Increase In Number Of Iterations Research Articles

Restoration of Astrophysical Images—The Case of Poisson Data with Additive Gaussian Noise

We consider the problem of restoring astronomical images acquired with charge coupled device cameras. The astronomical object is first blurred by the point spread function of the instrument-atmosphere set. The resulting convolved image is corrupted by a Poissonian noise due to low light intensity, then, a Gaussian white noise is added during the electronic read-out operation. We show first that the split gradient method (SGM) previously proposed can be used to obtain maximum likelihood (ML) iterative algorithms adapted in such noise combinations. However, when ML algorithms are used for image restoration, whatever the noise process is, instabilities due to noise amplification appear when the iteration number increases. To avoid this drawback and to obtain physically meaningful solutions, we introduce various classical penalization-regularization terms to impose a smoothness property on the solution. We show that the SGM can be extended to such penalized ML objective functions, allowing us to obtain new algorithms leading to maximum a posteriori stable solutions. The proposed algorithms are checked on typical astronomical images and the choice of the penalty function is discussed following the kind of object.

On stable iterative methods of gradient type for the inverse medium scattering problem

In this article we present a class of iterative methods for the inverse problem of 3D acoustic scattering on a penetrable inhomogeneity. We formulate the problem as an ill-posed nonlinear operator equation in a Hilbert space. The proposed methods are based on an approximation of this equation by a strongly convex finite-dimensional variational problem. The strong convexity of the approximating problem plays the key role in a theoretical justification of our approach to numerical approximation of solutions to ill-posed problems. Specifically, this property ensures the stability of the proposed iterative methods with respect to the errors in input data as an iteration number increases. We also present results of computational experiments.

Characterization of ordered-subsets expectation maximization with 3d post-reconstruction gauss filtering and comparison with filtered backprojection in99mTc SPECT

To characterize ordered-subset expectation maximization algorithm with a fixed 3D Gauss post-reconstruction filtering (OSEM) in 99mTc SPECT as for noise, contrast and spatial resolution with varying number of subset and iteration and to compare OSEM with an optimized set of parameters, with filtered backprojection (FBP) with filter parameters typical of brain and myocardial SPECT, both with and without Chang's method of attenuation correction (AC). SPECT images of a Jaszczak phantom with cold rod inserts, hot and cold spheres and capillary line sources were acquired. Different background activity concentrations of the phantom were simulated as well as different lesion-to-background activity ratios. OSEM reconstructions were halted after 5, 10 and 15 iterations using 4, 8 and 16 subsets. The effect of subset and iteration number over noise is additive: thus, it is possible to define an EM-equivalent iteration number that indicates the product between the subset and the iteration numbers. Noise increases linearly with increasing EM-equivalent iteration number. For each level of nominal contrast, the measured contrast after OSEM shows a little increase with increasing iteration number and saturates after 80 EM-equivalent iterations. The application of AC leads to diminished contrast values both in FBP and OSEM. The contrast of cold lesions after OSEM increases with increasing number of EM-equivalent iteration number: after 80 iterations the contrast values with OSEM overtake the ones obtained with FBP; contrast values diminished as background concentration raised. Resolution values did not change with increasing EM-equivalent iteration number and were higher than those obtained with FBP. The major findings of the present work are the demonstration of additivity of subset and iteration in OSEM over noise, with the possibility of defining an EM equivalent iteration number, and the superiority of OSEM with respect to FBP in terms of spatial resolution.

A New Tabu Search Method for Optimization With Continuous Parameters

A new tabu search algorithm for global optimization of multimodal functions with continuous variables is presented. The taboo list contains all points and a prohibited zone around each point that depends on the value of the objective function and decreases as the number of iteration increases. The numerical results obtained by solving problems 22 and 25 of the TEAM workshop demonstrate the speed effectiveness of the proposed method. It is compared favorably with other tabu search, genetic algorithm, and simulated annealing.

Bayesian Reconstruction in SPECT With Entropy Prior and Iterative Statistical Regularization

When reconstructing SPECT data using the maximum a posteriori algorithm with entropy-based prior (MAP-ENT), the effectiveness of the algorithm depends strongly upon the choice of regularization parameter. The problem of choosing an optimal parameter remains still an open question in SPECT. Convergence properties of the MAP-ENT algorithm depending on a regularization parameter are investigated in this paper. The main goal was to study the effect of iteratively adjusting the regularization parameter on stability of the reconstruction process. Numerical tests have shown that there is a tradeoff between the resolution and noise level of the image that changes with iterations. It entails the choice of an appropriate regularization parameter at each iteration step. The iterative regularization was performed in the following way: the "best" regularization parameter was selected at each iteration step by using the adaptive chi-square criterion. A comparison with the maximum-likelihood-based OS-EM algorithm has shown that both (OS-EM and MAP-ENT) algorithms rather confidently lead the solution to a 'feasible' image in a few iterations. Then, as the iteration number increases, the OS-EM solution passes the feasibility area and produces images that begin to deteriorate. The MAP-ENT algorithm retains the solution within the interval due to the dynamic choice of an appropriate regularization parameter.

