Search results for: regularization method Fourier spectral method

Authors: Zhenyu Zhao, Lei You

Abstract:

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

Keywords: Analytic continuation, ill-posed problem, regularization method Fourier spectral method, the discrepancy principle.

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Authors: Yiqin Lin, Liang Bao

Abstract:

This paper is devoted to the numerical solution of large-scale linear ill-posed systems. A multilevel regularization method is proposed. This method is based on a synthesis of the Arnoldi-Tikhonov regularization technique and the multilevel technique. We show that if the Arnoldi-Tikhonov method is a regularization method, then the multilevel method is also a regularization one. Numerical experiments presented in this paper illustrate the effectiveness of the proposed method.

Keywords: Discrete ill-posed problem, Tikhonov regularization, discrepancy principle, Arnoldi process, multilevel method.

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Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

Abstract:

Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: Fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization.

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Authors: Ou Xie, Zhenyu Zhao

Abstract:

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.

Keywords: Ill-posed problem, Unknown source, Poisson equation, Tikhonov regularization method, Discrepancy principle

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Authors: Mohamad Reza. Mohaghegh, Majid. Malek Jafarian

Abstract:

This research proposes an algorithm for the simulation of time-periodic unsteady problems via the solution unsteady Euler and Navier-Stokes equations. This algorithm which is called Time Spectral method uses a Fourier representation in time and hence solve for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). Mathematical tools used here are discrete Fourier transformations. It has shown tremendous potential for reducing the computational cost compared to conventional time-accurate methods, by enforcing periodicity and using Fourier representation in time, leading to spectral accuracy. The accuracy and efficiency of this technique is verified by Euler and Navier-Stokes calculations for pitching airfoils. Because of flow turbulence nature, Baldwin-Lomax turbulence model has been used at viscous flow analysis. The results presented by the Time Spectral method are compared with experimental data. It has shown tremendous potential for reducing the computational cost compared to the conventional time-accurate methods, by enforcing periodicity and using Fourier representation in time, leading to spectral accuracy, because results verify the small number of time intervals per pitching cycle required to capture the flow physics.

Keywords: Time Spectral Method, Time-periodic unsteadyflow, Discrete Fourier transform, Pitching airfoil, Turbulence flow

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Authors: Young-Seok Choi

Abstract:

We present a normalized LMS (NLMS) algorithm with robust regularization. Unlike conventional NLMS with the fixed regularization parameter, the proposed approach dynamically updates the regularization parameter. By exploiting a gradient descent direction, we derive a computationally efficient and robust update scheme for the regularization parameter. In simulation, we demonstrate the proposed algorithm outperforms conventional NLMS algorithms in terms of convergence rate and misadjustment error.

Keywords: Regularization, normalized LMS, system identification, robustness.

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Authors: M. K. Balyan

Abstract:

The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Keywords: Dynamical diffraction, hologram, object image, X-ray holography.

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

Abstract:

The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L₂. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: Arbitrary cross section waveguide, analytical regularization method, evolutionary equations of electromagnetic theory of time-domain, TM field.

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Authors: Khalid M. Aamir, Mohammad A. Maud

Abstract:

Power Spectral Density (PSD) of quasi-stationary processes can be efficiently estimated using the short time Fourier series (STFT). In this paper, an algorithm has been proposed that computes the PSD of quasi-stationary process efficiently using offline autoregressive model order estimation algorithm, recursive parameter estimation technique and modified sliding window discrete Fourier Transform algorithm. The main difference in this algorithm and STFT is that the sliding window (SW) and window for spectral estimation (WSA) are separately defined. WSA is updated and its PSD is computed only when change in statistics is detected in the SW. The computational complexity of the proposed algorithm is found to be lesser than that for standard STFT technique.

Keywords: Power Spectral Density (PSD), quasi-stationarytime series, short time Fourier Transform, Sliding window DFT.

