SVD Algorithm Research Articles

Regularization of the inverse heat conduction problem by the discrete Fourier transform

Two methods of solving the inverse heat conduction problem with employment of the discrete Fournier transform are presented in this article. The first one operates similarly to the SVD algorithm and consists in reducing the number of components of the discrete Fournier transform which are taken into account to determine the solution to the inverse problem. The second method is related to the regularization of the solution to the inverse problem in the discrete Fournier transform domain. Those methods were illustrated by numerical examples. In the first example, an influence of the boundary conditions disturbance by a random error on the solution to the inverse problem (its stability) was examined. In the second example, the temperature distribution on the inner boundary of the multiply connected domain was determined. Results of calculations made in both ways brought very good outcomes and confirm the usefulness of applying the discrete Fournier transform to solving inverse problems.

A fast SVD for multilevel block Hankel matrices with minimal memory storage

Motivated by the Cadzow filtering in seismic data processing, this paper presents a fast SVD method for multilevel block Hankel matrices. A seismic data presented as a multidimensional array is first transformed into a two dimensional multilevel block Hankel (MBH) matrix. Then the Lanczos process is applied to reduce the MBH matrix into a bidiagonal or tridiagonal matrix. Finally, the SVD of the reduced matrix is computed using the twisted factorization method. To achieve high efficiency, we propose a novel fast MBH matrix-vector multiplication method for the Lanczos process. In comparison with existing fast Hankel matrix-vector multiplication methods, our method applies 1-D, instead of multidimensional, FFT and requires minimum storage. Moreover, a partial SVD is performed on the reduced matrix, since complete SVD is not required by the Caszow filtering. Our numerical experiments show that our fast MBH matrix-vector multiplication method significantly improves both the computational cost and storage requirement. Our fast MBH SVD algorithm is particularly efficient for large size multilevel block Hankel matrices.

A fast and stable algorithm for downdating the singular value decomposition

In this paper, we modify a classical downdating SVD algorithm and reduce its complexity significantly. We use a structured low-rank approximation algorithm to compute an hierarchically semiseparable (HSS) matrix approximation to the eigenvector matrix of a diagonal matrix plus rank-one modification. The complexity of our downdating algorithm is analyzed. We further show that the structured low-rank approximation algorithm is backward stable. Numerous experiments have been done to show the efficiency of our algorithm. For some matrices with large dimensions, our algorithm can be much faster than that using plain matrix–matrix multiplication routine in Intel MKL in both sequential and parallel cases.

SVD-TLD Sensing Algorithm for EES-MIMO Radar

Based on Electromagnetic Environmental Sensory(EES)and Multiple-input Multiple-Out(MIMO) radar sensing algorithm , this paper presents SVD-TLD perception algorithm, which firstly use the cross-spectrum AR model parameter estimation, and secondly considering the cross-correlation matrix of the estimation error function disturbance and lastly taking into account of the two ends of the equation, using the cross-correlation function of the estimated measurement errors to affect the Total Least Squares (TLS) method . Compared with the AR model parameter estimation, the accuracy of SVD algorithm cross-spectral estimation has significantly improved, greatly reducing the amount of computation and is more conducive to real-time online computing.

Sparse Matrix of Image Denoising Method based on SVD

In this paper, based on the K - SVD and residual error than the low SNR image sparse representation denoising algorithm. On the basis of the foregoing contents, this paper expounds on the build process and mechanism analysis of the algorithm, the paper on the basis of the subjective evaluation reference peak signal-to-noise ratio (PSNR) as the objective evaluation standard. Can be seen from the results of simulation experiments for different kinds of image denoising, image sparse decomposition based on a complete atom library has a better effect of denoising algorithm often, this is because after complete the atoms in the dictionary has redundancy, to show more abundant characteristic information, can more effectively extract the image features. In the proposed algorithm, the K - SVD algorithm for image sparse decomposition to optimize dictionary and residual error than the threshold for accurate division of image information and provide evidence for image noise effectively, a combination of both in image denoising, especially in low SNR image denoising experiment obtained good effect. The experimental results also from another side shows the sparse decomposition based on a complete atom library on image denoising application potential.

