High Number Of Iterations Research Articles

Comparison of post-filtering and filtering between iterations for SPECT reconstruction

Iteratively reconstructed Single Photon Emission Computed Tomography (SPECT) images are known to become noisy and exhibit edge-artifacts at high iteration numbers. In order to suppress these undesirable image distortions some method of regularization has to be applied. One of the frequently applied regularization methods is low-pass filtering of the reconstructed image. In this paper SPECT images which have been filtered after a complete iterative reconstruction (post-filtering) are compared to SPECT images which have been filtered in-between each iteration step of the reconstruction (in-between filtering). The comparison of post-filtering and in-between filtering is made for two different kind of filters, a Gaussian filter and an edge-preserving diffusion filter. In order to make a fair comparison of the best possible performance of each method, the specific filters are automatically selected by varying the filter parameters until the difference between a phantom and corresponding filtered SPECT images is minimized (optimal filtering). The resulting minimum of the difference is used as the standard to compare the performance of the filter processes. The difference between optimized post-filtering and optimized in-between filtering is found to be small. In most the cases which were investigated, smoothing in-between iterations with optimized fixed kernels gives slightly less accurate results than optimized post-filtering or optimized in-between filtering. Since post-filtering is much easier to optimize than in-between filtering, post-filtering may be preferred to use in practice.

Selection of task-dependent diffusion filters for the post-processing of SPECT images

Iterative reconstruction from single photon emission computed tomography (SPECT) data requires regularization to avoid noise amplification and edge artefacts in the reconstructed image. This is often accomplished by stopping the iteration process at a relatively low number of iterations or by post-filtering the reconstructed image. The aim of this paper is to develop a method to automatically select an optimal combination of stopping iteration number and filters for a particular imaging situation. To this end different error measures between the distribution of a phantom and a corresponding filtered SPECT image are minimized for different iteration numbers. As a study example, simulated data representing a brain study are used. For post-reconstruction filtering, the performance of 3D linear diffusion (Gaussian filtering) and edge preserving 3D nonlinear diffusion (Catté scheme) is investigated. For reconstruction methods which model the image formation process accurately, error measures between the phantom and the filtered reconstruction are significantly reduced by performing a high number of iterations followed by optimal filtering compared with stopping the iterative process early. Furthermore, this error reduction can be obtained over a wide range of iteration numbers. Only a negligibly small additional reduction of the errors is obtained by including spatial variance in the filter kernel. Compared with Gaussian filtering, Catté diffusion can further reduce the error in some cases. For the examples considered, using accurate image formation models during iterative reconstruction is far more important than the choice of the filter.

Decay of correlations for the automorphism of the torus

We present new analytical results concerning Markov partitions, transition matrices and decay of correlations for hyperbolic algebraic automorphisms of the torus . A new numerical tool for the computation of the decay of correlations for automorphism is also illustrated. The tool, based on Markov partitions, allows us to calculate the correlation integrals for a large variety of functions and domains defined in and for a high number of iterations of the map. It can be used to test other numerical and analytical methods for estimating correlation decay.

Improving the convergence of iterative filtered backprojection algorithms

Several authors have proposed variations of the iterative filtered backprojection (IFBP) reconstruction algorithms claiming fast initial convergence rates. We have found that these algorithms are trying to minimize an unusual squared-error criterion in a suboptimal way. As a result, existing IFBP algorithms are inefficient in the minimization of the criterion, and may become unstable at higher iteration numbers. We show that existing IFBP algorithms can be modified to use the steepest descent technique by simply optimizing the step size at each iteration. Further gains in convergence rates can be achieved with conjugate gradient IFBP algorithms derived from the same criterion. The steepest descent and conjugate gradient IFBP algorithms are guaranteed to converge, unlike some IFBP algorithms, and will do so in fewer iterations than existing IFBP algorithms.

Numerical estimation of adsorption energy distributions from adsorption isotherm data with the expectation-maximization method

The expectation-maximization (EM) method of parameter estimation is used to calculate adsorption energy distributions of molecular probes from their adsorption isotherms. EM does not require prior knowledge of the distribution function, or the isotherm, requires no smoothing of the isotherm data, and converges with high stability toward the maximum-likelihood estimate. The method is therefore robust and accurate at high iteration numbers. The EM algorithm is tested with simulated energy distributions corresponding to unimodel Gaussian, bimodal Gaussian, Poisson distributions, and the distributions resulting from Misra isotherms. Theoretical isotherms are generated from these distributions using the Langmuir model, and then chromatographic band profiles are computed using the ideal model of chromatography. Noise is then introduced in the theoretical band profiles comparable to those observed experimentally. The isotherm is then calculated using the elution-by-characteristic points method. The energy distribution given by the EM method is compared to the original one. The results are contrasted to those obtained with the House and Jaycock algorithm HILDA and shown to be superior in terms of both robustness, accuracy, and information theory. 20 refs., 6 figs., 4 tabs.

Neural Networks for the Segmentation of Teleoperation Tasks

In recent years, research in telemanipulation has been concerned primarily with problems related to the control of teleoperators and their man-machine aspects. As the need for extensive teleoperation for the deployment and maintenance of space systems increases, research needs to focus on techniques to improve operator performance and reduce operator fatigue during telemanipulation. This paper describes the development of an approach to teleoperation task supervision that can be used in advanced man-machine interfaces to monitor teleoperation performance and to help operators with task-level feedback. A Segmentation Program has been designed to identify teleoperation task phases, independently of variations in working conditions and in phase duration and sensor values. The program uses neural networks to segment the force data of a peg-in-hole task into the task phase sequence. The network connections were trained with an off-line Hidden Markov Model of the peg-in-hole task providing specific transition times and task phase sequences. Two network architectures have been tested during simulation with real teleoperation data: the first is based on turning temporal sequences into spatial patterns; the second extends the first model by including network output in the input array. We found that the first architecture needed a higher number of iterations to learn the associations, while the latter had a higher convergency speed and recognition rate. The architecture with the best performance was used in the realtime implementation of the segmentation program on a teleoperation system. In experiments of peg-in-hole tasks, the network had a lower recognition rate than in simulation, but it showed unexpected generalization capabilities by correctly segmenting tasks whose phase sequence was significantly different from those sequences in the training data.

Comparison Between ML-EM And WLS-CG Algorithms For Spect Image Reconstruction

We have studied the properties of two iterative reconstruction algorithms, namely, the maximum likelihood with expectation maximization (ML-EM) and the weighted least squares with conjugate gradient (WLS-CG) algorithms, for use in compensation for attenuation and detector response in cardiac SPECT imaging. A realistic phantom, derived from a patient X-ray CT study to simulate ’OITP SPECT data, was used in the investigation. Both algorithms are effective in compensating for the nonuniform attenuation distribution in the thorax region and the spatially variant detector response function of the imaging system. At low iteration numbers, the addition of detector response compensation provides improvement in both spatial resolution and image noise when compared with attenuation compensation alone. However, at higher iteration numbers, there is a more rapid increase in image noise when detector response compensation is included, and the increase is more dramatic for the WLS-CG algorithm. In general, the convergence rate of the WLS-CG algorithm is about ten times that of the ML-EM algorithm. Also, the WLS-CG exhibits a faster increase in image noise at large iteration numbers than the ML-EM algorithm. This study is valuable in the search for useful and practical reconstruction methods for improved clinical cardiac SPECT imaging.