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Authors: Sarun Phibanchon

Abstract:

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

Keywords: soliton, iterative method, spectral method, plasma

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Authors: S.Solaymani, T.Ghodselahi, N.B.Nezafat, H.Zahrabi, A.Gelali

Abstract:

The morphological parameter of a thin film surface can be characterized by power spectral density (PSD) functions which provides a better description to the topography than the RMS roughness and imparts several useful information of the surface including fractal and superstructure contributions. Through the present study Nanoparticle copper/carbon composite films were prepared by co-deposition of RF-Sputtering and RF-PECVD method from acetylene gas and copper target. Surface morphology of thin films is characterized by using atomic force microscopy (AFM). The Carbon content of our films was obtained by Rutherford Back Scattering (RBS) and it varied from .4% to 78%. The power values of power spectral density (PSD) for the AFM data were determined by the fast Fourier transform (FFT) algorithms. We investigate the effect of carbon on the roughness of thin films surface. Using such information, roughness contributions of the surface have been successfully extracted.

Keywords: Atomic force microscopy, Fast Fourier transform, Power spectral density, RBS.

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Authors: Young-Seok Choi

Abstract:

We propose two affine projection algorithms (APA) with variable regularization parameter. The proposed algorithms dynamically update the regularization parameter that is fixed in the conventional regularized APA (R-APA) using a gradient descent based approach. By introducing the normalized gradient, the proposed algorithms give birth to an efficient and a robust update scheme for the regularization parameter. Through experiments we demonstrate that the proposed algorithms outperform conventional R-APA in terms of the convergence rate and the misadjustment error.

Keywords: Affine projection, regularization, gradient descent, system identification.

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Authors: R. Bremananth

Abstract:

Acoustic Imaging based sound localization using microphone array is a challenging task in digital-signal processing. Discrete Fourier transform (DFT) based near-field acoustical holography (NAH) is an important acoustical technique for sound source localization and provide an efficient solution to the ill-posed problem. However, in practice, due to the usage of small curtailed aperture and its consequence of significant spectral leakage, the DFT could not reconstruct the active-region-of-sound (AROS) effectively, especially near the edges of aperture. In this paper, we emphasize the fundamental problems of DFT-based NAH, provide a solution to spectral leakage effect by the extrapolation based on linear predictive coding and 2D Tukey windowing. This approach has been tested to localize the single and multi-point sound sources. We observe that incorporating extrapolation technique increases the spatial resolution, localization accuracy and reduces spectral leakage when small curtail aperture with a lower number of sensors accounts.

Keywords: Acoustic Imaging, Discrete Fourier Transform (DFT), k-space wavenumber, Near-Field Acoustical Holography (NAH), Source Localization, Spectral Leakage.

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Authors: Yanping Liao, Congcong He, Ruigang Zhao

Abstract:

The application of magnetocardiography signals to detect cardiac electrical function is a new technology developed in recent years. The magnetocardiography signal is detected with Superconducting Quantum Interference Devices (SQUID) and has considerable advantages over electrocardiography (ECG). It is difficult to extract Magnetocardiography (MCG) signal which is buried in the noise, which is a critical issue to be resolved in cardiac monitoring system and MCG applications. In order to remove the severe background noise, the Total Variation (TV) regularization method is proposed to denoise MCG signal. The approach transforms the denoising problem into a minimization optimization problem and the Majorization-minimization algorithm is applied to iteratively solve the minimization problem. However, traditional TV regularization method tends to cause step effect and lacks constraint adaptability. In this paper, an improved TV regularization method for denoising MCG signal is proposed to improve the denoising precision. The improvement of this method is mainly divided into three parts. First, high-order TV is applied to reduce the step effect, and the corresponding second derivative matrix is used to substitute the first order. Then, the positions of the non-zero elements in the second order derivative matrix are determined based on the peak positions that are detected by the detection window. Finally, adaptive constraint parameters are defined to eliminate noises and preserve signal peak characteristics. Theoretical analysis and experimental results show that this algorithm can effectively improve the output signal-to-noise ratio and has superior performance.

