SVD Based Image Processing Applications: State of The Art, Contributions and Research Challenges

Sadek, Rowayda A.

doi:10.14569/ijacsa.2012.030703

Cited by 73 publications

(8 citation statements)

References 17 publications

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“…The condition number depends on the properties of a particular integral operator and can indeed be large in many applications such as image processing [14][15][16][17], geophysics [18][19][20][21] and high energy physics [22][23][24][25][26]. However, as it is shown in section 2, the condition vector norms are used in eq.…”

Section: Proposed Methodsmentioning

confidence: 99%

A new method for obtaining a Born cross section using visible cross section data from e+e− colliders

Gribanov

Попов

2021

J. High Energ. Phys.

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In this paper, we propose a new method for obtaining a Born cross section using visible cross section data. It is assumed that the initial state radiation is taken into account in a visible cross section, while in a Born cross section this effect is ommited. Since the equation that connects Born and visible cross sections is an integral equation of the first kind, the problem of finding its numerical solution is ill-posed. Various regularization-based approaches are often used to solve ill-posed problems, since direct methods usually do not lead to an acceptable result. However, in this paper it is shown that a direct method can be successfully used to numerically solve the considered equation under the condition of a small beam energy spread and uncertainty. This naive method is based on finding a numerical solution to the integral equation by reducing it to a system of linear equations. The naive method works well because the kernel of the integral operator is a rapidly decreasing function of the variable x. This property of the kernel leads to the fact that the condition number of the matrix of the system of linear equations is of the order of unity, which makes it possible to neglect the ill-posedness of the problem when the above condition is satisfied. The advantages of the naive method are its model independence and the possibility of obtaining the covariance matrix of a Born cross section in a simple way.It should be noted that there are already a number of methods for obtaining a Born cross section using visible cross section data, which are commonly used in e+e− experiments. However, at least some of these methods have various disadvantages, such as model dependence and relative complexity of obtaining a Born cross section covariance matrix. It should be noted that this paper focuses on the naive method, while conventional methods are hardly covered. The paper also discusses solving the problem using the Tikhonov regularization, so that the reader can better understand the difference between regularized and non-regularized solutions. However, it should be noted that, in contrast to the naive method, regularization methods can hardly be used for precise obtaining of a Born cross section. The reason is that the regularized solution is biased and the covariance matrix of this solution do not represent the correct covariance matrix of a Born cross section.

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Section: Proposed Methodsmentioning

confidence: 99%

A new method for obtaining a Born cross section using visible cross section data from e+e− colliders

Gribanov

Попов

2021

J. High Energ. Phys.

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“…Whilst it may seem trivial to solve this equation, the inverse of a nonsquare matrix is non-existent (which is true for almost all the cases, since total number of single-speckle pixels is much greater than the number of captured speckles). The solution to this computation problem is to use the Moore-Penrose pseudo-inverse of the matrix C, which can be calculated from the singular value decomposition: [16][17][18] U and V are unitary matrices, Σ is a diagonal matrix with the singular values and T denotes the matrix transpose. Matrix Σ −1 is obtained by reciprocating the main diagonal of the Σ matrix (singular values) and then transposing the resulted matrix.…”

Section: Strain Measurementmentioning

confidence: 99%

Low-cost fiber Bragg grating interrogation with a femtosecond laser written scattering chip

Falak

Sun

Vettenburg

et al. 2023

Laser Applications in Microelectronic and Optoelectronic Manufacturing (LAMOM) XXVIII

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Fiber Bragg gratings are the most popular type of optical fiber sensor. However, its commercial use is frequently limited by high cost and complexity of the interrogation unit. Here, an interrogator based on a femtosecond laser written silica scattering chip is designed and implemented. Such device can directly reconstruct strain, from the scattering speckle patterns, with a resolution of 70 µϵ (microstrain) within the range of 180-700 µϵ, limited by the slippage of the fiber coating, with the potential to be reduced with the system improvements.

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“…Angle measurement is obtained using singular value decomposition (SVD) and principal component analysis (PCA) as described elsewhere. 1,3,[5][6][7][8] Initially, the system was used to measure polarization rotation using a 1050 nm laser with 20 pm linewidth beam which was linearly polarized through a Glan-Thompson polarizer (Thorlabs, GTH10M) and a half waveplate (Thorlabs, WPHSM05-1064) (Fig. 2a).…”

Section: Polarization Angle Detectionmentioning

confidence: 99%

Magnetic field sensing using laser written birefringent scattering medium

Falak

Lee

et al. 2023

European Workshop on Optical Fibre Sensors (EWOFS 2023)

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We demonstrate a polarization analyser based on processing of speckle patterns generated by a scattering medium. Each speckle pattern at a given wavelength and polarization state is unique and deterministic, and thus the polarization angle alters the speckle pattern motif. The polarization state of a given input light is obtained using reconstructive linear algebra methods. The system consists of a femtosecond laser written scattering chip and a CMOS sensor and contains no moving parts, making the proposed solution is low-cost and compact. The linear polarization angle was accurately reconstructed over a 0-20° test range, with 6 arcminutes (1/10° ) standard error. To demonstrate an application as a polarimeter, we used the system to measure Faraday rotation in a SF59 lead silicate glass within an electromagnet. The magnetic field was successfully traced by determining the induced changes in the input beam’s linear polarization angle in the range 0-80 mT with 10 mT standard error.

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SVD Based Image Processing Applications: State of The Art, Contributions and Research Challenges

Cited by 73 publications

References 17 publications

A new method for obtaining a Born cross section using visible cross section data from e+e− colliders

A new method for obtaining a Born cross section using visible cross section data from e+e− colliders

Low-cost fiber Bragg grating interrogation with a femtosecond laser written scattering chip

Magnetic field sensing using laser written birefringent scattering medium

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