scholarly journals Singular value automata and approximate minimization

2019 ◽  
Vol 29 (9) ◽  
pp. 1444-1478 ◽  
Author(s):  
Borja Balle ◽  
Prakash Panangaden ◽  
Doina Precup
Keyword(s):  
Singular Value Decomposition ◽  
Finite Rank ◽  
Singular Value ◽  
Linear Operators ◽  
Hankel Matrices ◽  
Weighted Automata ◽  
Approximate Minimization ◽  
Value Decomposition ◽  
Svd Decomposition

AbstractThe present paper uses spectral theory of linear operators to construct approximatelyminimal realizations of weighted languages. Our new contributions are: (i) a new algorithm for the singular value decomposition (SVD) decomposition of finite-rank infinite Hankel matrices based on their representation in terms of weighted automata, (ii) a new canonical form for weighted automata arising from the SVD of its corresponding Hankelmatrix, and (iii) an algorithmto construct approximateminimizations of given weighted automata by truncating the canonical form.We give bounds on the quality of our approximation.

scholarly journals Observation Strategies Based on Singular Value Decomposition for Ocean Analysis and Forecast

Water ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 3445
Author(s):  
Maria Fattorini ◽  
Carlo Brandini
Keyword(s):  
Singular Value Decomposition ◽  
Maximum Error ◽  
Ocean Model ◽  
Singular Value ◽  
Practical Applications ◽  
Positioning Strategy ◽  
Value Decomposition ◽  
Observation Strategies

In this article, we discuss possible observing strategies for a simplified ocean model (Double Gyre (DG)), used as a preliminary tool to understand the observation needs for real analysis and forecasting systems. Observations are indeed fundamental to improve the quality of forecasts when data assimilation techniques are employed to obtain reliable analysis results. In addition, observation networks, particularly in situ observations, are expensive and require careful positioning of instruments. A possible strategy to locate observations is based on Singular Value Decomposition (SVD). SVD has many advantages when a variational assimilation method such as the 4D-Var is available, with its computation being dependent on the tangent linear and adjoint models. SVD is adopted as a method to identify areas where maximum error growth occurs and assimilating observations can give particular advantages. However, an SVD-based observation positioning strategy may not be optimal; thus, we introduce other criteria based on the correlation between points, as the information observed on neighboring locations can be redundant. These criteria are easily replicable in practical applications, as they require rather standard studies to obtain prior information.

scholarly journals A Novel Blind and Robust Video Watermarking Technique in Fast Motion Frames Based on SVD and MR-SVD

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Imen Nouioua ◽  
Nouredine Amardjia ◽  
Sarra Belilita
Keyword(s):  
Singular Value Decomposition ◽  
Video Quality ◽  
Singular Value ◽  
Video Watermarking ◽  
Digital Video Watermarking ◽  
Video Frames ◽  
Fast Motion ◽  
Good Transparency ◽  
Value Decomposition

In this work, a novel and efficient digital video watermarking technique based on the Singular Value Decomposition performed in the Multiresolution Singular Value Decomposition domain is proposed. While most of the existing watermarking schemes embed the watermark in all the video frames, which is time-consuming and also affects the perceptibly of the video quality, the proposed method chooses only the fast motion frames in each shot to host the watermark. In doing so, the number of frames to be processed is consequently reduced and a better quality of the watermarked video is also ensured since the human visual system cannot notice the variations in fast moving regions. The watermark information is embedded by Quantization Index Modulation which is a blind watermarking algorithm. The experimental results demonstrate that the proposed method can achieve a very good transparency, while being robust against various kinds of attacks such as filtering, noising, compression, and frame collusion. Compared with several methods found in the literature, the proposed method gives a better robustness.

Singular Value Decomposition-Based Generalized Side Lobe Canceller Beamforming Method for Ultrasound Imaging

2018 ◽  
Vol 32 (07) ◽  
pp. 1854017 ◽  
Author(s):  
Han-Wu Luo ◽  
Fang Li ◽  
Guang Sun ◽  
Shi-Gang Cui ◽  
Nan Lin
Keyword(s):  
Singular Value Decomposition ◽  
Contrast Ratio ◽  
Side Lobe ◽  
Minimum Variance ◽  
Singular Value ◽  
Signal Space ◽  
Velocity Error ◽  
Sample Covariance ◽  
Value Decomposition