Decomposition of a planar vector field into irrotational and rotational components

A formulation of the boundary value problem in a finite domain for the scalar potential and the stream function is given: the basic decomposition equation is assumed as boundary condition. The problem is singular: the existence of solutions, which are determined up to conjugate harmonic functions, is proved. The basic properties of the spectrum of the homogeneous operator associated to the boundary value problem for the potentials are derived. The discrete equations are obtained by means of the finite volume method. It is verified that the main properties of the continuous problem are maintained in the discrete equations. We address the computation of minimum norm solutions, which are obtained by means of the SVD algorithm. Numerical experiments have been performed in different situations of the assigned vector field (presence of zero points, size of the finite domain, degree of stochasticity of the field) to estimate the effects on the decomposition–reconstruction operations.

A novel SVD and LS-SVM combination algorithm for blind watermarking

This paper proposes a novel algorithm for blind watermarking by applying singular value decomposition and least squares support vector machine into watermark embedding and detection. In coding process, singular value decomposition is performed on coefficient blocks to obtain singular values after host image is transformed into integer wavelet transform domain. Subsequently, watermark image is embedded into transformed image by adaptively modulating the sample feature vectors constructed by singular values. In decoding process, the trained least square support vector machine is employed to extract the watermark image blindly by classifying samples derived from watermarked image. Experimental results show that the proposed scheme is not only robust against common noise-like attacks, such as noise, filter, crop, sharpen and JPEG compression, but also robust against geometrical distortions.

Sense-through-wall human detection using the UWB radar with sparse SVD

In this paper, a method for through-wall human detection based on the singular values decomposition of the measurement matrices is presented. After demonstrating the sparsity of the matrices using the CLEAN algorithm, an SVD algorithm based on the Lanczos process is applied to compute their singular values. We also analyze the singular values of matrices constructed by difference square techniques for different types of walls and compare our algorithm with a 2-D imaging approach proposed by researchers in Time Domain Company. Detection results show that our method performs well in the gypsum wall, brick wall, and wooden door.

Application of second generation wavelets to blind spherical deconvolution

We address the problem of spherical deconvolution in a non-parametric statistical framework, where both the signal and the operator kernel are subject to measurement errors. After a preliminary treatment of the kernel, we apply a thresholding procedure to the signal in a second generation wavelet basis. Under standard assumptions on the kernel, we study the minimax performances of the resulting algorithm in terms of Lp losses (p≥1) on Besov spaces on the sphere. We hereby extend the application of second generation spherical wavelets to the blind spherical deconvolution framework. It is important to stress that the procedure is adaptive with regard to both the target function sparsity and the kernel blurring effect. We end with the study of a concrete example, putting into evidence the improvement of our procedure on the recent blockwise SVD algorithm of Delattre et al. (2012).

Disclosing the extensive crystal chemistry of Ivabradine hydrochloride, in its pure and solvated phases

Powder diffraction data are presented for Ivabradine hydrochloride (pure and solvated forms), a drug marketed worldwide for symptomatic treatment of angina pectoris and inappropriate sinus tachycardia. [Ivrabradine: 3-[3-({[(7S)-3,4-dimethoxy bicyclo[4.2.0]octa-1,3,5-trien-7-yl]methyl}(methyl)amino)propyl]-7,8-dimethoxy-2,3,4,5-tetrahydro-1H-3-benzazepin-2-one]. Many are the different (polymorphic or solvated) phases claimed in the scientific or forensic literature. We have here prepared monophasic samples of six different ivabradine hydrochloride species. Exposure to water vapours, at room temperature, of the anhydrous δ-d form generated pure powders of the tetrahydrate form (the β-form). Two different anhydrous forms (β-d and α) were prepared by gentle, or extensive, heating of the β and δ-d forms, respectively. Acetonitrile and acetone solvates (hereafter called δ1- and δ2-forms) were obtained by precipitation methods from concentrated solutions. Diffraction data were collected on laboratory equipment with Ni-filtered CuKα radiation; cell parameters and space groups were determined from ab initio indexing procedures using the SVD algorithm.

Divide and Conquer the CS Decomposition

We develop a divide-and-conquer algorithm for the bidiagonal CS decomposition (CSD). This complements an earlier algorithm based on simultaneous QR iteration. The new algorithm is designed to provide the efficiency gains of familiar divide-and-conquer algorithms on both serial and parallel architectures. The solution uses many components of existing algorithms, particularly the bidiagonal SVD algorithm of Gu and Eisenstat, but extra steps and reparameterizations are required to maintain orthogonality and consistent singular vectors, especially when the singular vectors are ill conditioned. The algorithm supports the stable computation of the generalized singular value decomposition (GSVD) in addition to the CSD.

A Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients

We propose a data-driven stochastic method (DSM) to study stochastic partial differential equations (SPDEs) in the multiquery setting. An essential ingredient of the proposed method is to construct a data-driven stochastic basis under which the stochastic solutions to the SPDEs enjoy a compact representation for a broad range of forcing functions and/or boundary conditions. Our method consists of offline and online stages. A data-driven stochastic basis is computed in the offline stage using the Karhunen--Loève (KL) expansion. A two-level preconditioning optimization approach and a randomized SVD algorithm are used to reduce the offline computational cost. In the online stage, we solve a relatively small number of coupled deterministic PDEs by projecting the stochastic solution into the data-driven stochastic basis constructed offline. Compared with a generalized polynomial chaos method (gPC), the ratio of the computational complexities between DSM (online stage) and gPC is of order $O((m/N_p)^2)$. Here $m$ and $N_p$ are the numbers of elements in the basis used in DSM and gPC, respectively. Typically we expect $m\ll N_p$ when the effective dimension of the stochastic solution is small. A timing model, which takes into account the offline computational cost of DSM, is constructed to demonstrate the efficiency of DSM. Applications of DSM to stochastic elliptic problems show considerable computational savings over traditional methods even with a small number of queries. We also provide a method for an a posteriori error estimate and error correction.

Image Denoising using K-SVD Algorithm based on Gabor Wavelet Dictionary

denoising problem can be addressed as an inverse problem. One of the most recent approaches to solve an inverse problem is a sparse decomposition over overcomplete dictionaries. In sparse representation, images are represented as a linear combination of dictionary atoms. In this paper, we propose an algorithm for image denoising based on Orthogonal Matching Pursuit (OMP) for determining sparse representation over Gabor Wavelet adaptive dictionary by K- SVD algorithm. The results of this algorithm have more efficiency of image recovery than using DCT dictionary.

Spectral Separation of Quantum Dots within Tissue Equivalent Phantom Using Linear Unmixing Methods in Multispectral Fluorescence Reflectance Imaging

Introduction Non-invasive Fluorescent Reflectance Imaging (FRI) is used for accessing physiological and molecular processes in biological media. The aim of this article is to separate the overlapping emission spectra of quantum dots within tissue-equivalent phantom using SVD, Jacobi SVD, and NMF methods in the FRI mode. Materials and Methods In this article, a tissue-like phantom and an optical setup in reflectance mode were developed. The algorithm of multispectral imaging method was then written in Matlab environment. The setup included the diode-pumped solid-state lasers at 479 nm, 533 nm, and 798 nm, achromatic telescopic, mirror, high pass and low pass filters, and EMCCD camera. The FRI images were acquired by a CCD camera using band pass filter centered at 600 nm and high pass max at 615 nm for the first region and high pass filter max at 810 nm for the second region. The SVD and Jacobi SVD algorithms were written in Matlab environment and compared with a Non-negative Matrix Factorization (NMF) and applied to the obtained images. Results PSNR, SNR, CNR of SVD, and NMF methods were obtained as 39 dB, 30.1 dB, and 0.7 dB, respectively. The results showed that the difference of Jacobi SVD PSNR with PSNR of NMF and modified NMF algorithm was significant (p<0.0001). The statistical results showed that the Jacobi SVD was more accurate than modified NMF. Conclusion In this study, the Jacobi SVD was introduced as a powerful method for obtaining the unmixed FRI images. An experimental evaluation of the algorithm will be done in the near future.

An Improved Channel Estimation Method for LTE Uplink

As users of the increasing demand for multimedia services, 3GPP long term evolution system proposed the Long Term Evolution, LTE. LTE is the most important improvements with a new air interface technology to provide users with higher peak rates. Accurate channel estimation is to ensure the transmission quality of LTE system and the key to its advantages. In pursuit of lower bit error rate (BER), this paper based on pilot signals TDD LTE system on the uplink channel estimation algorithm. Use LS algorithm, MMSE algorithm and svd algorithm. Based on these three improved svd algorithm, it gave the simulation results.