On Conditioning of a Schwarz Method for Singularly Perturbed Convection–diffusion Equations in the Case of Disturbances in the Data of the Boundary-value Problem

AbstractIn this paper we discuss conditioning of a discrete Schwarz method on piecewise–uniform meshes with an example of a one-dimensional singularly perturbed boundary-value problem. We consider a Dirichlet problem for singularly perturbed ordinary differential equations with convection terms and a small perturbation parameter ε. To solve the problem numerically we use an ε-uniformly convergent (in the maximum norm) difference scheme on special piecewise–uniform meshes. For this base scheme we construct a decomposition scheme based on a Schwarz technique with overlapping subdomains, which converges ε-uniformly with respect to both the number of mesh points and the number of iterations. The step-size of such special meshes is extremely small in the neighborhood of the layer and changes sharply on its boundary, that (as was shown by A.A. Samarskii) can generally lead to a loss of well-conditioning of the above schemes. For the decomposition scheme we study the conditioning of the system (difference scheme) and the conditioning of the system matrix (difference operator), and also the influence of perturbations in the data of the boundary-value problem on disturbances of its numerical solutions. We derive estimates for the disturbances of the numerical solutions (in the maximum norm) depending on the subdomain in which the disturbance of the data appears. It is shown that the condition number of the difference operator associated with the Schwarz method, just as for the base scheme, is not ε-uniformly bounded. However, these difference schemes are well-conditioned ε-uniformly (with the ε-uniform estimate for the condition number being the same as for the schemes on uniform meshes for regular problems) when the right-hand side of the discrete equations is considered in a “natural” norm, i.e., in the maximum norm with a special weight multiplier. In the case of the boundary-value problem with perturbed data we give conditions under which the solution of the iterative scheme based on the overlapping Schwarz method is convergent ε-uniformly to the solution of this Dirichlet problem as the number of mesh points and the number of iterations increase.

SNS Superconducting RF cavity modeling-iterative learning control

The Spallation Neutron Source (SNS) Superconducting RF (SRF) linear accelerator is operated with a pulsed beam. For the SRF control system to track the repetitive electromagnetic field reference trajectory, both feedback and feedforward controllers have been proposed. The feedback controller is utilized to guarantee the closed loop system stability and the feedforward controller is used to improve the tracking performance for the repetitive reference trajectory and to suppress repetitive disturbances. As the iteration number increases, the feedforward controller decreases the tracking error. Numerical simulations demonstrate that inclusion of the feedforward controller significantly improves the control system performance over its performance with just the feedback controller.

Optimization of regularization of attenuation and scatter-corrected /sup 99m/Tc cardiac SPECT studies for defect detection using hybrid images

Through means of a receiver-operating-characteristics study, we optimize the iteration number and three-dimensional (3-D) Gaussian postfiltering of /sup 99m/Tc cardiac emission ordered-subset expectation-maximization (OSEM) reconstructions that implement corrections for both attenuation and scatter. Hybrid images, wherein artificial perfusion defects were added to clinical patient studies that were read as being normally perfused, were used for this optimization. The test conditions included three different iteration numbers of OSEM (1, 5 and 10) using four angles per subset, followed by 3-D Gaussian low-pass filtering at each iteration level. The level of Gaussian low-pass filtering was varied using standard deviations (/spl sigma/) of 0.6, 0.75, 1 and 1.25 pixels, in addition to a case where no postfiltering was applied. Four observers read 80 images for each of the 15 test conditions being investigated, providing confidence ratings as to the presence or absence of perfusion defects. Results indicate that at all iterations, optimum detection performance is obtained for a broad plateau or range of postfilters (/spl sigma/=0.6 to 1 pixel). As expected, a gradual reduction in performance is seen at either end of this broad maximum where the images either have been very heavily smoothed or have very little postfiltering. Finally, one iteration of OSEM appears to be the appropriate choice since no significant improvement in detection accuracy was observed with increasing iteration number as long as the reconstructions are postfiltered with /spl sigma/ in the range of 0.6 to 1 pixel.

Choice of collimator for cardiac SPET when resolution compensation is included in iterative reconstruction.

