Singular Value Decomposition Decomposition Research Articles

Noise reduction analysis of deformation data based on CEEMD-PE-SVD modeling

In the field of high slope deformation monitoring, the deformation data obtained are often characterized by high volatility, strong nonlinearity, and noise content, due to the influence of factors such as the surrounding environment, human operation, and the complexity of the project. To overcome these problems, this paper proposes deformation data based on the coupling of complementary ensemble empirical modal decomposition (CEEMD), permutation entropy (PE), and singular value decomposition (SVD). Firstly, CEEMD decomposition is performed on the deformation data. Secondly, a randomness test is performed on the obtained modal components, and if the entropy value of the component arrangement entropy is greater than 0.5, SVD decomposition will be used for noise reduction. Finally, the components that meet the conditions are reconstructed to realize the noise reduction of the deformation data. The results show that the algorithm model has an excellent noise elimination effect, which can reflect the internal detail information of deformation data and provide a well-established method for future research on the processing of deformation monitoring data.

Data distillation in computational pathology by choosing few representants of the original variance: A use case in ovarian cancer

In computational pathology, a typical Whole Slide Image may easily reach a size of 3–4 Gigabytes, while a database, with hundred of cases, might reach Terabytes. In this scenario, training any model is expensive and therefore the possibility of reducing the size of the training data is appealing. This paper presents a method to summarize the information of a data set, a function of the variance, by selecting the most informative samples. The first step of the whole strategy consists in projecting small image patches (100 × 100) to a feature space and discretize it with a simple k-means to obtain the feature space vocabulary. The groups obtained by the k-means are the vocabulary words and therefore any small patch is represented by the centroid of the group to which such patch is projected. A second step, a probabilistic Latent Semantic Analysis constructs groups of words known as topics by computing frequencies of words in documents, which are larger patches containing between 450 and 500 small patches. A third step collects the documents representing 80 % of the topic variance, their patches are assembled and a Singular Value Decomposition (SVD) is applied to these patches. The Data Distillation process chooses only the small patches belonging to the topics showing higher variance in the matrix of eigenvalues S from the SVD decomposition. The method efficacy was evaluated by comparing the performance of models trained either with 40 % of an actual ovarian cancer dataset selected using this method and the entire dataset without any selection. Results show the F-score obtained with these two sets was similar, about 0.87, with different classifiers, namely Support Vector Machine and a Multilayer Perceptron.

A vital signsignal noise suppression method for wearable piezoelectric devices.

This paper tackles the problem of noise suppression during vital signsignal monitoring. Physiological signal monitoring is a significant and promising medical monitoring method, and wearable medical monitoring devices based on piezoelectric polymer sensors are a trending way for their advantages of being flexible in the shape, portable to use, and comfortable to wear. However, this raises the question that the measured signal contains much more noise components. To avoid the following shortcoming of low signal to noise ratio (SNR), a noise suppression method based on improved wavelet threshold and empirical mode decomposition combined with singular value decomposition (SVD) screening the intrinsic mode function (IMF) components is proposed. A wavelet transform is first used under the combination of hard and soft thresholds to focus the target range in the low-frequency region where the energy of the physiological signal is concentrated. Then, a complete ensemble empirical mode decomposition is used to decompose the signal effectively, which can resist the influence of random noises. Meanwhile, a SVD decomposition procedure was used to filter out the lower correlated IMF components to retain the validity of the original signal. We verified the effectiveness of the proposed method through simulated and measured experiments as well as the advantages and disadvantages of the algorithm compared with other physiological signal denoising algorithms through SNR filtering results, power spectrum distribution, and other perspectives. The results proved that the proposed method could effectively remove more detailed noise and improve the SNR of the signal efficiently, which is more conducive to the demand for auxiliary medical diagnosis in the future.

An efficient randomized QLP algorithm for approximating the singular value decomposition