Keywords: Constraint parameters, derivative matrix, magnetocardiography, regular term, total variation.

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Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

Abstract:

As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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Authors: Jyotsna Singh, Parul Garg, Alok Nath De

Abstract:

In this paper, we present a non-blind technique of adding the watermark to the Fourier spectral components of audio signal in a way such that the modified amplitude does not exceed the maximum amplitude spread (MAS). This MAS is due to individual Discrete fourier transform (DFT) coefficients in that particular frame, which is derived from the Energy Spreading function given by Schroeder. Using this technique one can store double the information within a given frame length i.e. overriding the watermark on the host of equal length with least perceptual distortion. The watermark is uniformly floating on the DFT components of original signal. This helps in detecting any intentional manipulations done on the watermarked audio. Also, the scheme is found robust to various signal processing attacks like presence of multiple watermarks, Additive white gaussian noise (AWGN) and mp3 compression.

Keywords: Discrete Fourier Transform, Spreading Function, Watermark, Pseudo Noise Sequence, Spectral Masking Effect

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Authors: J. P. Dubois

Abstract:

Pulse code modulation is a widespread technique in digital communication with significant impact on existing modern and proposed future communication technologies. Its widespread utilization is due to its simplicity and attractive spectral characteristics. In this paper, we present a new approach to the spectral analysis of PCM signals using Riemann-Stieltjes integrals, which is very accurate for high bit rates. This approach can serve as a model for similar spectral analysis of other competing modulation schemes.

Keywords: Coding, discrete Fourier, power spectral density, pulse code modulation, Riemann-Stieltjes integrals.

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Authors: F. Ekoue, A. Fouache d'Halloy, D. Gigon, G Plantamp, E. Zajdman

Abstract:

This work focuses on analysis of classical heat transfer equation regularized with Maxwell-Cattaneo transfer law. Computer simulations are performed in MATLAB environment. Numerical experiments are first developed on classical Fourier equation, then Maxwell-Cattaneo law is considered. Corresponding equation is regularized with a balancing diffusion term to stabilize discretizing scheme with adjusted time and space numerical steps. Several cases including a convective term in model equations are discussed, and results are given. It is shown that limiting conditions on regularizing parameters have to be satisfied in convective case for Maxwell-Cattaneo regularization to give physically acceptable solutions. In all valid cases, uniform convergence to solution of initial heat equation with Fourier law is observed, even in nonlinear case.

Keywords: Maxwell-Cattaneo heat transfers equations, fourierlaw, heat conduction, numerical solution.

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Authors: R. B. Ogunrinde, C. C. Jibunoh

Abstract:

In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: Spectral decomposition, eigenvalues of the Jacobian, linear RHS, homogeneous linear systems.

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Authors: Xueting Liu, Daojin Song, Chuandai Dong, Hongkui Li

Abstract:

From a set of shifted, blurred, and decimated image , super-resolution image reconstruction can get a high-resolution image. So it has become an active research branch in the field of image restoration. In general, super-resolution image restoration is an ill-posed problem. Prior knowledge about the image can be combined to make the problem well-posed, which contributes to some regularization methods. In the regularization methods at present, however, regularization parameter was selected by experience in some cases and other techniques have too heavy computation cost for computing the parameter. In this paper, we construct a new super-resolution algorithm by transforming the solving of the System stem Є=An into the solving of the equations X+A*X-1A=I , and propose an inverse iterative method.

Keywords: High-resolution MAP image, Reconstruction, Image interpolation, Motion Estimation, Hermitian positive definite solutions.

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Authors: Mahamed G.H. Omran, Andries P Engelbrecht, Ayed Salman

Abstract:

An end-member selection method for spectral unmixing that is based on Particle Swarm Optimization (PSO) is developed in this paper. The algorithm uses the K-means clustering algorithm and a method of dynamic selection of end-members subsets to find the appropriate set of end-members for a given set of multispectral images. The proposed algorithm has been successfully applied to test image sets from various platforms such as LANDSAT 5 MSS and NOAA's AVHRR. The experimental results of the proposed algorithm are encouraging. The influence of different values of the algorithm control parameters on performance is studied. Furthermore, the performance of different versions of PSO is also investigated.

