Iterative Decomposition Method Research Articles

To Relay or Not to Relay in Cognitive Radio Sensor Networks

A recent investigation on the medium access control (MAC) layer in cognitive radio networks (CRNs) proposed the primary packet relaying by the secondary node maintaining an extra queue used for this particular addable functionality. Nevertheless, relaying of primary packets may introduce delays on secondary packets called secondary delay and may require an additional power budget to forward the primary packets. Power budget is particularly crucial when a type of sensor network is deployed using devices of limited power resources. In this paper, admission control is employed to efficiently manage this packet-wise relaying process in cognitive radio sensor networks (CRSNs). To be specific, we assume a cognitive packet-relaying scenario with two pairs of primary and secondary users, i.e., transmitter and receiver. We analyze and formulate the secondary delay and the required power budget of the secondary sensor node in relation to the acceptance factor (i.e., admission control parameter) that indicates whether the primary packets are admitted for relaying or not. Having defined the above, we present a tradeoff between the secondary delay and the required power budget by tuning the acceptance factor, which can be tailored to specific chosen values. Based on this behavior, we formulate an optimization problem to minimize the secondary delay over the admission control parameter subject to a limit on the required power budget. Additionally, the constraints related to the stabilities of all individual queues at the primary and secondary networks are taken into account in the proposed optimization problem, due to their interdependence relations. The solution of this problem is provided using iterative decomposition methods, i.e., dual and primal decompositions, using Lagrange multipliers that simplify the original complicated problem and result in a final equivalent dual problem that includes the initial Karush–Kuhn–Tucker (KKT) conditions. We obtain the optimal acceptance factor, while in addition, we highlight the opportunities for extra delay minimization that is provided by relaxing the initial constraints through changing the values of the Lagrange multipliers. Finally, we present the behavior of the secondary delay, assuming infinite and finite queues and assessing thereby the overflow and blocking probabilities, respectively.

MO‐FG‐204‐03: Using Edge‐Preserving Algorithm for Significantly Improved Image‐Domain Material Decomposition in Dual Energy CT

Purpose:To significantly improve dual energy CT (DECT) imaging by establishing a new theoretical framework of image‐domain material decomposition with incorporation of edge‐preserving techniques.Methods:The proposed algorithm, HYPR‐NLM, combines the edge‐preserving non‐local mean filter (NLM) with the HYPR‐LR (Local HighlY constrained backPRojection Reconstruction) framework. Image denoising using HYPR‐LR framework depends on the noise level of the composite image which is the average of the different energy images. For DECT, the composite image is the average of high‐ and low‐energy images. To further reduce noise, one may want to increase the window size of the filter of the HYPR‐LR, leading resolution degradation. By incorporating the NLM filtering and the HYPR‐LR framework, HYPR‐NLM reduces the boost material decomposition noise using energy information redundancies as well as the non‐local mean. We demonstrate the noise reduction and resolution preservation of the algorithm with both iodine concentration numerical phantom and clinical patient data by comparing the HYPR‐NLM algorithm to the direct matrix inversion, HYPR‐LR and iterative image‐domain material decomposition (Iter‐DECT).Results:The results show iterative material decomposition method reduces noise to the lowest level and provides improved DECT images. HYPR‐NLM significantly reduces noise while preserving the accuracy of quantitative measurement and resolution. For the iodine concentration numerical phantom, the averaged noise levels are about 2.0, 0.7, 0.2 and 0.4 for direct inversion, HYPR‐LR, Iter‐ DECT and HYPR‐NLM, respectively. For the patient data, the noise levels of the water images are about 0.36, 0.16, 0.12 and 0.13 for direct inversion, HYPR‐LR, Iter‐DECT and HYPR‐NLM, respectively. Difference images of both HYPR‐LR and Iter‐DECT show edge effect, while no significant edge effect is shown for HYPR‐NLM, suggesting spatial resolution is well preserved for HYPR‐NLM.Conclusion:HYPR‐NLM provides an effective way to reduce the generic magnified image noise of dual–energy material decomposition while preserving resolution.This work is supported in part by NIH grants 7R01HL111141 and 1R01‐EB016777. This work is also supported by the Natural Science Foundation of China (NSFC Grant No. 81201091), Fundamental Research Funds for the Central Universities in China, and Fund Project for Excellent Abroad Scholar Personnel in Science and Technology.

