David R. Gilland

Fully Bayesian estimation of Gibbs hyperparameters for emission computed tomography data

In recent years, many investigators have proposed Gibbs prior models to regularize images reconstructed from emission computed tomography data. Unfortunately, hyperparameters used to specify Gibbs priors can greatly influence the degree of regularity imposed by such priors and, as a result, numerous procedures have been proposed to estimate hyperparameter values, from observed image data. Many of these, procedures attempt to maximize the joint posterior distribution on the image scene. To implement these methods, approximations to the joint posterior densities are required, because the dependence of the Gibbs partition function on the hyperparameter values is unknown. Here, the authors use recent results in Markov chain Monte Carlo (MCMC) sampling to estimate the relative values of Gibbs partition functions and using these values, sample from joint posterior distributions on image scenes. This allows for a fully Bayesian procedure which does not fix the hyperparameters at some estimated or specified value, but enables uncertainty about these values to be propagated through to the estimated intensities. The authors utilize realizations from the posterior distribution for determining credible regions for the intensity of the emission source. The authors consider two different Markov random field (MRF) models-the power model and a line-site model. As applications they estimate the posterior distribution of source intensities from computer simulated data as well as data collected from a physical single photon emission computed tomography (SPECT) phantom.

Estimation of images and nonrigid deformations in gated emission CT

In this paper, we propose and test a new iterative algorithm to simultaneously estimate the nonrigid motion vector fields and the emission images for a complete cardiac cycle in gated cardiac emission tomography. We model the myocardium as an elastic material whose motion does not generate large amounts of strain. As a result, our method is based on minimizing an objective function consisting of the negative logarithm of a maximum likelihood image reconstruction term, the standard biomechanical model of strain energy, and an image matching term that ensures a measure of agreement of intensities between frames. Simulations are obtained using data for the four-dimensional (4-D) NCAT phantom. The data models realistic noise levels in a typical gated myocardial perfusion SPECT study. We show that our simultaneous algorithm produces images with improved spatial resolution characteristics and noise properties compared with those obtained from postsmoothed 4-D maximum likelihood methods. The simulations also demonstrate improved motion estimates over motion estimation using independently reconstructed images

Three-dimensional motion estimation with image reconstruction for gated cardiac ECT

The primary goal of this work was to develop and evaluate a new method for simultaneous three-dimensional motion estimation and image reconstruction for gated cardiac emission computed tomography (ECT). The method employs a two-step iterative procedure for obtaining the motion and reconstructed image estimates. The method was evaluated using both simulated and physical phantoms designed to mimic myocardial perfusion imaging in ECT. In both the simulated and physical phantom studies, the images reconstructed by the simultaneous method showed improved noise characteristics relative to a standard iterative algorithm. The percent error of the motion estimate ranged from 16% to 59% for the simulated phantom study, and 45% to 65% for the physical phantom study, depending on the position within the myocardium.

Modeling the axial extension of a transmission line source within iterative reconstruction via multiple transmission sources

Reconstruction algorithms for transmission tomography have generally assumed that the photons reaching a particular detector bin at a particular angle originate from a single point source. In this paper, we highlight several cases of extended transmission sources, in which it may be useful to approach the estimation of attenuation coefficients as a problem involving multiple transmission point sources. Examined in detail is the case of a fixed transmission line source with a fan-beam collimator. This geometry can result in attenuation images that have significant axial blur. Herein it is also shown, empirically, that extended transmission sources can result in biased estimates of the average attenuation, and an explanation is proposed. The finite axial resolution of the transmission line source configuration is modeled within iterative reconstruction using an expectation-maximization algorithm that was previously derived for estimating attenuation coefficients from single photon emission computed tomography (SPECT) emission data. The same algorithm is applicable to both problems because both can be thought of as involving multiple transmission sources. It is shown that modeling axial blur within reconstruction removes the bias in the average estimated attenuation and substantially improves the axial resolution of attenuation images.

Motion estimation for cardiac emission tomography by optical flow methods.

This paper describes a new method for estimating the 3D, non-rigid object motion in a time sequence of images. The method is a generalization of a standard optical flow algorithm that is incorporated into a successive quadratic approximation framework. The method was evaluated for gated cardiac emission tomography using images obtained from a mathematical, 4D phantom and a physical, dynamic phantom. The results showed that the proposed method offers improved motion estimation accuracy relative to the standard optical flow method. Convergence of the proposed algorithm was evidenced with a monotonically decreasing objective function value with iteration. Practical application of the motion estimation method in cardiac emission tomography includes quantitative myocardial motion estimation and 4D, motion-compensated image reconstruction.

Respiratory motion correction in gated cardiac SPECT using quaternion-based, rigid-body registration

In this article, a new method is introduced for estimating the motion of the heart due to respiration in gated cardiac SPECT using a rigid-body model with rotation parametrized by a unit quaternion. The method is based on minimizing the sum of squared errors between the reference and the deformed frames resulting from the usual optical flow constraint by using an optimized conjugate gradient routine. This method does not require any user-defined parameters or penalty terms, which simplifies its use in a clinical setting. Using a mathematical phantom, the method was quantitatively compared to the principal axis method, as well as an iterative method in which the rotation matrix was represented by Euler angles. The quaternion-based method was shown to be substantially more accurate and robust across a wide range of extramyocardial activity levels than the principal axis method. Compared with the Euler angle representation, the quaternion-based method resulted in similar accuracy but a significant reduction in computation times. Finally, the quaternion-based method was investigated using a respiratory-gated cardiac SPECT acquisition of a human subject. The motion-corrected image has increased sharpness and myocardial uniformity compared to the uncorrected image.