The rank-revealing pivoted QLP decomposition approximates the computationally prohibitive singular value decomposition (SVD) via two consecutive column-pivoted QR (CPQR) decomposition. It furnishes information on all four fundamental subspaces of the matrix. In this paper, we introduce a randomized version of the QLP decomposition called Rand-QLP. Operating on a matrix A, Rand-QLP gives A=QLPT, where Q and P are orthonormal, and L is lower-triangular. Under the assumption that the rank of the input matrix is k, we derive several error bounds for Rand-QLP: bounds for the first k approximate singular values and for the trailing block of the middle factor L, which show that the decomposition is rank-revealing; bounds for the distance between approximate subspaces and the exact ones for all four fundamental subspaces of a given matrix; and bounds for the errors of low-rank approximations constructed by the columns of Q and P. Rand-QLP is able to effectively leverage modern computational architectures, due to the utilization of random sampling and the unpivoted QR decomposition, thus addressing a serious bottleneck associated with classical algorithms such as the SVD, CPQR and most recent matrix decomposition algorithms. We utilize a modern computing architecture to assess the performance behavior of different algorithms. In comparison to CPQR and the SVD, Rand-QLP respectively achieves a speedup of up to 5 times and 6.6 times on the CPU and up to 3.8 times and 4.4 times with the hybrid GPU architecture. In terms of quality of approximation, our results on synthetic and real data show that the approximations by Rand-QLP are comparable to those of pivoted QLP and the optimal SVD, and in most cases are considerably better than those of CPQR.

Robust and secured watermarking using Ja-Fi optimization for digital image transmission in social media

Widespread transmission of digital image in social media has come up with security, confidentiality and authentication issues. Ensuring copyright protection of digital images shared through social media has become inevitable. To address these issues, a robust and secure digital image watermarking scheme using Redundant discrete wavelet transform (RDWT) - Singular value decomposition (SVD) hybrid transform is proposed in this paper. In the proposed scheme, digital image is divided into 4 × 4 non-overlapping blocks, and low information blocks are selected for embedding to ensure higher imperceptibility. For watermark embedding 1-level RDWT is applied on the selected blocks followed by SVD decomposition to make the proposed scheme highly robust against common attacks. One watermark bit is embedded in each left and right singular SVD matrices by adjusting the coefficients. This makes the proposed scheme free from false positive error and achieve high embedding capacity. Before embedding, watermark encryption is done by using a pseudo random key. The pseudo random key is generated adaptively from the cover image by using discrete wavelet transform saliency map, block mean approach and cosine functions. High imperceptibility and robustness is indispensable for the digital images shared through social media. But, these watermarking characteristics are in trade-off. In the proposed scheme, the trade-off is balanced by using optimized scaling factor (embedding strength). Scaling factor is optimized by using the proposed JAYA-Firefly (Ja-Fi) optimization. Experimental results demonstrate that the proposed scheme provides high imperceptibility, robustness, embedding capacity and security. Furthermore, performance comparison with the recent state-of-the-art schemes affirms that the proposed scheme has superior performance.

De-Noising of Magnetotelluric Signals by Discrete Wavelet Transform and SVD Decomposition

Magnetotelluric (MT) sounding data can easily be damaged by various types of noise, especially in industrial areas, where the quality of measured data is poor. Most traditional de-noising methods are ineffective to the low signal-to-noise ratio of data. To solve the above problem, we propose the use of a de-noising method for the detection of noise in MT data based on discrete wavelet transform and singular value decomposition (SVD), with multiscale dispersion entropy and phase space reconstruction carried out for pretreatment. No “over processing” takes place in the proposed method. Compared with wavelet transform and SVD decomposition in synthetic tests, the proposed method removes the profile of noise more completely, including large-scale noise and impulse noise. For high levels or low levels of noise, the proposed method can increase the signal-to-noise ratio of data more obviously. Moreover, application to the field MT data can prove the performance of the proposed method. The proposed method is a feasible method for the elimination of various noise types and can improve MT data with high noise levels, obtaining a recovery in the response. It can improve abrupt points and distortion in MT response curves more effectively than the robust method can.

Research on Noise Reduction Method of Pressure Pulsation Signal of Draft Tube of Hydropower Unit Based on ALIF-SVD

Aiming at the problem that it is difficult to extract the characteristics of the draft tube pressure fluctuation signal under the background of strong noise, this study proposes a dual noise reduction method based on adaptive local iterative filtering (ALIF) and singular value decomposition (SVD). First, perform ALIF decomposition of the signal to be decomposed to obtain a series of IMF components, calculate the sample entropy of each component, select some IMF components to reconstruct according to the set sample entropy threshold, and then perform SVD decomposition on the reconstructed signal, and according to the location of the singular value difference spectrum mutation point, the appropriate number of reconstructions is selected for reconstruction, so as to achieve the double noise reduction effect. The ALIF-SVD dual noise reduction method proposed in this study is compared with the single ALIF, EMD, and EMD-SVD dual noise reduction method through simulation, and the correlation coefficient, signal-to-noise ratio, and mean square error are used to evaluate the noise reduction. It is found that the ALIF-SVD dual noise reduction method avoids the phenomenon of modal aliasing in the decomposition process, effectively removes the noise, and can retain the useful information of the original signal, and the noise reduction effect is better. A unit of a hydropower station in China is further selected as the research object, and its draft tube pressure fluctuation data were analyzed for noise reduction. It was found that this method can accurately extract the signal characteristics under strong noise background, so as to determine the type of pressure fluctuation of the unit, which is helpful to improve the fault recognition rate of hydraulic turbines. And it provides some technical support for the safe and stable operation of hydropower units and the promotion of condition-based maintenance strategy and improves the intelligent level of hydropower station operation management.