An iterative decomposition method for scatterer reconstruction in [formula omitted

In this paper we investigate an iterative method to reconstruct the unknown scatter in R3, with only the far-field pattern for just one incident wave. We introduce a general boundary condition and prove its Fréchet derivative. Then this iterative method is able to implement without the boundary condition of the scatterer provided. In practical, one can obtain a better reconstruction without a forward solver at each step. The numerical experiments show the feasibility of this method.

Formulations and exact solution approaches for the degree preserving spanning tree problem

Given a connected and undirected graph G, the degree preserving spanning tree problem (DPSTP) asks for a spanning tree of G with the maximum number of vertices having the same degree in the tree and in G. These are called full degree vertices. We introduce integer programming formulations, valid inequalities and four exact solution approaches based on different formulations. Two branch‐and‐bound procedures, a branch‐and‐cut (BC) algorithm and an iterative probing combinatorial Benders decomposition method are introduced here. The problem of optimally lifting one of the classes of valid inequalities proposed here is equivalent to solving a DPSTP instance, for a conveniently defined subgraph of G. We thus apply one of the proposed methods to optimally lift these cuts, within the other solution methods. In doing so, two additional algorithms, a hybrid Benders decomposition and a hybrid BC are proposed. Extensive computational experiments are conducted with the solution algorithms introduced in this study. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(4), 329–343 2015

Sub-Domain Decomposition Iterative Method Combined With ACA: An Efficient Technique for the Scattering From a Large Highly Conducting Rough Sea Surface

The sub-domain decomposition iterative method (SDIM) is presented to solve efficiently a large linear system obtained by sampling the boundary integral equations from the method of moments. Then, this new technique is tested on the electromagnetic scattering problem from a large highly conducting one-dimensional rough sea surface. The diagonal blocks are the local impedance matrices corresponding to the geometry sub-domains while the off-diagonal blocks are the coupling matrices describing the interaction between two different sub-domains. The principle of SDIM is to invert the impedance matrix by blocks reducing significantly the complexity in comparison to a direct LU inversion of the whole impedance matrix. In addition, to accelerate the matrix-vector products and to reduce the memory requirement, the adaptive cross approximation (ACA) is applied to compress the sub-domain coupling matrices. For microwave frequencies, the results show that SDIM converges rapidly and faster for the TM polarization. Moreover, the mean compression ratio of ACA is of the order of 98%, which makes this method very efficient.

Re-examination of Chinese semantic processing and syntactic processing: evidence from conventional ERPs and reconstructed ERPs by residue iteration decomposition (RIDE).

A number of studies have explored the time course of Chinese semantic and syntactic processing. However, whether syntactic processing occurs earlier than semantics during Chinese sentence reading is still under debate. To further explore this issue, an event-related potentials (ERPs) experiment was conducted on 21 native Chinese speakers who read individually-presented Chinese simple sentences (NP1+VP+NP2) word-by-word for comprehension and made semantic plausibility judgments. The transitivity of the verbs was manipulated to form three types of stimuli: congruent sentences (CON), sentences with a semantically violated NP2 following a transitive verb (semantic violation, SEM), and sentences with a semantically violated NP2 following an intransitive verb (combined semantic and syntactic violation, SEM+SYN). The ERPs evoked from the target NP2 were analyzed by using the Residue Iteration Decomposition (RIDE) method to reconstruct the ERP waveform blurred by trial-to-trial variability, as well as by using the conventional ERP method based on stimulus-locked averaging. The conventional ERP analysis showed that, compared with the critical words in CON, those in SEM and SEM+SYN elicited an N400–P600 biphasic pattern. The N400 effects in both violation conditions were of similar size and distribution, but the P600 in SEM+SYN was bigger than that in SEM. Compared with the conventional ERP analysis, RIDE analysis revealed a larger N400 effect and an earlier P600 effect (in the time window of 500–800 ms instead of 570–810ms). Overall, the combination of conventional ERP analysis and the RIDE method for compensating for trial-to-trial variability confirmed the non-significant difference between SEM and SEM+SYN in the earlier N400 time window. Converging with previous findings on other Chinese structures, the current study provides further precise evidence that syntactic processing in Chinese does not occur earlier than semantic processing.

