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Implementation of restoring method for reading bar code
Kadlčík, Libor ; Bartušek, Karel (referee) ; Mikulka, Jan (advisor)
Bar code stores information in the form of series of bars and gaps with various widths, and therefore can be considered as an example of bilevel (square) signal. Magnetic bar codes are created by applying slightly ferromagnetic material to a substrate. Sensing is done by reading oscillator, whose frequency is modulated by presence of the mentioned ferromagnetic material. Signal from the oscillator is then subjected to frequency demodulation. Due to temperature drift of the reading oscillator, the demodulated signal is accompanied by DC drift. Method for removal of the drift is introduced. Also, drift-insensitive detection of presence of a bar code is described. Reading bar codes is complicated by convolutional distortion, which is result of spatially dispersed sensitivity of the sensor. Effect of the convolutional distortion is analogous to low-pass filtering, causing edges to be smoothed and overlapped, and making their detection difficult. Characteristics of convolutional distortion can be summarized into point-spread function (PSF). In case of magnetic bar codes, the shape of the PSF can be known in advance, but not its width of DC transfer. Methods for estimation of these parameters are discussed. The signal needs to be reconstructed (into original bilevel form) before decoding can take place. Variational methods provide effective way. Their core idea is to reformulate reconstruction as an optimization problem of functional minimization. The functional can be extended by other functionals (regularizations) in order to considerably improve results of reconstruction. Principle of variational methods will be shown, including examples of use of various regularizations. All algorithm and methods (including frequency demodulation of signal from reading oscillator) are digital. They are implemented as a program for a microcontroller from the PIC32 family, which offers high computing power, so that even blind deconvolution (when the real PSF also needs to be found) can be finished in a few seconds. The microcontroller is part of magnetic bar code reader, whose hardware allows the read information to be transferred to personal computer via the PS/2 interface or USB (by emulating key presses on virtual keyboard), or shown on display.
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Blind Image Deconvolution of Electron Microscopy Images
Schlorová, Hana ; Odstrčilík, Jan (referee) ; Walek, Petr (advisor)
V posledních letech se metody slepé dekonvoluce rozšířily do celé řady technických a vědních oborů zejména, když nejsou již limitovány výpočetně. Techniky zpracování signálu založené na slepé dekonvoluci slibují možnosti zlepšení kvality výsledků dosažených zobrazením pomocí elektronového mikroskopu. Hlavním úkolem této práce je formulování problému slepé dekonvoluce obrazů z elektronového mikroskopu a hledání vhodného řešení s jeho následnou implementací a porovnáním s dostupnou funkcí Matlab Image Processing Toolboxu. Úplným cílem je tedy vytvoření algoritmu korigujícícho vady vzniklé v procesu zobrazení v programovém prostředí Matlabu. Navržený přístup je založen na regularizačních technikách slepé dekonvoluce.
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Regularization methods for discrete inverse problems in single particle analysis
Havelková, Eva ; Hnětynková, Iveta (advisor) ; Plešinger, Martin (referee)
The aim of this thesis is to investigate applicability of regulariza- tion by Krylov subspace methods to discrete inverse problems arising in single particle analysis (SPA). We start with a smooth model formulation and describe its discretization, yielding an ill-posed inverse problem Ax ≈ b, where A is a lin- ear operator and b represents the measured noisy data. We provide theoretical background and overview of selected methods for the solution of general linear inverse problems. Then we focus on specific properties of inverse problems from SPA, and provide experimental analysis based on synthetically generated SPA datasets (experiments are performed in the Matlab enviroment). Turning to the solution of our inverse problem, we investigate in particular an approach based on iterative Hybrid LSQR with inner Tikhonov regularization. A reliable stopping criterion for the iterative part as well as parameter-choice method for the inner regularization are discussed. Providing a complete implementation of the proposed solver (in Matlab and in C++), its performance is evaluated on various SPA model datasets, considering high levels of noise and realistic distri- bution of orientations of scanning angles. Comparison to other regularization methods, including the ART method traditionally used in SPA,...
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Modifications of stochastic objects
Kadlec, Karel ; Štěpán, Josef (advisor) ; Dostál, Petr (referee)
In this thesis, we are concerned with the modifications of the stochastic processes and the random probability measures. First chapter is devoted to modifications of the stochastic process to the space of continuous functions, modifications of submartingale to the set of right-continuous with finite left-hand limits functions and separable modifications of stochastic process. In the second chapter is the attention on the regularization of random probability measure in Markov kernel focused. In particular, we work with random probability measures on the Borel subset of the Polish space, or Radon separable topological space.
