penalized likelihood, maximum a posteriori, and nonlinear least squares estimation. For such estimators, exact analytical expressions for the mean and variance are usually unavailable. Therefore, investigators usually resort to numerical simulations to examine the properties of the mean and variance of such estimators. This paper describes approximate expressions for the mean and variance of implicitly defined estimators of unconstrained continuous parameters. We derive the approximations using the implicit function theorem, the Taylor expansion, and the chain rule. The expressions are defined solely in terms of the partial derivatives of whatever objective function one uses for estimation. As illustrations, we demonstrate that the approximations work well in two tomographic imaging applications with Poisson statistics. We also describe a “plug-in” approximation that provides a remarkably accurate estimate of variability even from a single noisy Poisson sinogram measurement. The approximations should be useful in a wide range of estimation problems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85819/1/Fessler99.pd

Effect of reconstruction and filtering on kinetic parameter estimation bias and reliability for dynamic SPECT : a simulation study

Author name used in this publication: Dagan FengCentre for Multimedia Signal Processing, Department of Electronic and Information Engineering2004-2005 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Hybrid Poissoflolynomial Objective Functions for Tomographic Image Reconstruction from Transmission Scans

This paper describes rapidly converging algorithms for computing attenuation maps from Poisson transmission measurements using penalized-likelihood objective functions. We demonstrate that an under-relaxed cyclic coordinate-ascent algorithm converges faster than the convex algorithm of Lange (see ibid., vol.4, no.10, p.1430-1438, 1995), which in turn converges faster than the expectation-maximization (EM) algorithm for transmission tomography. To further reduce computation, one could replace the log-likelihood objective with a quadratic approximation. However, we show with simulations and analysis that the quadratic objective function leads to biased estimates for low-count measurements. Therefore we introduce hybrid Poisson/polynomial objective functions that use the exact Poisson log-likelihood for detector measurements with low counts, but use computationally efficient quadratic or cubic approximations for the high-count detector measurements. We demonstrate that the hybrid objective functions reduce computation time without increasing estimation bias.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86023/1/Fessler100.pd