In clinical cardiac single-photon emission tomography (SPET) studies, collimators of different spatial resolution and geometric efficiency are available for imaging. In selecting the appropriate collimator for clinical use, there is a trade-off between spatial resolution, which can limit the contrast of the reconstructed image, and detection efficiency, which determines the noise in the image. Our objective was to assess which collimator is best suited for cardiac SPET when reconstruction is performed with and without compensation for distance-dependent resolution (CDR). The dynamic MCAT thorax phantom was used to simulate 180 degree technetium-99m cardiac data, acquired using either a general-purpose (GP) or high-resolution (HR) collimator. For GP and HR, the resolution at 15 cm was 11.5 mm and 9.5 mm respectively, and the corresponding relative efficiency was 1.0 and 0.52 respectively. Distance-dependent resolution, attenuation and noise were included in the projection data; scatter was not included. Ordered subsets expectation maximisation reconstruction (subset size 4) was performed with and without CDR. Results were evaluated by comparing the myocardial recovery coefficient and contrast between myocardium and ventricle relative to the original phantom, each plotted for different noise levels corresponding to increasing iteration number. The study demonstrated that, without CDR, HR gave the best results. However, for any given noise level with CDR, GP gave superior recovery and contrast. These findings were confirmed in a physical phantom study. Results suggest that improved reconstruction can be achieved using a GP collimator in combination with resolution compensation.

A high-order iterative learning controller with initial state learning

A common assumption in iterative learning control (ILC) is that the initial states in eachrepetitive operation should be inside a given ball centred at the desired initial states. Thisassumption is critical to the stability analysis, and the size of the ball will directly affectthe final output-trajectory tracking errors. However, the initial state may be unobtainable.In this paper, the assumption can be removed by using a high-order initial-state learningscheme together with a high-order D-type ILC updating law. Nonlinear time-dependentuncertain systems are investigated. Uniform bounds of the tracking errors are obtained.These bounds depend only on the bounds of the differences of the uncertainties anddisturbances between two successive system repetitions, and not on the re-initializationerrors. The unknown desired initial states can be identified through learning iterations.Furthermore, better learning transient behaviour can be expected as the iteration numberincreases, by using the high-order scheme. This result is illustrated by simulations.Keywords: Learning control; repetitive systems; nonlinear systems; uncertainty; trackingcontrol; re-initialization error.

One-Dimensional Model of Magnetic Domain Wall with Self-Induced Anisotropy

A one-dimensional model of the domain wall with a spatially varying easy axis angle is presented. First, the easy axis profile is set to the ideal Bloch wall profile, and the resulting wall profile and wall energy are calculated. This procedure of setting the easy axis profile to the domain wall profile is performed iteratively using numerical techniques. At each iteration the wall profile is calculated using energy minimization. A more gradual evolution of the easy axis profile is also modelled, tilting the easy axis profile towards the domain wall profile with increasing iteration number. For both the abrupt and the gradual evolution, the domain wall width continues to increase and domain wall energy continues to decrease with increasing iteration number. Except for the initial ideal Bloch wall, the exchange energy of the wall is greater than its anisotropy energy. The depinning field to free the pinned wall is also calculated and found to reach an asymptotic value of ≃0.55 HK.

Bayesian classification of polarimetric SAR images using adaptive a priori probabilities

The problem of classifying earth terrain by observed polarimetric scattering properties is tackled with an iterative Bayesian scheme using a priori probabilities adaptively. The first classification is based on the use of fixed and not necessarily equal a priori probabilities, and successive iterations change the a priori probabilities adaptively. The approach is applied to an SAR image in which a single water body covers 10 percent of the image area. The classification accuracy for ocean, urban, vegetated, and total area increase, and the percentage of reclassified pixels decreases greatly as the iteration number increases. The iterative scheme is found to improve the a posteriori classification accuracy of maximum likelihood classifiers by iteratively using the local homogeneity in polarimetric SAR images. A few iterations can improve the classification accuracy significantly without sacrificing key high-frequency detail or edges in the image.

An iterative learning control of robot manipulators

An iterative learning scheme comprising a unique feedforward learning controller and a linear feedback controller is presented. In the feedback loop, the fixed-gain PD controller provides a stable open neighborhood along a desired trajectory. In the feedforward path, on the other hand, a learning control strategy is exploited to predict the desired actuator torques. It is shown that the predicted actuator torque converges to the desired one as the iteration number increases. The convergence is established based on the Lyapunov stability theory. The proposed learning scheme is structurally simple and computationally efficient. Moreover, it possesses two major advantages: the ability to reject unknown deterministic disturbances and the ability to adapt itself to the unknown system parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Spectral computation of Tandem mirror equilibria with Finite Larmor Radius effects

A direct iterative method of solving for Tandem equilibria by moving magnetic field lines in a manner to satisfy the linearized equilibrium equations converges much more rapidly than standard relaxation techniques, typically in under a fifty iterations. At the highest β’s the number of iterations increase, but is still far less than other methods. In quadrupole tandem mirror equilibrium, octupole and higher distortions of the flux surfaces are important which forces us to abandon finite differences in the angle-like flux variable and resort to a spectral decomposition to solve the equilibrium equations. We display equilibria at the high β expected for MFTF-B and show how Finite Larmor Radius (FLR) effects strongly suppress these azimuthal distortions.