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Regularization methods for discrete inverse problems in single particle analysis
Havelková, Eva ; Hnětynková, Iveta (advisor)
The aim of this thesis is to investigate applicability of regulariza- tion by Krylov subspace methods to discrete inverse problems arising in single particle analysis (SPA). We start with a smooth model formulation and describe its discretization, yielding an ill-posed inverse problem Ax ≈ b, where A is a lin- ear operator and b represents the measured noisy data. We provide theoretical background and overview of selected methods for the solution of general linear inverse problems. Then we focus on specific properties of inverse problems from SPA, and provide experimental analysis based on synthetically generated SPA datasets (experiments are performed in the Matlab enviroment). Turning to the solution of our inverse problem, we investigate in particular an approach based on iterative Hybrid LSQR with inner Tikhonov regularization. A reliable stopping criterion for the iterative part as well as parameter-choice method for the inner regularization are discussed. Providing a complete implementation of the proposed solver (in Matlab and in C++), its performance is evaluated on various SPA model datasets, considering high levels of noise and realistic distri- bution of orientations of scanning angles. Comparison to other regularization methods, including the ART method traditionally used in SPA,...
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Methods for enforcing non-negativity of solution in Krylov regularization
Hoang, Phuong Thao ; Hnětynková, Iveta (advisor) ; Pozza, Stefano (referee)
The purpose of this thesis is to study how to overcome difficulties one typically encounters when solving non-negative inverse problems by standard Krylov subspace methods. We first give a theoretical background to the non-negative inverse problems. Then we concentrate on selected modifications of Krylov subspace methods known to improve the solution significantly. We describe their properties, provide their implementation and propose an improvement for one of them. After that, numerical experiments are presented giving a comparison of the methods and analyzing the influence of the present parameters on the behavior of the solvers. It is clearly demonstrated, that the methods imposing nonnegativity perform better than the unconstrained methods. Moreover, our improvement leads in some cases to a certain reduction of the number of iterations and consequently to savings of the computational time while preserving a good quality of the approximation.
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Regularization techniques based on the least squares method
Kubínová, Marie ; Hnětynková, Iveta (advisor)
Title: Regularization Techniques Based on the Least Squares Method Author: Marie Michenková Department: Department of Numerical Mathematics Supervisor: RNDr. Iveta Hnětynková, Ph.D. Abstract: In this thesis we consider a linear inverse problem Ax ≈ b, where A is a linear operator with smoothing property and b represents an observation vector polluted by unknown noise. It was shown in [Hnětynková, Plešinger, Strakoš, 2009] that high-frequency noise reveals during the Golub-Kahan iterative bidiagonalization in the left bidiagonalization vectors. We propose a method that identifies the iteration with maximal noise revealing and reduces a portion of high-frequency noise in the data by subtracting the corresponding (properly scaled) left bidiagonalization vector from b. This method is tested for different types of noise. Further, Hnětynková, Plešinger, and Strakoš provided an estimator of the noise level in the data. We propose a modification of this estimator based on the knowledge of the point of noise revealing. Keywords: ill-posed problems, regularization, Golub-Kahan iterative bidiagonalization, noise revealing, noise estimate, denoising 1
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Regularization properties of Krylov subspace methods
Kučerová, Andrea ; Hnětynková, Iveta (advisor) ; Kučera, Václav (referee)
The aim of this thesis is to study and describe regularizing properties of iterative Krylov subspace methods for finding a solution of linear algebraic ill- posed problems contaminated by white noise. First we explain properties of this kind of problems, especially their sensitivity to small perturbations in data. It is shown that classical methods for solving approximation problems (such as the least squares method) fail here. Thus we turn to explanation of regularizing pro- perties of projections onto Krylov subspaces. Basic Krylov regularizing methods are considered, namely RRGMRES, CGLS, and LSQR. The results are illustrated on model problems from Regularization toolbox in MATLAB. 1
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Regularization methods for discrete inverse problems in single particle analysis
Havelková, Eva ; Hnětynková, Iveta (advisor) ; Plešinger, Martin (referee)
The aim of this thesis is to investigate applicability of regulariza- tion by Krylov subspace methods to discrete inverse problems arising in single particle analysis (SPA). We start with a smooth model formulation and describe its discretization, yielding an ill-posed inverse problem Ax ≈ b, where A is a lin- ear operator and b represents the measured noisy data. We provide theoretical background and overview of selected methods for the solution of general linear inverse problems. Then we focus on specific properties of inverse problems from SPA, and provide experimental analysis based on synthetically generated SPA datasets (experiments are performed in the Matlab enviroment). Turning to the solution of our inverse problem, we investigate in particular an approach based on iterative Hybrid LSQR with inner Tikhonov regularization. A reliable stopping criterion for the iterative part as well as parameter-choice method for the inner regularization are discussed. Providing a complete implementation of the proposed solver (in Matlab and in C++), its performance is evaluated on various SPA model datasets, considering high levels of noise and realistic distri- bution of orientations of scanning angles. Comparison to other regularization methods, including the ART method traditionally used in SPA,...
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