Frequency-Aware SVD Decomposition and its Application to Color Magnification and Motion Denoising

Videos are full of dynamic changes along both the spatial and temporal dimensions. Large, jerky short-term motions make it difficult to extract significant changes from videos such as subtle color changes and long-term motions occurring in time-lapse sequences. In this paper, we introduce two singular value decomposition (SVD)-based video decomposition schemes to clearly reveal such changes. The first scheme involves enhancing the visual characteristics of small subtle color changes in the presence of a wide variety of motion patterns by magnifying their pixel intensities. The second scheme removes short-term motions that visually distract attention from the underlying content of video sequences such as time-lapse videos, snowing scene, and maritime surveillance. Both schemes involve the decomposition of videos into spatiotemporal slices in which each slice is further decomposed into several singular components. The low-rank components that primarily represent background and color intensity information are then temporally processed to magnify the magnitude of the signal at the subtle color change target frequency. At the same time, an approach similar to that used in denoising time-lapse sequences is applied to temporally filter the singular components representing sparse information, thereby removing jittery short-term motions while preserving long-term motions, which are represented by both low-rank and unfiltered sparse components. We demonstrate promising color magnification and motion denoising results that can be obtained much faster than results estimated using state-of-the-art techniques.

Rigid 3D Registration: A Simple Method Free of SVD and Eigen-Decomposition

The 3-D registration is extensively required in many industrial applications involving 3-D perception and reconstruction. However, conventional methods consisting of singular value decomposition (SVD) or eigendecomposition are all hard to be implemented and are difficult to be ported using simple digital circuit prototypes. A novel solution is obtained to solve the rigid 3-D registration problem, motivated by previous eigendecomposition approaches. Different from existing solvers, the proposed algorithm does not require sophisticated matrix operations, e.g., SVD or eigenvalue decomposition. Instead, the optimal eigenvector of the point cross-covariance matrix can be computed within several iterations. It is also proven that the optimal rotation matrix can be directly computed for cases without the need for a quaternion. The simple framework provides a very easy approach, even without floating-number processing. Simulations on noise-corrupted point clouds have verified the robustness and computation speed of the proposed method. The final results indicate that the proposed algorithm is accurate, robust, and owns over 60%–80% less computation time than representatives. It has also been applied to real-world applications for faster robotic visual perception.

Adaptive pre-whiten filtering for the free induction decay transversal signal in weak magnetic detection

The free induction decay (FID) transversal signal is always employed by a proton precession magnetometer (PPM) to evaluate the time-domain geomagnetic field. Nevertheless, the signal-to-noise ratio (SNR) is an important factor that severely affects the detection accuracy of the magnetic field due to uncontrollable interference sources, including random noise and power frequency noise. In this study, aiming to boost the SNR of the FID transversal signal, a novel filtering algorithm based on a prewhiten (PW) strategy is proposed and the PW filtering was combined with singular value decomposition (SVD) for further noise reduction. This method aims to generate adaptive PW input data before filtering, further decorrelating the noise to reduce the impact of varying noise levels in the received FID signals. The efficiency of the proposed joint filtering framework, dubbed PW-SVD, was evaluated by comparing with two state-of-the-art methods, i.e., SVD and principal component analysis and decomposition, using the same data. The results demonstrated that the proposed PW-SVD method obtained the smallest root mean square error and the highest signal-to-noise ratio improvement among all the compared methods, especially for the strong-noisy scenario, which enhances the environmental adaptability of a PPM.

