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Compressive sampling for effective target tracking in a sensor network
Klimeš, Ondřej ; Veselý, Vítězslav (referee) ; Rajmic, Pavel (advisor)
The master's thesis deals with target tracking. For this a decentralized sensor network using distributed particle filter with likelihood consensus is used. This consensus is based on a sparse representation of local likelihood function in a suitable chosen dictionary. In this thesis two dictionaries are compared: the widely used Fourier dictionary and our proposed B-splines. At the same time, thanks to the sparsity of distributed data, it is possible to implement compressed sensing method. The results are compared in terms of tracking error and communication costs. The thesis also contains scripts and functions in MATLAB.
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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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Magnetic resonance imaging via optimization methods
Onderlička, Tomáš ; Šorel,, Michal (referee) ; Rajmic, Pavel (advisor)
Magnetic resonance imaging is a diagnostic method to form images of the organs in the body. Long acquisition times are the main disadvantage, however it is possible to accelerate the data acquisition with the method of compressed sensing by sensing fewer samples and formulating an optimization method for image reconstruction. The aim of this thesis is to describe and compare the common optimization methods and to create a software capable of solving them. Another objective is to observe how much the data acquisition can be accelarated without the loss of image quality when dealing with real data. The most promising method in the experiment was total generalized variation (TGV) regularization which was able to reconstruct an image with a proper quality using only a quarter of the data.
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Graphical user interface for magnetic resonance data reconstruction
Marcin, Michal ; Rajmic, Pavel (referee) ; Mangová, Marie (advisor)
The aim of the bachelor thesis was to create graphical user interface for processing magnetic resonance data. For this purpose, the Matlab development environment was used. The basic principles of magnetic resonance, the ways of scanning and the graphical imaging as well as mathematical methods are described in the first part. The method of compression scanning and imaging of real images using laboratory mice is described in the text. In the second part of the thesis, the graphical user environment and its functions are described. The program is able to simulate and display the Shepp-Logan phantom model according to specified parameters. The created application allows the reconstruction and processing of simulated as well as real data.
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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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Encryption of Messages and Images Using Compressed Sensing
Daňková, M.
The article deals with compressed sensing used to encrypt data. It allows performing signal capturing, its compression and encryption at the same time. The measurement matrix is generated using a secret key and is exploited for encryption. The article shows an example of its utilization at text and image message, moreover the Arnold transform is used in colour images for increasing security.
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Exploitng sparse signal representations in capturing and recovery of nuclear magnetic resonance data
Hrbáček, Radek ; Zátyik, Ján (referee) ; Rajmic, Pavel (advisor)
This thesis deals with the nuclear magnetic resonance field, especially spectroscopy and spectroscopy imaging, sparse signal representation and low-rank approximation approaches. Spectroscopy imaging methods are becoming very popular in clinical praxis, however, long measurement times and low resolution prevent them from their spreading. The goal of this thesis is to improve state of the art methods by using sparse signal representation and low-rank approximation approaches. The compressed sensing technique is demonstrated on the examples of magnetic resonance imaging speedup and hyperspectral imaging data saving. Then, a new spectroscopy imaging scheme based on compressed sensing is proposed. The thesis deals also with the in vivo spectrum quantitation problem by designing the MRSMP algorithm specifically for this purpose.
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Compressed sensing for MRI perfusion imaging
Daňková, M. ; Rajmic, P. ; Jiřík, Radovan
Perfusion MRI is a diagnostic method in medicine. The signal captured from the affected area can be described by the curve of lognormal distribution. The standard way of obtaining the measurements is very slow and does not comply with today's challenging requirements. Using compressed sensing, we propose to acquire much less coefficients, having minimal effect on the signal reconstruction (using the assumption that the data is a sum of low-rank matrix and sparse matrix in row spectrum).
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