Simultaneous motion estimation and image reconstruction from gated data

In this paper we investigate the problem of simultaneously estimating the non-rigid motion vector field and the emission images in dynamic medical imaging procedures, such as gated cardiac ECT. We consider the case of two datasets, which, for instance, may be applied to the problem of determining the motion and emission intensities of the myocardium between end-diastole and end-systole gated cardiac data. Our method is based on minimizing an objective function consisting of a maximum likelihood image reconstruction term; the strain energy of an elastic material; and an image matching term that ensures a measure of agreement between the reference and deformed gated images. Minimization is achieved by a two-step iterative algorithm which alternately updates the motion vector field and the gated images. Simulations using exact and noisy datasets for a simple 2D phantom demonstrate the feasibility of the proposed method.

Molecular Imaging of the Breast Using a Variable-Angle Slant-Hole Collimator

Purpose: The purpose of this work is to develop an improved method for 3D molecular imaging of the breast using limited angle SPECT. Methods: The proposed method uses a variable-angle slant-hole (VASH) collimator. Rather than rotate the camera around the breast, the VASH collimator allows limited angle, tomographic acquisition while the detector remains stationary and flush against the compression paddle. This design minimizes object-to-detector distance for high spatial resolution. Theoretical analysis is presented of VASH spatial resolution and sensitivity, including depth-of-interaction (DOI) effects and magnification. The theory is compared with Monte Carlo simulation results for a point source and breast phantom including a compression paddle. An iterative reconstruction method for the slant hole data is used. Results: The theoretical model of the VASH system showed good agreement with Monte Carlo simulations based on spatial resolution, including DOI effects, and sensitivity. For 140 keV photons and a NaI(Tl) scintillator, the DOI effect resulted in roughly a 2 mm loss in spatial resolution only in depth dimension; in the other two dimensions the spatial resolution was not affected by DOI. In reconstructed breast phantom images, VASH out-performed a parallel hole SPECT approach in terms of contrast-to-noise ratio. Conclusions: The proposed method for breast imaging using limited angle SPECT and a VASH collimator demonstrated the potential for superior spatial resolution/sensitivity. In addition to high spatial resolution/sensitivity, the system design has advantages of simple detector motion, ability to image close to the chest wall and conducive to on-board biopsy and multi-modal imaging with mammography.

Approximate 3D iterative reconstruction for SPECT.

Compared with slice-by-slice approaches for SPECT reconstruction, three-dimensional iterative methods provide a more accurate physical model and an improved SPECT image. Clinical application of these methods, however, is limited primarily to their computational demands. This paper investigates the methods for approximate 3D iterative reconstruction that greatly reduce this demand by excluding from the reconstruction the smaller magnitude elements of the system matrix. A new method is described which is designed to control the resulting bias in the SPECT image for a given reduction in computation. The approximate methods were compared to fully 3D iterative reconstruction in terms of SPECT image bias and visual quality. All methods were incorporated into the ML-EM algorithm and applied to data from 3D mathematical and experimental brain phantoms. The SPECT images reconstructed by the approximate methods exhibited a positive bias throughout the image that was in general smaller with the new method (in the rage of 2%-6%). The bias was smallest in locally hot regions and largest in locally cold regions. The high quality brain phantom images demonstrated the capability of the new method in realistic imaging contexts. The time per iteration for an entire 3D brain phantom on a modern workstation using the approximate 3D method was 7.0 s.

Wall Motion Estimation for Gated Cardiac Emission Tomography: Physical Phantom Evaluation

The purpose of this work was to develop a physical phantom for testing the accuracy of cardiac wall motion estimation algorithms, and to use the phantom to evaluate several motion estimation and reconstruction methods, including a simultaneous image reconstruction/wall motion estimation algorithm we have developed. Our approach was to attach radioactive markers to the myocardial wall of a dynamic cardiac phantom and to trace the motion of the markers throughout the cardiac cycle via gated SPECT acquisition. Then, without moving the phantom, and after the markers were allowed to decay to negligible levels, the myocardium was injected with 99mTc and a gated SPECT scan was acquired. From the gated myocardial emission data, two wall motion estimation methods were evaluated. The first method was by applying an optical flow algorithm to an optimized OSEM reconstruction of the myocardial emission data. The second was by applying our simultaneous image reconstruction/motion estimation algorithm to the myocardial emission data. The error in the estimated motion fields was described by the average Euclidean distance between the motion of the markers and the estimated motion. Values of 0.15 and 0.14 were found for the average Euclidean distance for the optical flow method applied to OSEM and the simultaneous method, respectively. Image quality was also evaluated and, in agreement with our previous findings, the simultaneous method produced myocardial images with improved noise characteristics and better uniformity in terms of the activity distribution within the myocardium.