Noise suppression of microseismic data based on a fast singular value decomposition algorithm

Raw data from microseismic monitoring is usually contaminated with ambient noise, which severely decreases the quality of the data and further affects the accuracy of arrival-based or amplitude-based source imaging performance., and thusThus, noise suppression of microseismic data plays an indispensable role in event detection during hydraulic fracturing. We investigatedeveloped a new way to effectively suppress noise from microseismic data via cross-correlation of traces from multiple microseismic channels. The cross-correlation between a reference trace and all available traces is computed to estimated the optimal time shifts between the waveforms in different channels. When the time shifts are estimated, the microseismic data can be rearranged to enhance the spatial correlation of the microseismic events. Next, a singular value decomposition (SVD) step is applied to extract the eigen-components or eigen-images of the noisy traces and to reject the noise in the data. When neighbor waveforms are too close, a windowed processing strategy is required to obtain well-flattened gather for the SVD processing. Considering that the SVD calculation is computationally expensive, we propose a fast SVD decomposition algorithm by derivation. The proposed method is easy to implement and can obtain robust performance in denoising multi-channel microseismic dataset. We validate the performance on both synthetic and real microseismic datasets. The proposed method can also be combined with active-source seismic data to efficiently suppress strong random background noise.

Fast approximate truncated SVD

SummaryThis paper presents a new method for the computation of truncated singular value decomposition (SVD) of an arbitrary matrix. The method can be qualified as deterministic because it does not use randomized schemes. The number of operations required is asymptotically lower than that using conventional methods for nonsymmetric matrices and is at a par with the best existing deterministic methods for unstructured symmetric ones. It slightly exceeds the asymptotical computational cost of SVD methods based on randomization; however, the error estimate for such methods is significantly higher than for the presented one. The method is one‐pass, that is, each value of the matrix is used just once. It is also readily parallelizable. In the case of full SVD decomposition, it is exact. In addition, it can be modified for a case when data are obtained sequentially rather than being available all at once. Numerical simulations confirm accuracy of the method.

A robust approach to singular spectrum analysis

AbstractSingular spectrum analysis (SSA) is a nonparametric method for time series analysis and forecasting that incorporates elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems, and signal processing. Although this technique has shown to be advantageous over traditional model‐based methods, in particular, one of the steps of the SSA algorithm, which refers to the singular value decomposition (SVD) of the trajectory matrix, is highly sensitive to data contamination. Specifically, and because SVD decomposition is least squares based, the presence of a single outlier, if extreme, may be enough to draw the leading principal component towards itself resulting in possible misinterpretations, which may subsequently, in particular and in the case of time series analysis, lead to reduced quality of model fit and forecast accuracy. In order to alleviate this problem, a robust SSA algorithm is proposed, where a robust SVD procedure replaces the least squares based one in the original SSA procedure. The SSA and the robust SSA approaches are compared in terms of model fit quality via Monte Carlo simulations that contemplate both clean and noisy/contaminated time series. The adequacy and value of the proposed approach is then compared with the standard SSA using real data about the industrial production index.

Shot boundary detection via adaptive low rank and svd-updating

Usually considered as the first step in content-based video retrieval, shot boundary detection (SBD) is crucial to subsequent high-level applications like video summarization. The paper proposes an accurate video shot boundary detection method based on singular value decomposition (SVD), through the use of different mathematical theorems and interpretations. In our contribution, adaptive feature extraction is performed using the Frobenius norm of low rank approximation matrices. Each frame will be mapped into k˜-dimensional vector in the singular space according to each segment. The classification of continuity values is then achieved via double thresholding technique for detecting the hard cuts. For gradual transitions detection, the folding-in technique, known as SVD-updating, is used for the first time in video shot boundary detection. This allows for accurate detection in reduced computational time, as it is no longer necessary to recalculate the whole SVD decomposition for segment correction. Experimental results on four different datasets, including the TRECVid 2001, 2002 and 2005 SBD tasks, show the effectiveness of our detector, which outperforms recent related methods in detecting both hard and gradual transitions.

Multibiometric Identification System based on SVD and Wavelet Decomposition

Biometric systems refer to the systems used for human recognition based on their characteristics. These systems are widely used in security institutions and access control. In this work three biometric sources were used for identification purposes. Singular value decomposition (SVD) was employed as a tool for feature extraction and artificial neural network (ANN) was used as pattern recognition for the model. High accuracy was obtained from this work with 95% recognition rate.

An improved color image watermarking scheme based on Schur decomposition

A novel colour image watermarking scheme based on Schur decomposition is proposed in this paper. By analysing the 3 × 3 unitary matrix U via Schur decomposition, the strong similarity relation between U2,1 and U3,1 is found. This relation will represent one kind of embedded watermark information, i.e., '1' or '0', and will be used to extract watermark from 3 × 3 unitary matrix U in the blind manner. Moreover, the proposed method requires lower computational complexity than other methods based on singular value decomposition (SVD) since Schur decomposition is only an intermediate step in SVD decomposition. In addition, the proposed method does not have the false-positive detection problem like that based on SVD. The experimental results show that the proposed scheme has better performance in terms of invisibility, robustness, capacity and real-time feature.