Approximation of Higher-order Singular Initial and Boundary Value Problems by Iterative Decomposition and Bernstein Polynomial Methods

DOI: 10.9734/BJMCS/2015/17157 Editor(s): (1) Dijana Mosi c, Department of Mathematics, University of Niˇs, Serbia. Reviewers: (1) Anonymous, University of Azad Jammu & Kashmir, Muzaffarabad, Pakistan. (2) A. Qayyum, Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Malaysia. (3) Anonymous, USA. Complete Peer review History: http://sciencedomain.org/review-history/9850

An Algorithm for the Approximation of Fractional Differential-Algebraic Equations with Caputo-type Derivatives

In this paper, we propose an algorithm to obtain approximate solutions of Fractional Differential-Algebraic Equations with Caputo-type derivatives. The method, Iterative Decomposition Method presents solutions as rapidly convergent infinite series of easily computable terms. Numerical examples are considered to highlight the significant features of the IDM, as well as illustrate the efficiency and accuracy of the method, when compared with known methods.

Nonlinear integer transportation problem with additional supply and consumption points

An iterative decomposition method based on the sequential solution of two-dimensional problems subject to constraints from different groups is successfully applied to the case of integer transportation problems with convex objective functions and ascribed suppliers and consumers is proposed. Through the introduction of new variables, it has been possible to extend the constructions of the algorithm in which the central point is the solution of optimization problems with two constraints. A detailed analysis of these problems is presented in the present paper.

A possible modification of groundwater flow equation using coordinate transformations

We described a groundwater model with prolate spheroid coordinates, and introduced a new parameter, namely τ the silhouette influence of the geometric under which the water flows. At first, we supposed that the silhouette influence approaches zero; under this assumption, the modified equation collapsed to the ordinary groundwater flow equation. We proposed an analytical solution to the standard version of groundwater as a function of time, space and uncertainty factor α. Our proposed solution was in good agreement with experimental data. We presented a good approximation to the exponential integral. We obtained an asymptotic special solution to the modified equation by means of the Adomian decomposition and variational iteration methods.

Variational Statement and Domain Decomposition Algorithms for Bitsadze-Samarskii Nonlocal Boundary Value Problem for Poisson’s Two-Dimensional Equation

The Bitsadze-Samarskii nonlocal boundary value problem is considered. Variational formulation is done. The domain decomposition and Schwarz-type iterative methods are used. The parallel algorithm as well as sequential ones is investigated.

Numerical Approximation of Fractional Integro-differential Equations by an Iterative Decomposition Method

In this paper, an attempt is made to approximate the solution of linear and nonlinear fractional integro-differential equations, by applying an iterative decomposition method. The approximate solution of each problem is presented as a rapidly convergent series of easily computable terms. Results obtained are compared favourably with known results to illustrate the accuracy and efficiency of the method.

TU-F-18A-06: Dual Energy CT Using One Full Scan and a Second Scan with Very Few Projections

Purpose: The conventional dual energy CT (DECT) requires two full CT scans at different energy levels, resulting in dose increase as well as imaging errors from patient motion between the two scans. To shorten the scan time of DECT and thus overcome these drawbacks, we propose a new DECT algorithm using one full scan and a second scan with very few projections by preserving structural information. Methods: We first reconstruct a CT image on the full scan using a standard filtered-backprojection (FBP) algorithm. We then use a compressed sensing (CS) based iterative algorithm on the second scan for reconstruction from very few projections. The edges extracted from the first scan are used as weights in the Objectives: function of the CS-based reconstruction to substantially improve the image quality of CT reconstruction. The basis material images are then obtained by an iterative image-domain decomposition method and an electron density map is finally calculated. The proposed method is evaluated on phantoms. Results: On the Catphan 600 phantom, the CT reconstruction mean error using the proposed method on 20 and 5 projections are 4.76% and 5.02%, respectively. Compared with conventional iterative reconstruction, the proposed edge weighting preserves object structures and achieves a better spatial resolution. With basis materials of Iodine and Teflon, our method on 20 projections obtains similar quality of decomposed material images compared with FBP on a full scan and the mean error of electron density in the selected regions of interest is 0.29%. Conclusion: We propose an effective method for reducing projections and therefore scan time in DECT. We show that a full scan plus a 20-projection scan are sufficient to provide DECT images and electron density with similar quality compared with two full scans. Our future work includes more phantom studies to validate the performance of our method.

