Application of Quasi Monte Carlo Integration Technique in Em Scattering From Finite Cylinders

Mishra, M. K.; Gupta, Nisha

doi:10.2528/pierl09050806

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…It provides greater contrast between the different soft tissues of the body than computed tomography (CT) does, making it especially useful in neurological (brain), musculoskeletal, cardiovascular, and oncological (cancer) imaging [2,3]. The diagnostic values of MRI are greatly magnified by the automated and accurate classification of the MR images [4,5].…”

Section: Introductionmentioning

confidence: 99%

Magnetic Resonance Brain Image Classification by an Improved Artificial Bee Colony Algorithm

Zhang¹,

Wu²,

Wang³

2011

PIER

168

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Abstract-Automated and accurate classification of magnetic resonance (MR) brain images is a hot topic in the field of neuroimaging. Recently many different and innovative methods have been proposed to improve upon this technology. In this study, we presented a hybrid method based on forward neural network (FNN) to classify an MR brain image as normal or abnormal. The method first employed a discrete wavelet transform to extract features from images, and then applied the technique of principle component analysis (PCA) to reduce the size of the features. The reduced features were sent to an FNN, of which the parameters were optimized via an improved artificial bee colony (ABC) algorithm based on both fitness scaling and chaotic theory. We referred to the improved algorithm as scaled chaotic artificial bee colony (SCABC). Moreover, the K-fold stratified cross validation was employed to avoid overfitting. In the experiment, we applied the proposed method on the data set of T2-weighted MRI images consisting of 66 brain images (18 normal and 48 abnormal). The proposed SCABC was compared with traditional training methods such as BP, momentum BP, genetic algorithm, elite genetic algorithm with migration, simulated annealing, and ABC. Each algorithm was run 20 times to reduce randomness. The results show that our SCABC can obtain the least mean MSE and 100% classification accuracy.

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Section: Introductionmentioning

confidence: 99%

Magnetic Resonance Brain Image Classification by an Improved Artificial Bee Colony Algorithm

Zhang¹,

Wu²,

Wang³

2011

PIER

168

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“…The electromagnetic scattering by canonical physical objects is important in many applications [1][2][3][4][5][6][7][8]. For the case of dielectric cylinder with finite length, an exact analytical solution is still elusive, and several approximation approaches have been proposed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Characterization of the Validity Region of the Extended T-Matrix Method for Scattering From Dielectric Cylinders With Finite Length

Yan¹,

et al. 2009

PIER

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Abstract-The T-matrix approach is effective in analyzing electromagnetic scattering from finite scatterers. Yet for scatterers with extreme geometry, this approach may fail. One example is its inability to analyze scattering from dielectric cylinders with large aspect ratios. To deal with such difficulty, recently we proposed a method based on an extension of the T-matrix approach, where a long cylinder is hypothetically divided into a cluster of identical sub-cylinders, for each the T matrix can be numerically stably calculated. Special care was paid to fulfill the boundary conditions at the hypothetic surface of any two neighboring sub-cylinders. The resultant coupled equations are different from that of multi-scatterer theory. The model results were in good agreement with experiment data available in the literature. However, the validity region of the proposed method was not fully characterized. Now we have developed and validated a method of moment (MoM) code, and are in a position to carry on the task of characterizing the validity region. The proposed method is found to be applicable to dielectric cylinders of arbitrary length as long as the T matrix is attainable for the elementary sub-cylinder. The conditions for the T matrix to be numerically stably calculated in terms of the equivalent volumetric radius and relative dielectric constant are also empirically obtained.

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“…We are interested in problems where the singularity arises along a manifold in [0, 1] d . For motivation, see the engineering applications by Mishra and Gupta in [10] and several other papers. Apart from a few remarks, we focus solely on the problem where there is a singularity along the line x 1 = x 2 in [0, 1] 2 .…”

Section: Introductionmentioning

confidence: 99%

Quasi-Monte Carlo for an Integrand with a Singularity Along a Diagonal in the Square

Basu

Owen

2018

Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

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Quasi-Monte Carlo methods are designed for integrands of bounded variation, and this excludes singular integrands. Several methods are known for integrands that become singular on the boundary of the unit cube [0, 1] d or at isolated possibly unknown points within [0, 1] d . Here we consider functions on the square [0, 1] 2 that may become singular as the point approaches the diagonal line x 1 = x 2 , and we study three quadrature methods. The first method splits the square into two triangles separated by a region around the line of singularity, and applies recently developed triangle QMC rules to the two triangular parts. For functions with a singularity 'no worse than |x 1 − x 2 | −A is' for 0 < A < 1 that method yields an error of O((log(n)/n) (1−A)/2 ). We also consider methods extending the integrand into a region containing the singularity and show that method will not improve upon using two triangles. Finally, we consider transforming the integrand to have a more QMC-friendly singularity along the boundary of the square. This then leads to error rates of O(n −1+ε+A ) when combined with some corner-avoiding Halton points or with randomized QMC but it requires some stronger assumptions on the original singular integrand.

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Application of Quasi Monte Carlo Integration Technique in Em Scattering From Finite Cylinders

Cited by 4 publications

References 10 publications

Magnetic Resonance Brain Image Classification by an Improved Artificial Bee Colony Algorithm

Magnetic Resonance Brain Image Classification by an Improved Artificial Bee Colony Algorithm

Characterization of the Validity Region of the Extended T-Matrix Method for Scattering From Dielectric Cylinders With Finite Length

Quasi-Monte Carlo for an Integrand with a Singularity Along a Diagonal in the Square

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