An image watermarking scheme in wavelet domain with optimized compensation of singular value decomposition via artificial bee colony

Digital image watermarking is the process of authenticating a digital image by embedding a watermark into it and thereby protecting the image from copyright infringement. This paper proposes a novel robust image watermarking scheme developed in the wavelet domain based on the singular value decomposition (SVD) and artificial bee colony (ABC) algorithm. The host image is transformed into an invariant wavelet domain by applying redistributed invariant wavelet transform, subsequently the low frequency sub-band of wavelet transformed image is segmented into non-overlapping blocks. The most suitable embedding blocks are selected using the human visual system for the watermark embedding. The watermark bits are embedded into the target blocks by modifying the first column coefficients of the left singular vector matrix of SVD decomposition with the help of a threshold and the visible distortion caused by the embedding is compensated by modifying the coefficients of the right singular vector matrix employing compensation parameters. Furthermore, ABC is employed to obtain the optimized threshold and compensation parameters. Experimental results, compared with the related existing schemes, demonstrated that the proposed scheme not only possesses the strong robustness against image manipulation attacks, but also, is comparable to other schemes in term of visual quality.

The Contourlet Domain Comic Zero Watermarking Algorithm based on Discrete Cosine Transform and Singular Value Decomposition

Through to analyze the characteristics of the digital cartoon image, proposed a based on discrete cosine transform (DCT) and singular value decomposition (SVD) combined contourlet transform with zero watermarking algorithm, the algorithm first for image contourlet transform and then make the low-frequency subband DCT and SVD decomposition again after operation block, the largest singular value as the image feature extracting for zero watermarking structure. In order to improve the security of the algorithm, introducing into visual cryptography processing the watermark image, the zero watermarking features obtained and secret sharing for the logic operation is zero watermarking characteristics of the final value.. The simulation results show that the algorithm has strong robustness.

SVD-based digital image watermarking using adaptive generated watermark

In this paper, an evolutionary-based algorithm for digital image watermarking is proposed. Robustness and imperceptibility are two important properties of digital image watermarking which conflict with each other. A singular value decomposition (SVD)-based intelligent algorithm is applied to make a trade-off between robustness and imperceptibility. In the proposed algorithm, first, the original image is divided into 8×8 blocks. Then some special blocks are transformed into discrete cosine transform (DCT) domain. SVD decomposition of DCT coefficients of special blocks is the next stage of the method. Finally, a binary watermark image is embedded into the singular values by a quantisation method. The major property of the proposed method is the generation of a binary watermark image using genetic algorithm to solve the optimisation problem between robustness and imperceptibility. So the watermark could be variable and image adaptive. The simulation results show improvement in robustness of the proposed method against several attacks such as noise contamination, filtering, joint photographic experts group (JPEG) compression and some geometrical attacks like cropping, rotation and rescaling in comparison with a recently similar existing work.

Near optimal performance joint semi-blind channel estimation and data detection techniques for Alamouti coded single-carrier (SC) MIMO communication systems

In this paper, two novel joint semi-blind channel estimation and data detection techniques are proposed and investigated for Alamouti coded single-carrier (SC) multiple-input multiple-output (MIMO) communication system using Rayleigh flat fading channel model. In the first novel semi-blind technique, blind channel estimation can be performed by using singular value decomposition (SVD) of received output autocorrelation matrix and training based channel estimation for orthogonal training symbols can be performed by using orthogonal pilot maximum likelihood (OPML) algorithm. Further using, that semi-blind channel estimate and received output, data detection is performed by using Maximum likelihood (ML) detection. Finally we derived new training symbols from error covariance matrix of estimated data and known orthogonal training symbols, which further applied to OPML algorithm for final channel estimate. In the second novel semi-blind technique, blind channel estimation can be performed by using matrix triangularization based on householder QR decomposition (H-QRD) of received output autocorrelation matrix instead of SVD decomposition. Other steps are same as the first novel technique to calculate data detection and final channel estimation. Simulation results are presented under 2-PSK, 4-PSK, 8-PSK and 16-QAM data modulation schemes using 2 transmitters and different combinations of receiver antennas to investigate the performances of novel techniques compare to conventional whitening rotation (WR) and rotation optimization maximum likelihood (ROML) based semi-blind channel estimation techniques. Result demonstrates that novel techniques outperform others by achieving near optimal performance.