Review on Singular-Value-Decomposition-Based Digital Watermarking Algorithm in Combination with Image Features

The combination of image features with singular value decomposition algorithm and digital watermarking algorithm based on wavelet transform respectively makes possible the advancement from pixel watermarking to content watermarking, which effectively solves the contradiction between perceptibility and robustness of conventional watermarking algorithm. Therefore, stronger robustness and lower perceptibility of watermarking are achieved. This paper first gives a review on conventional singular-value-decomposition-based digital watermarking algorithm, and then makes a thorough analysis of its respective features, advantages and defects. Improved feature extraction schemes of digital watermark which combine image features with SVD algorithm as well as the application algorithm in feature extraction based on improved SVD algorithm are put forward for the comparative analysis of corresponding principles and processing effects. The experimental results indicate that the content-based (instead of pixel-based) watermarking algorithm can better satisfy the perceptibility and robustness of digital watermarking, with huge application potentials and more development space

上海软X射线自由电子激光束流准直

The SXFEL has stringent restrictions on beam emittance growth, and the traditional optical alignment can no longer meet its requirements, but the beam-based alignment(BBA) method allows more precise alignment, further reducing the linac errors to meet SXFEL requirements. In undulator sections, orbit changes are not only caused by misalignments of quadrupole magnet position, but also the errors of undulator magnet. In order to achieve alignment accuracy over long distance, the quadrupole magnet errors and beam position monitor (BPM) offset are obtained by measuring. BPM data under different conditions and using SVD algorithm for calculation and analysis,With the method above, software based on Matlab has been designed and comparedwith other software simulation results demonstrate that the orbit offset could be reduced by one order.

IRIS Feature Extraction and Classification using FPGA

An approach of singular value (SVD) of a (mxn) 2-D matrix has been popularly used by researchers for representing a 2-D image by a set of less than or equal to n values sequenced in descending order of which a subset of only first few values which are significant is treated as a set of features for that image. These features are further used for image recognition and classification. Though many papers as reviewed from literature have discussed about this implantation using software/MATLAB approach, rarely a paper appears on hardware implementation of SVD algorithm for image processing applications. This paper presents the details of a hardware architecture developed by us to implement SVD algorithm and then presents the results of implementation of this architecture in the Xilinx field programmable gate array Virtex5 to extract the features of an iris image. A comparison between the feature values extracted by MATLAB and those obtained by hardware simulation using Xilinx ISE tool indicates a very good match validating the hardware architecture. A hamming distance classifier using appropriate threshold values stored in ROM is used to classify the iris images. DOI: http://dx.doi.org/10.11591/ijece.v2i2.158 Full Text: PDF

A NOVEL TEXTURE-BASED MULTI-LINEAR ANALYSIS ALGORITHM FOR FACE RECOGNITION

In this paper, a multi-linear approach based on texture features for face recognition is proposed. First, we extract fragment-based texture features of the facial images using the local binary pattern (LBP) descriptors, which capture both shape and texture information and also are robust to illumination variations. Second, we propose high-order orthogonal iteration (HOOI) algorithm that obtains optimum truncated factor-specific modes, which are not guaranteed in the standard N-mode SVD algorithm, in an iterative manner. Finally, we apply HOOI to obtain a compact and effective representation of the facial images based on the texture features. Our representation yields improved facial recognition rates relative to standard eigenface, tensorface, and other popular algorithms, especially when the facial images are confronted by a variety of viewpoints and illuminations. To evaluate the validity of our approach, a series of experiments are performed on the CMU-PIE facial databases.

A Wavelet Based Hybrid SVD Algorithm for Digital Image Watermarking

In this paper we propose a hybrid image watermarking algorithm which satisfies both imperceptibility and robustness requirements. Our proposed work provide an optimum solution by using singular values of Wavelet Transformation’s HL and LH sub bands to embed watermark. Further to increase and control the strength of the watermark, we use a scale factor. An optimal watermark embedding method is developed to achieve minimum watermarking distortion. A secret embedding key is designed to securely embed the fragile watermarks so that the new method is robust to counterfeiting, even when the malicious attackers are fully aware of the watermark embedding algorithm. Experimental results are provided in terms of peak signal to noise ratio (PSNR), normalized cross correlation (NCC) and gain factor to demonstrate the effectiveness of the proposed algorithm. Image operations such as JPEG compression from malicious image attacks and, thus, can be used for semi-fragile watermarking.