Iterative image‐domain decomposition for dual‐energy CT

Dual energy CT (DECT) imaging plays an important role in advanced imaging applications due to its capability of material decomposition. Direct decomposition via matrix inversion suffers from significant degradation of image signal-to-noise ratios, which reduces clinical values of DECT. Existing denoising algorithms achieve suboptimal performance since they suppress image noise either before or after the decomposition and do not fully explore the noise statistical properties of the decomposition process. In this work, the authors propose an iterative image-domain decomposition method for noise suppression in DECT, using the full variance-covariance matrix of the decomposed images. The proposed algorithm is formulated in the form of least-square estimation with smoothness regularization. Based on the design principles of a best linear unbiased estimator, the authors include the inverse of the estimated variance-covariance matrix of the decomposed images as the penalty weight in the least-square term. The regularization term enforces the image smoothness by calculating the square sum of neighboring pixel value differences. To retain the boundary sharpness of the decomposed images, the authors detect the edges in the CT images before decomposition. These edge pixels have small weights in the calculation of the regularization term. Distinct from the existing denoising algorithms applied on the images before or after decomposition, the method has an iterative process for noise suppression, with decomposition performed in each iteration. The authors implement the proposed algorithm using a standard conjugate gradient algorithm. The method performance is evaluated using an evaluation phantom (Catphan©600) and an anthropomorphic head phantom. The results are compared with those generated using direct matrix inversion with no noise suppression, a denoising method applied on the decomposed images, and an existing algorithm with similar formulation as the proposed method but with an edge-preserving regularization term. On the Catphan phantom, the method maintains the same spatial resolution on the decomposed images as that of the CT images before decomposition (8 pairs/cm) while significantly reducing their noise standard deviation. Compared to that obtained by the direct matrix inversion, the noise standard deviation in the images decomposed by the proposed algorithm is reduced by over 98%. Without considering the noise correlation properties in the formulation, the denoising scheme degrades the spatial resolution to 6 pairs/cm for the same level of noise suppression. Compared to the edge-preserving algorithm, the method achieves better low-contrast detectability. A quantitative study is performed on the contrast-rod slice of Catphan phantom. The proposed method achieves lower electron density measurement error as compared to that by the direct matrix inversion, and significantly reduces the error variation by over 97%. On the head phantom, the method reduces the noise standard deviation of decomposed images by over 97% without blurring the sinus structures. The authors propose an iterative image-domain decomposition method for DECT. The method combines noise suppression and material decomposition into an iterative process and achieves both goals simultaneously. By exploring the full variance-covariance properties of the decomposed images and utilizing the edge predetection, the proposed algorithm shows superior performance on noise suppression with high image spatial resolution and low-contrast detectability.

Ensemble level multiscale finite element and preconditioner for channelized systems and applications

We consider multiscale flow in porous media. We assume that we can characterize the ensemble of all possible flow scenarios, that is, we can describe all possible permeability configurations needed for the simulations. We construct coarse basis functions that can provide inexpensive coarse approximations that are: (1) adequate for all possible flow scenarios in the given ensemble, (2) robust with respect to the small scales and high variations in each flow scenario. The coarse approximations developed here can be used as a multiscale finite element method, or as the coarse solver in a two-level domain decomposition iterative method. The methods presented here extend, to the ensemble case, some of the results in [J. Galvis, Y. Efendiev, Domain decomposition preconditioners for multiscale flows in high-contrast media: reduced dimension coarse spaces, SIAM Multiscale Model. Simul. 8 (5) (2010) 1621–1644] and [Y. Efendiev, J. Galvis, X.H. Wu, Multiscale finite element methods for high-contrast problems using local spectral basis functions, J. Comput. Phys. 230 (4) (2011) 937–955]. Specifically, ensembles of permeability fields with high-contrast channels and inclusions are considered. Our main objective here is to construct special multiscale basis functions for the whole ensemble of flow scenarios. The coarse basis functions are pre-computed for (selected or constructed) permeability fields with certain topological properties. This procedure is a preprocessing step and it avoids constructing basis functions (or computing upscaling parameters) for each permeability realization. Then, for any permeability, the solution of elliptic equation can be project to the space spanned by these pre-computed basis functions. We apply this coarse multiscale solver to the design of two-level domain decomposition preconditioner. Numerical experiments show that the ensemble level multiscale finite element method converges to the reference solution. Numerical experiments also show that the ensemble level domain decomposition preconditioner condition number is independent of the high-contrast in the coefficient.