Keywords: End-members selection, multispectral satellite imagery, particle swarm optimization, spectral unmixing.

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Authors: K-L. Areerak, K-N. Areerak

Abstract:

The paper deals with the comparison study of harmonic detection methods for a shunt active power filter. The %THD and the power factor value at the PCC point after compensation are considered for the comparison. There are three harmonic detection methods used in the paper that are synchronous reference frame method, synchronous detection method, and DQ axis with Fourier method. In addition, the ideal current source is used to represent the active power filter by assuming an infinitely fast controller action of the active power filter. The simulation results show that the DQ axis with Fourier method provides the minimum %THD after compensation compared with other methods. However, the power factor value at the PCC point after compensation is slightly lower than that of synchronous detection method.

Keywords: Harmonic detection, shunt active power filter, DQaxis with Fourier, power factor.

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Authors: Khalid M. Aamir, Mohammad A. Maud

Abstract:

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. In this paper, recursive version of the Wiener-Khintchine theorem has been derived by using the sliding DFT approach meant for computation of STFT. The computational complexity of the proposed recursive Wiener-Khintchine algorithm, for a window size of N, is O(N).

Keywords: Power Spectral Density (PSD), Wiener-KhintchineTheorem, Periodogram, Short Time Fourier Transform (STFT), TheSliding DFT.

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Authors: Nikhat Nawaz, S. Srinivasulu, P. Kesava Rao

Abstract:

Feature extraction plays an important role in many remote sensing applications. Automatic extraction of water bodies is of great significance in many remote sensing applications like change detection, image retrieval etc. This paper presents a procedure for automatic extraction of water information from remote sensing images. The algorithm uses the relative location of R color component of the chromaticity diagram. This method is then integrated with the effectiveness of the spatial scale transformation of whole method. The whole method is based on water index fitted from spectral library. Experimental results demonstrate the improved accuracy and effectiveness of the integrated method for automatic extraction of water bodies.

Keywords: Chromaticity, Feature Extraction, Remote Sensing, Spectral library, Water Index.

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Authors: Helle Hein, Ülo Lepik

Abstract:

A gradient learning method to regulate the trajectories of some nonlinear chaotic systems is proposed. The method is motivated by the gradient descent learning algorithms for neural networks. It is based on two systems: dynamic optimization system and system for finding sensitivities. Numerical results of several examples are presented, which convincingly illustrate the efficiency of the method.

Keywords: Chaos, Dynamical Systems, Learning, Neural Networks

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Authors: C. Ganesh Babu, P. T. Vanathi

Abstract:

In this paper we present an enhanced noise reduction method for robust speech recognition using Adaptive Gain Equalizer with Non linear Spectral Subtraction. In Adaptive Gain Equalizer method (AGE), the input signal is divided into a number of subbands that are individually weighed in time domain, in accordance to the short time Signal-to-Noise Ratio (SNR) in each subband estimation at every time instant. Instead of focusing on suppression the noise on speech enhancement is focused. When analysis was done under various noise conditions for speech recognition, it was found that Adaptive Gain Equalizer method algorithm has an obvious failing point for a SNR of -5 dB, with inadequate levels of noise suppression for SNR less than this point. This work proposes the implementation of AGE when coupled with Non linear Spectral Subtraction (AGE-NSS) for robust speech recognition. The experimental result shows that out AGE-NSS performs the AGE when SNR drops below -5db level.

Keywords: Adaptive Gain Equalizer, Non Linear Spectral Subtraction, Speech Enhancement, and Speech Recognition.

