Conventional Iterative Techniques Research Articles

Multi-channel Optimization Generative Model for Stable Ultra-Sparse-View CT Reconstruction.

Score-based generative model (SGM) has risen to prominence in sparse-view CT reconstruction due to its impressive generation capability. The consistency of data is crucial in guiding the reconstruction process in SGM-based reconstruction methods. However, the existing data consistency policy exhibits certain limitations. Firstly, it employs partial data from the reconstructed image of iteration process for image updates, which leads to secondary artifacts with compromising image quality. Moreover, the updates to the SGM and data consistency are considered as distinct stages, disregarding their interdependent relationship. Additionally, the reference image used to compute gradients in the reconstruction process is derived from intermediate result rather than ground truth. Motivated by the fact that a typical SGM yields distinct outcomes with different random noise inputs, we propose a Multi-channel Optimization Generative Model (MOGM) for stable ultra-sparse-view CT reconstruction by integrating a novel data consistency term into the stochastic differential equation model. Notably, the unique aspect of this data consistency component is its exclusive reliance on original data for effectively confining generation outcomes. Furthermore, we pioneer an inference strategy that traces back from the current iteration result to ground truth, enhancing reconstruction stability through foundational theoretical support. We also establish a multi-channel optimization reconstruction framework, where conventional iterative techniques are employed to seek the reconstruction solution. Quantitative and qualitative assessments on 23 views datasets from numerical simulation, clinical cardiac and sheep's lung underscore the superiority of MOGM over alternative methods. Reconstructing from just 10 and 7 views, our method consistently demonstrates exceptional performance.

Convergence rate for the hybrid iterative technique to explore the real root of nonlinear problems

This study explored the convergence rate of the hybrid numerical iterative technique (HNIT) for the solution of nonlinear problems (NLPs) of one variable ( f (x) = 0) . It is sightseen that convergence rate is two for the HNIT. By the HNIT, several algebraic and transcendental NLPs of one variable have been illustrated as an approximate real root for efficient performance. In many instances, HNIT is more vigorous and attractive than well-known conventional iterative techniques (CITs). The computational tool MATLAB has been used for the solution of iterative techniques.

Genetic algorithm approach with an adaptive search space based on EM algorithm in two-component mixture Weibull parameter estimation

A mixture of two Weibull distributions (WW) has a variety of usage area from reliability analysis to wind speed modeling. Maximum likelihood (ML) method is the most frequently used method in parameter estimation of WW. Due to the nonlinear nature of the log-likelihood function of WW, usage of iterative techniques is a necessary process. Conventional iterative techniques such as Newton Raphson (NR) require considerable analytical preparatory to work to obtain gradient and may lead to numerical difficulties such as convergence problems. The aim of this paper is to present a genetic algorithm (GA) with an adaptive search space based on the Expectation–Maximization (EM) algorithm to obtain the ML estimators of the parameters of WW. The simulation study is conducted to compare the performances of ML estimators obtained using NR algorithm, EM algorithm, simulated annealing algorithm, and the proposed GA. Furthermore, real data examples are used to compare the efficiency of proposed GA with the existing methods in the literature. Simulation results and real data examples show that the proposed GA has superiority over other techniques in terms of efficiency.

Clinical evaluation of reconstruction and acquisition time for pediatric 18F-FDG brain PET using digital PET/CT.

18F-2-fluoro-2-deoxyglucose (FDG) positron emission tomography (PET) plays an important role in the diagnosis, evaluation and treatment of childhood epilepsy. The selection of appropriate acquisition and reconstruction parameters, however, can be challenging with the introduction of advanced hardware and software functionalities. To quantify the diagnostic performance of a block-sequential regularized expectation maximization (BSREM) tool and reduced effective counts in brain PET/CT for pediatric epilepsy patients on a digital silicon photomultiplier system. We included 400 sets of brain PET/CT images from 25 pediatric patients (0.5-16years old) in this retrospective study. Patient images were reconstructed with conventional iterative techniques or BSREM with varied penalization factor (β), at varied acquisition time (45s, 90s, 180s, 300s) to simulate reduced count density. Two pediatric nuclear medicine physicians reviewed images in random order - blinded to patient, reconstruction method and imaging time - and scored technical quality (noise, spatial resolution, artifacts), clinical quality (image quality of the cortex, basal ganglia and thalamus) and overall diagnostic satisfaction on a 5-point scale. Reconstruction with BSREM improved quality and clinical scores across all count levels, with the greatest benefits in low-count conditions. Image quality scores were greatest at 300-s acquisition times with β=500 (overall; noise; artifacts; image quality of the cortex, basal ganglia and thalamus) or β=200 (spatial resolution). No statistically significant difference in the highest graded reconstruction was observed between imaging at 180s and 300s with an appropriately implemented penalization factor (β=350-500), indicating that a reduction in dose or acquisition time is feasible without reduction in diagnostic satisfaction. Clinical evaluation of pediatric 18F-FDG brain PET image quality was shown to be diagnostic at reductions of count density by 40% using BSREM with a penalization factor of β=350-500. This can be accomplished while maintaining confidence of achieving a diagnostic-quality image.