In the previous studies, eigenspace-based minimum variance (ESBMV) algorithms were proposed, however, the quality of the algorithm will degrade in low signal to noise occasions. In this study, a singular value decomposition generalized side lobe canceller (SVD-GSC) beamforming method based on the GSC is proposed. The sample covariance matrix is eigendecomposed, and a kind of further SVD is introduced to establish the noise space and the signal space, respectively. After that, the weighting vectors acquired by GSC are projected into the left singular space of the desired signal space. The performance of the proposed method is investigated by both of the simulation and experimental data. And the sound velocity error is also investigated in this paper. The imaging quality of point targets are measured by the [Formula: see text][Formula: see text]dB main lobe width and the peak side lobe (PSL). The contrast ratio (CR) is introduced to describe the quality of cyst phantom. Both the point targets and cyst phantom simulation show that the proposed SVD-GSC performs better in terms of spatial resolution, PSL and CR. Furthermore, the proposed method has a stronger robustness than the traditional GSC.

scholarly journals CRITIQUE OF SOLUTIONS IN LINEARIZED INVERSE PROBLEMS: NUMERICAL EXPERIMENTS IN TRAVELTIME TOMOGRAPHY

2017 ◽  
Vol 34 (4) ◽  
Author(s):  
Silvia L. Bejarano ◽  
Amin Bassrei
Keyword(s):  
Singular Value Decomposition ◽  
Inverse Problems ◽  
Numerical Experiments ◽  
Singular Value ◽  
Traveltime Tomography ◽  
Value Decomposition

ABSTRACT. In this work, we evaluated the quality of the solution of numerical experiments in traveltime tomography, in linear and linearized cases, using singular value decomposition. The simulations were performed using...Keywords: inverse problems, traveltime tomography, resolution matrices, Barbieri method, regularization. RESUMO. Neste trabalho avaliamos a qualidade da solução em experimentos numéricos em tomografia de tempo de trânsito, nos casos linear e linearizado, utilizando o método de decomposição por valores singulares...Palavras-chave: problemas inversos, tomografia de tempos de trânsito, matrizes de resolução, método de Barbieri, regularização.

Digital Watermarking in the Transform Domain with Emphasis on SVD

2011 ◽  
pp. 46-66
Author(s):  
Maria Calagna
Keyword(s):  
Singular Value Decomposition ◽  
Digital Watermarking ◽  
Spatial Data ◽  
Singular Value ◽  
Transform Domain ◽  
Value Decomposition ◽  
Watermarking Scheme ◽  
Multimedia File

The chapter illustrates watermarking based on the transform domain. It argues that transform-based watermarking is robust to possible attacks and imperceptible with respect to the quality of the multimedia file we would like to protect. Among those transforms commonly used in communications, we emphasize the use of singular value decomposition (SVD) for digital watermarking. The main advantage of this choice is flexibility of application. In fact, SVD may be applied in several fields where data are organized as matrices, including multimedia and communications. We present a robust SVD-based watermarking scheme for images. According to the detection steps, the watermark can be determined univocally, while other related works present flaws in watermark detection. A case study of our approach refers to the protection of geographical and spatial data in case of the raster representation model of maps.

scholarly journals GPR Clutter Reflection Noise-Filtering through Singular Value Decomposition in the Bidimensional Spectral Domain

2021 ◽  
Vol 13 (10) ◽  
pp. 2005
Author(s):  
Rui Jorge Oliveira ◽  
Bento Caldeira ◽  
Teresa Teixidó ◽  
José Fernando Borges
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Spectral Domain ◽  
Roman Villa ◽  
Useful Signal ◽  
3D Gpr ◽  
Effective Signal ◽  
Value Decomposition ◽  
Ground Penetrating

Usually, in ground-penetrating radar (GPR) datasets, the user defines the limits between the useful signal and the noise through standard filtering to isolate the effective signal as much as possible. However, there are true reflections that mask the coherent reflectors that can be considered noise. In archaeological sites these clutter reflections are caused by scattering with origin in subsurface elements (e.g., isolated masonry, ceramic objects, and archaeological collapses). Its elimination is difficult because the wavelet parameters similar to coherent reflections and there is a risk of creating artefacts. In this study, a procedure to filter the clutter reflection noise (CRN) from GPR datasets is presented. The CRN filter is a singular value decomposition-based method (SVD), applied in the 2D spectral domain. This CRN filtering was tested in a dataset obtained from a controlled laboratory environment, to establish a mathematical control of this algorithm. Additionally, it has been applied in a 3D-GPR dataset acquired in the Roman villa of Horta da Torre (Fronteira, Portugal), which is an uncontrolled environment. The results show an increase in the quality of archaeological GPR planimetry that was verified via archaeological excavation.

scholarly journals A Robust Medical Images Watermarking Using FDCuT-DCT-SVD

2020 ◽  
Vol 13 (6) ◽  
pp. 266-278
Author(s):  
Ledya Novamizanti ◽  
◽  
Ida Wahidah ◽  
Ni Wardana ◽  
◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Discrete Cosine Transform ◽  
High Frequency ◽  
Medical Image ◽  
Medical Images ◽  
Singular Values ◽  
Singular Value ◽  
Watermark Image ◽  
Value Decomposition