An Efficient Method for Detecting Slow-Moving Weak Targets in Sea Clutter Based on Time–Frequency Iteration Decomposition

The echo scattered from a slow-moving weak target on sea surface is nonstationary due to the influence of waves. Time-frequency distributions are good tools to analyze it. In this paper, we propose a method for detecting slow-moving weak targets in sea clutter, which is based on time-frequency iteration decomposition. This method consists of three stages. First, we present a fast signal synthesis method (FSSM) based on eigenvalue decomposition. The FSSM can synthesize a signal faster and more accurately from the Wigner distribution (WD). Then, we present a signal iteration decomposition method (IDM) from the masked WD and the FSSM. By the IDM, the small component of a signal can be obtained, even when it is very close to a large component in the time-frequency plane. Finally, the proposed method results from the IDM and two criteria. Here the two criteria are defined to select the target signal. The proposed method is evaluated by X-band sea echo with a weak simulated target or a real target. The results demonstrate that it not only detects the slow-moving weak target but also shows its instantaneous state.

A posteriori analysis and adaptive error control for operator decomposition solution of coupled semilinear elliptic systems

SUMMARYIn this paper, we develop an a posteriori error analysis for operator decomposition iteration methods applied to systems of coupled semilinear elliptic problems. The goal is to compute accurate error estimates that account for the combined effects arising from numerical approximation (discretization) and operator decomposition iteration. In an earlier paper, we considered ‘triangular’ systems that can be solved without iteration. In contrast, operator decomposition iterative methods for fully coupled systems involve an iterative solution technique. We construct an error estimate for the numerical approximation error that specifically addresses the propagation of error between iterates and provide a computable estimate for the iteration error arising because of the decomposition of the operator. Finally, we develop an adaptive discretization strategy to systematically reduce the discretization error.Copyright © 2013 John Wiley & Sons, Ltd.

Iterative decomposition method for small foot-print LiDAR waveform

针对传统LiDAR波形数据分解方法受噪声影响严重、对复杂重叠及微弱回波分解能力不足的缺点，提出了一种新波形分解方法.通过计算滤波前后波形的幅值变化，估计波形的随机与背景噪声; 采用逐层剥离的策略，从原始波形数据中不断分解出波形分量，直到剩余波形中最大峰值小于一定的阈值; 利用L-BFGS算法优化初始参数，获得波形分量参数的最优解; 最后对位置过近的波形分量进行合并.该方法计算速度快，探测微弱回波能力强，显著提高分解后点云的密度与精度.对大量LiDAR波形数据进行了分解，验证了其有效性.

New variational iteration decomposition method for solving twelfth order boundary value problems

New variational iteration decomposition method for solving twelfth order boundary value problems

2011年4月11日福島県浜通りの地震（<I>M</I><SUB>j</SUB>7.0）の震源過程

The rupture process of the April 11, 2011 Fukushima Hamadori earthquake (Mj 7.0), which is one of the induced earthquakes by the 2011 Tohoku earthquake (Mw 9.0), is investigated using near-field strong motion waveforms. After the Fukushima Hamadori earthquake, distinct normal fault type surface ruptures were recognized in the source area. Those surface ruptures line up along the previously-known fault traces, Idosawa fault and Yunotake fault, which exist about 10km apart each other in echelon. We first apply the iterative decomposition method to confirm that these faults acted at the almost same instant whether or not. Additionally, relocation of hypocenters of aftershocks using double-difference method is performed. These results show that the two normal faults slipped with the delay of about 10 s. Two fault segments are assumed according to those results and the multi time window inversion method is applied to determine detailed rupture process on the faults. As the result, total moment of 1.1×1019Nm (Mw 6.6) and the maximum slip of 2.5m on the Idosawa segment are recovered. The result shows that the Idosawa segment acted first and the Yunotake segment slipped after that. Finally, the static Coulomb failure stress change (ΔCFF) on the Yunotake segment gained by the slip on the Idosawa segment is calculated. The ΔCFF in the large slip area on the Yunotake segment is positive and it suggests that the stress change gained by the Idosawa segment induced the slip on the Yunotake segment.