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Authors: Wan-Hyun Cho, In-Seop Na, Seong-ChaeSeo, Sang-Kyoon Kim, Soon-Young Park

Abstract:

In this paper, we propose the variational approach to solve single image defogging problem. In the inference process of the atmospheric veil, we defined new functional for atmospheric veil that satisfy edge-preserving regularization property. By using the fundamental lemma of calculus of variations, we derive the Euler-Lagrange equation foratmospheric veil that can find the maxima of a given functional. This equation can be solved by using a gradient decent method and time parameter. Then, we can have obtained the estimated atmospheric veil, and then have conducted the image restoration by using inferred atmospheric veil. Finally we have improved the contrast of restoration image by various histogram equalization methods. The experimental results show that the proposed method achieves rather good defogging results.

Keywords: Image defogging, Image restoration, Atmospheric veil, Transmission, Variational approach, Euler-Lagrange equation, Image enhancement.

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Authors: Somayeh Sadeghi, Hamid A. Jalab, Sajjad Dadkhah

Abstract:

Due to availability of powerful image processing software and improvement of human computer knowledge, it becomes easy to tamper images. Manipulation of digital images in different fields like court of law and medical imaging create a serious problem nowadays. Copy-move forgery is one of the most common types of forgery which copies some part of the image and pastes it to another part of the same image to cover an important scene. In this paper, a copy-move forgery detection method proposed based on Fourier transform to detect forgeries. Firstly, image is divided to same size blocks and Fourier transform is performed on each block. Similarity in the Fourier transform between different blocks provides an indication of the copy-move operation. The experimental results prove that the proposed method works on reasonable time and works well for gray scale and colour images. Computational complexity reduced by using Fourier transform in this method.

Keywords: Copy-Move forgery, Digital Forensics, Image Forgery.

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Authors: Shabbar Naqvi, Jonathan M. Garibaldi

Abstract:

Breast cancer is one of the most frequent occurring cancers in women throughout the world including U.K. The grading of this cancer plays a vital role in the prognosis of the disease. In this paper we present an overview of the use of advanced computational method of fuzzy inference system as a tool for the automation of breast cancer grading. A new spectral data set obtained from Fourier Transform Infrared Spectroscopy (FTIR) of cancer patients has been used for this study. The future work outlines the potential areas of fuzzy systems that can be used for the automation of breast cancer grading.

Keywords: Breast cancer, FTIR, fuzzy inference system, principal component analysis

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Authors: Navneet Singh Deora, Aastha Deswal, H. N. Mishra

Abstract:

Pasta is one of the most widely consumed food products around the world. Rapid determination of the moisture content in pasta will assist food processors to provide online quality control of pasta during large scale production. Rapid Fourier transform near-infrared method (FT-NIR) was developed for determining moisture content in pasta. A calibration set of 150 samples, a validation set of 30 samples and a prediction set of 25 samples of pasta were used. The diffuse reflection spectra of different types of pastas were measured by FT-NIR analyzer in the 4,000-12,000cm^-1 spectral range. Calibration and validation sets were designed for the conception and evaluation of the method adequacy in the range of moisture content 10 to 15 percent (w.b) of the pasta. The prediction models based on partial least squares (PLS) regression, were developed in the near-infrared. Conventional criteria such as the R², the root mean square errors of cross validation (RMSECV), root mean square errors of estimation (RMSEE) as well as the number of PLS factors were considered for the selection of three pre-processing (vector normalization, minimum-maximum normalization and multiplicative scatter correction) methods. Spectra of pasta sample were treated with different mathematic pre-treatments before being used to build models between the spectral information and moisture content. The moisture content in pasta predicted by FT-NIR methods had very good correlation with their values determined via traditional methods (R² = 0.983), which clearly indicated that FT-NIR methods could be used as an effective tool for rapid determination of moisture content in pasta. The best calibration model was developed with min-max normalization (MMN) spectral pre-processing (R² = 0.9775). The MMN pre-processing method was found most suitable and the maximum coefficient of determination (R²) value of 0.9875 was obtained for the calibration model developed.

Keywords: FT-NIR, Pasta, moisture determination.

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