One way to prevent image duplication is by applying watermarking techniques. In this work, the watermarking process is applied to medical images using the Fast Discrete Curvelet Transforms (FDCuT), Discrete Cosine Transform (DCT), and Singular Value Decomposition (SVD) methods. The medical image of the host is transformed using FDCuT so that three subbands are obtained. High Frequency (HF) subband selected for DCT and SVD applications. Meanwhile, SVD was also applied to the watermark image. The singular value on the host image is exchanged with the singular value on the watermark. Insertion of tears by exchanging singular values does not cause the quality of medical images to decrease significantly. The experimental results prove that the proposed FDCuT-DCT-SVD algorithm produces good imperceptibility. The proposed algorithm is also resistant to various types of attacks, including JPEG compression, noise enhancement attacks, filtering attacks, and other common attacks.

scholarly journals GPR Clutter Reflection Noise Filtering Through Singular Value Decomposition in the Bidimensional Spectral Domain

2021 ◽  
Author(s):  
Rui Jorge Oliveira ◽  
Bento Caldeira ◽  
Teresa Teixidó ◽  
José Fernando Borges
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Spectral Domain ◽  
Roman Villa ◽  
Useful Signal ◽  
3D Gpr ◽  
Effective Signal ◽  
Value Decomposition ◽  
Ground Penetrating

Usually, in ground-penetrating radar (GPR) datasets the user defines the limits between the useful signal and the noise through standard filtering to isolate the effective signal as much as possible. However, there are true reflections that mask the coherent reflectors that can be considered noise. In archaeological sites these clutter reflections are caused by scattering with origin in subsurface elements (e.g., isolated masonry, ceramic objects and archaeological collapses). Its elimination is difficult because the wavelet parameters similar to coherent reflections and there is a risk of creating artifacts. In this study a procedure to filtering the clutter reflection noise (CRN) from GPR datasets is presented. The CRN filter is a singular value decomposition-based method (SVD), applied in the 2D spectral domain. This CRN filtering was tested in a dataset obtained from a controlled laboratory environment, to establish a mathematical control of this algorithm. Also, it has been applied in a 3D-GPR dataset acquired in the Roman villa of Horta da Torre (Fronteira, Portugal), which is an uncontrolled environment. The results show an increase in the quality of archaeological-GPR planimetry that were verified via archaeological excavation.

Robust damped rank-reduction method for simultaneous denoising and reconstruction of 5-D seismic data

Geophysics ◽  
2020 ◽  
pp. 1-143
Author(s):  
Yapo Abolé Serge Innocent Oboué ◽  
Wei Chen ◽  
Hang Wang ◽  
Yangkang Chen
Keyword(s):  
Singular Value Decomposition ◽  
Seismic Data ◽  
Moving Average ◽  
Random Noise ◽  
Singular Value ◽  
Truncated Singular Value Decomposition ◽  
Rank Reduction ◽  
Residual Noise ◽  
Value Decomposition

We have developed a new method for simultaneous denoising and reconstruction of 5-D seismic data corrupted by random noise and missing traces. Several algorithms have been proposed for seismic data restoration based on rank-reduction methods. More recently, a damping operator has been introduced into the conventional truncated singular value decomposition (TSVD) formula to further remove residual noise, the presence of which disturbs the quality of the seismic results. Despite the success of the damped rank-reduction (DRR) method when the observed data have an extremely low signal-to-noise ratio (SNR), random noise is still a limiting factor for obtaining perfect quality of the result. Therefore, how to accurately solve the simultaneous denoising and reconstruction problem with high fidelity is still challenging. We assume that introducing only the damping operator into the TSVD formula is not enough to remove the random noise and restore the useful signal well. Here, by combining the soft thresholding operator and the moving-average filter, we first develop a new operator, which we call soft thresholding moving-average (STMA) operator. Then, by introducing the STMA operator into the DRR framework, we develop a new algorithm known as the robust damped rank-reduction (RDRR) method, which aims at mixing the advantages of the STMA operator and the damping operator. The STMA operator is applied to the Hankel matrix after damped truncated singular value decomposition (DTSVD) to better remove the residual noise. Examples of the proposed approach on synthetic and field 5-D seismic data demonstrate the better performance in terms of the visual examination and numerical test compared with the DRR approach. The proposed method aims at producing an effective low-rank filter and, thus, can perfectly enhance the SNR of the simultaneously denoised and reconstructed results with higher accuracy.

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