Selective Harmonics Elimination for PWM Inverters Using the PSO Optimization Technique

Harmonic minimization in PWM inverters is a complex optimization problem which involves non-linear transcendental equations having multiple local minima. In this paper, a solution to the harmonic minimization problem using the particle swarm optimization (PSO) has been proposed to solve the SHE problem. It overcomes the complicated computations associated with conventional iterative techniques. As an example, in this paper a bipolar PWM inverter with seven switching angles per quarter cycle with varying modulation index is considered, and the optimum switching angles are calculated offline to eliminate the 5th,7th, 11th,13th,17th and 19th harmonics. The simulated results are also validated by experiment.

An efficient computational method for mechanical analysis of bimodular structures based on parametric variational principle

The aim of this paper is to develop a stable and efficient computational method for static analysis of bimodular materials and structures, which exhibit different mechanical behaviors in tension and compression. Based on the parametric variational principle (PVP) and finite element method (FEM), a unified constitutive equation with parametric variables is established in the principal stress directions. Eventually, the original problem is evolved into a standard complementary quadratic programming problem that can be solved easily. Compared with conventional iterative techniques, the proposed method does not need the pre-assumption of stress states as well as the update of elastic and stiffness matrices and thus presents an excellent convergence behavior. Numerical examples demonstrate the validity and efficiency of this method.

Harmonic Minimization in Multilevel Inverters Using Modified Species-Based Particle Swarm Optimization

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Harmonic minimization in multilevel inverters is a complex optimization problem that involves nonlinear transcendental equations having multiple local minima. In this paper, a solution to the harmonic minimization problem using a novel particle swarm optimization (PSO) approach based on species-based PSO (SPSO) is presented. The original SPSO is modified, which increased the robustness of algorithm to find global optimum of the search space. The proposed method is able to find the optimum switching angles when their number is increased, while it is not possible to determine them using either conventional iterative techniques or resultant theory method. Theoretical results are verified by experiments and simulations for an 11-level H-bridge inverter. Results show that the proposed method effectively minimizes a large number of specific harmonics, and the output voltage results in very low total harmonic distortion and switching frequency. </para>

Application of constrained least-squares techniques to IMRT treatment planning

Purpose: The purpose of this work was to apply the method of constrained least-squares to inverse treatment planning and to explore its potential for providing a fast interactive planning environment for intensity-modulated radiation therapy (IMRT). Methods and Materials: The description of the dose inside a patient is a linear matrix transformation of beamlet weights. The constrained least-squares method adds additional matrix operators and produces beamlet weights by a direct linear transformation. These matrix operators contain a priori knowledge about the radiation distribution. The constrained least-squares technique was applied to obtain IMRT plans for prostate and paraspinal cancer patients and compared with the corresponding plans optimized using the CORVUS inverse planning system. Results: It was demonstrated that a constrained least-squares technique is suitable for IMRT plan optimization with significantly increased computing speed. For the two cases we have tested, the constrained least-squares method was an order of magnitude faster than conventional iterative techniques because of the avoidance of the iterative calculations. We also found that the constrained least-squares method is capable of generating clinically acceptable treatment plans with less trial-and-error adjustments of system variables, and with improved target volume coverage as well as sensitive structure sparing in comparison with that obtained using CORVUS. Conclusions: The constrained least-squares method has the advantage that it does not require iterative calculation and thus significantly speeds up the therapeutic plan optimization process. Besides shedding important insight into the inverse planning problem, the technique has strong potential to provide a fast and interactive environment for IMRT treatment planning.

Applications of solutions to non-linear energy budget equations

A fourth-order (quartic) and second-order equation is developed to solve the energy budget equation for latent energy flux density. The solutions are compared with conventional iterative techniques and the linearized Penman-Monteith form. The fourth-order and second-order equations are then used to show that the generally accepted expression for equilibrium evapotranspiration is theoretically incorrect, both for infinite aerodynamic resistance and for zero vapor pressure deficit. The new methods give new insights for the analysis of canopy-air temperature differences, interactions between canopy resistance and vapor pressure deficit, the Priestley-Taylor equation, and the Jarvis-McNaughton concept of atmospheric coupling.

A flux preserving method of coupling first and second order equations to simulate the flow of plasma between the protonosphere and the ionosphere

This paper describes a numerical method developed to solve the interhemispheric flow of thermal plasma, heat and momentum along closed magnetic field tubes in the plasmasphere. The essence of our technique incorporates the best aspects of two former approaches into a single unified code. The first is the so-called shooting or searching method, which employs integro-differential equations, and the second involves the solution of second order nonlinear partial differential equations by conventional iterative techniques. The former method attains optimal performance above ∼2000 km, and the latter below this altitude. The combined approach yields a satisfactory solution over an entire geomagnetic flux tube, encompassing two low altitude regimes, in the northern and southern ionospheres, and a high altitude regime spanning the distance between them. We demonstrate that the solution is stable and simulate the collapse of the postsunset ionosphere.