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Increasing Resolution in Perfusion Magnetic Resonance Imaging Using Compressed Sensing
Mangová, Marie ; Polec,, Jaroslav (referee) ; Šmídl, Václav (referee) ; Rajmic, Pavel (advisor)
Perfusion magnetic resonance imaging is a medical diagnostic method which requires high spatial and temporal resolution simultaneously to capture dynamics of an intravenous contrast agent which is used to perfusion measurement. However, magnetic resonance imaging has physical limits which do not allow to have this resolution simultaneously. This thesis deals with compressed sensing which enables to reconstruct measured data from relatively few acquired samples (below Nyquist rate) while resolution required to perfusion analysis is increased. This aim could be achieved with suitably proposed apriory information about sensed data and model proposal. The reconstruction is then done as an optimization problem. Doctoral thesis brings several new reconstruction models, further proposes method to debias this estimates and examines influence of compressed sensing onto perfusion parameters. Whole thesis is ended with extension of compressed sensing into three-dimensional data. Here, the influence of reconstruction onto perfusion parameters is also described. In summary, the thesis shows that due to compressed sensing, temporal resolution can be increased with the fixed spatial resolution or spatial resolution can be increased with the fixed temporal resolution.
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Interactive applets supporting teaching digital image processing
Křivánek, Jiří ; Mangová, Marie (referee) ; Rajmic, Pavel (advisor)
This thesis deals with the creation of applications for support of education computer graphics. The aim is to create a simple application which will show the functioning of the various methods. I implemented convolution methods for image filtering, dithering engaged in the distribution errors, bit planes that show each bit plane image, gamma correction to lighten or darken the image and procedural textures. All these methods are created in the form of Java applets.
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Compressed sensing in magnetic resonance perfusion imaging.
Mangová, Marie ; Veselý, Vítězslav (referee) ; Rajmic, Pavel (advisor)
Magnetic resonance perfusion imaging is a today's very promising method for medicine diagnosis. This thesis deals with a sparse representation of signals, low-rank matrix recovery and compressed sensing, which allows overcoming present physical limitations of magnetic resonance perfusion imaging. Several models for reconstruction of measured perfusion data is introduced and numerical methods for their software implementation, which is an important part of the thesis, is mentioned. Proposed models are verified on simulated and real perfusion data from magnetic resonance.
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Modern restoration of audio containing missing portions
Skyva, Pavel ; Mangová, Marie (referee) ; Rajmic, Pavel (advisor)
This bachelor thesis deals with modern method of audio signal restoration. The reconstruction is primarily based on sparse signal representations. In thesis is described the way of searching sparse coefficients using proximal Douglas-Rachford algorithm and following computation of reconstructed signal using this coefficients. The algorithm of reconstruction is implemented in the MATLAB software with toolbox LTFAT included. Results of the reconstruction are compared using objective evaluation method Signal-to-Noise ratio (SNR).
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Modern audio signal restoration methods
Kalník, Jan ; Mangová, Marie (referee) ; Rajmic, Pavel (advisor)
This bachelor thesis deals with modern methods of audio signal inpainting. Main methods used will be sparse signal representations. Those will be implemented into MATLAB software using LTFAT and UNLocBoX toolboxes. Next we would like to accomplish the best results with the audio inpainting and then compare these results as well as subjectively as objectively.
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Implemetation of signal processing problems for teaching purposes
Ševčík, Zdeněk ; Rajmic, Pavel (referee) ; Mangová, Marie (advisor)
This thesis is focused on Fourier series, phasor diagram, signal resampling and amplitude modulation. All of there problems are analyzed in theoretical part of thesis. Here are derived all three form of Fourier series, described signal sampling, decimation and interpolation. Next thesis is focused on signal modulation and closer deal with amplitude modulation of harmonic and inharmonic signal. In practical part is example of calculation of Fourier siries for a specific signal, example of signal resampling and example of amplitude modulation for harmonic and inharmonic signal. Objective of practical part is creates programs focused on these problems. Programs should be interactive and their purpose is demonstrate the problem to students.
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Looking for an optimal aiming point in playing darts
Mareček, Petr ; Rajmic, Pavel (referee) ; Mangová, Marie (advisor)
The thesis deals with recommendation optimal point of dartboard. The first part is theoretical, where is described issue of probability, distribution of variation and significant distribution of variation. At the end of theoretical part is described the Fourier transfrom. The second part of the thesis deals with the design and implementation of web application. The design and implemention of web application uses the theoretical part for assigment optimal point of dartboard.
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Interactive web applications supporting education
Tvorogov, Ivan ; Mangová, Marie (referee) ; Rajmic, Pavel (advisor)
The project mainly aims to the development of applications for viewing lossless data compression algorithms. A theoretical part is devoted to description of theory from the area of lossless data compression algorithms and basic description of the language of HTML5, JavaScript, and CSS that will be used during the development. A practical part is focused on proposal and implementation of particular applications.
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Interactive software tools for teaching signal and image processing
Had, Pavel ; Rajmic, Pavel (referee) ; Mangová, Marie (advisor)
This thesis deals with the development of interactive applets for educational purposes. There are four applets: linear image combinations, least squares method and linear regression, discrete linear convolution in 2D, and interpolation in 1D. Each part of this thesis consists of a theoretical analysis of a given problem and its implementation in JavaScript. Specific applets then illustrate the problem so that it can be easily understood.
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