Showing papers on "Ordered subset expectation maximization published in 1997"

Iterative process for reconstructing cone-beam tomographic images

Abstract: In the present invention, an iterative process is provided for cone-beam tomography (parallel-beam and fan-beam geometries are considered as its special cases), and applied to metal artifact reduction and local reconstruction from truncated data, as well as image noise reduction. In different embodiments, these iterative processes may be based upon the emission computerized tomography (CT) expectation maximization (EM) formula and/or the algebraic reconstruction technique (ART). In one embodiment, generation of a projection mask and computation of a 3D spatially varying relaxation factor are utilized to compensate for beam divergence, data inconsistence and incompleteness.

Scatter compensation methods in 3D iterative SPECT reconstruction: A simulation study

Abstract: Effects of different scatter compensation methods incorporated in fully 3D iterative reconstruction are investigated. The methods are: (i) the inclusion of an 'ideal scatter estimate' (ISE); (ii) like (i) but with a noiseless scatter estimate (ISE-NF); (iii) incorporation of scatter in the point spread function during iterative reconstruction ('ideal scatter model', ISM); (iv) no scatter compensation (NSC); (v) ideal scatter rejection (ISR), as can be approximated by using a camera with a perfect energy resolution. The iterative method used was an ordered subset expectation maximization (OS-EM) algorithm. A cylinder containing small cold spheres was used to calculate contrast-to-noise curves. For a brain study, global errors between reconstruction and 'true' distributions were calculated. Results show that ISR is superior to all other methods. In all cases considered, ISM is superior to ISE and performs approximately as well as (brain study) or better than (cylinder data) ISE-NF. Both ISM and ISE improve contrast-to-noise curves and reduce global errors, compared with NSC. In the case of ISE, blurring of the scatter estimate with a Gaussian kernel results in slightly reduced errors in brain studies, especially at low count levels. The optimal Gaussian kernel size is strongly dependent on the noise level.

Selection of projection set and the order of calculation in ordered subsets expectation maximization method

Abstract: In ordered subsets expectation maximization (OS-EM) the projection data are grouped into subsets and a pixel in a reconstructed image is updated by using projections in each subset. The aim of the study is to analyze the relationship between the quality of images and the selection of subsets or the access order of calculation among the subsets. The image quality was assessed with the mean square error, chi-square error and newly proposed error measures defined in the frequency domain. The results showed the recovery speed of the low to middle frequency components of an image is increased by the access order in calculation, in which the total number of subsets is divided by two or three, and subsets are accessed with the order separating neighboring subsets as much as possible.

On accelerated cross-reference maximum likelihood estimates for positron emission tomography

Abstract: The state of art of positron emission tomography (PET) takes into account the accidental coincidence events and attenuation. The maximum likelihood estimator can handle this kind of random variation in the reconstruction of a PET image. However, the reconstruction is ill-posed and needs regularization. The boundary information, either from an expert or from the other medical modality of the same object, like the X-ray CT scan, MRT, and so forth, can be used to regularize the reconstruction. The authors have investigated new, efficient and robust approaches to extract the related but incomplete boundary information. Fast algorithms adapted from the expectation/conditional maximization (ECM) and space alternating generalized expectation maximization (SAGE) algorithms are proposed to accelerate the computation. The method of generalized approximate cross validation (GACV) is adjusted to select the penalty parameter from observed data quickly. The Monte Carlo studies demonstrate the improvement.

Direct reconstruction of single-photon emission computed tomography images using retained matrix elements.

Abstract: In clinical applications, two methods of single-photon emission computed tomography (SPECT) reconstruction are widely used. These are filtered backprojection and iterative reconstruction. Filtered backprojection is fast and produces acceptable images. Iterative reconstruction is slow, but produces images of greater accuracy than backprojection. The authors sought to develop a method of SPECT reconstruction that would have the advantages of both established methods: close in speed to backprojection and with the accuracy of iterative reconstruction. This was accomplished by computing a direct solution to the set of linear equations governing SPECT reconstruction. We tested this method of SPECT reconstruction using a set of projections from a cold rod and sphere phantom. Direct reconstruction produced images having equivalent resolution to backprojected images, but with double the contrast ratio. The direct method required 10 seconds of computation per slice on a Macintosh Quadra 950 (Apple Computer; Cupertin, CA), significantly faster than most iterative methods.

Improvements of the ML-EL-algorithm for reconstruction of positron emission tomography images

Abstract: Positron emission tomography (PET) is a technique that has opened new facilities to study the metabolic activity of the human body. In the last years many algorithms have been developed for reconstructing tomography images. The often used maximum likelihood expectation maximization algorithm (ML-EM) seems to be a stable method and was developed by Shepp and Vardi in 1982. However, the ML-EM algorithm causes some serious problems in the context of the application considered. It is an iterative procedure and converges to a stationary point, however, the reconstructed image seems to be distorted by superposed high frequency noise. It is shown, that the ML-EM-algorithm is not based on significant statistical properties in our problem, which has been verified by investigations. As a consequence of these results the algorithm has been modified in two ways. First, the expectation step has been replaced by a deterministic algorithm with accelerated convergence behaviour. Second, prior information is used to improve the statistical performance of the algorithm. Consequently, the algorithm has been changed to a maximum a posteriori estimator.

Synergetically generalized expectation maximization algorithm for ECT

Abstract: A synergetically generalized expectation maximization (SGEM) reconstruction algorithm is proposed, which builds on the expectation maximization approach to maximize the data likelihood, but also takes additional account of multinomial probability models. The authors show how the maximum likelihood expectation maximization algorithm, transformed to its additive form, can be extended by several further additive terms to improve lesion contrast and smoothness of the reconstructed image. Based upon locally correlated Markov random field priors in the form of Gibbs functions, Bayesian reconstruction for maximum a posteriori estimation is applied to include prior models of isotope concentration. For simultaneous image reconstruction and segmentation, a mixture model for clustering of the data is applied in which mixture parameters are recalculated for each iteration. Additional filtering of the data during the expectation maximization process can be done using well-known models from filter theory. The authors describe the application of a nonlinear inhibition filter which is used by the human visual system. The method is illustrated by applications to data from SPECT scans.