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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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Search for a dictionary for audiosignals
Martinek, Václav ; Záviška, Pavel (referee) ; Rajmic, Pavel (advisor)
This thesis should answer what constitutes audiosignal. It deals with the dictionary learning based on sparse representations of signals. This thesis describing algorithms, which are important for the creation of learning dictionaries. We find a comparison of signal representation using Fourier transform and learned vocabulary. It describes the creation of a database of musical sounds.
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Two video-processing problems by means of nontraditional methods
Kánský, Antonín ; Mangová, Marie (referee) ; Rajmic, Pavel (advisor)
The aim of this work is to solve two problems from the field of video editing by means of sparse representation of signals. The problematics of the traditional realisation of two effects, which are background separation of and separation background from moving foreground, is clarified here, as well as the problematics of sparse signals. The solutions was achieved through the method of Principal component analysis (PCP). The resulting algorithm is implemented and tested by simulated and real data.
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Audio inpainting algorithms
Bartlová, Hana ; Veselý, Vítězslav (referee) ; Rajmic, Pavel (advisor)
This thesis deals with audio inpainting problem. Firstly, basic concepts are summarized. Then, sparse representation of signals is introduced along with several algorithms. In the main part dedicated to the audio inpainting, the problem is defined and actual methods are presented and compared. The newest approach using the harmonic strucure of sound signals is then introduced, followed by several experiments and evaluation. Lastly, an algorithm ensuring the maximal computational efficiency is derived.
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An alternative JPEG coder/decoder
Jirák, Jakub ; Kiska, Tomáš (referee) ; Rajmic, Pavel (advisor)
The JPEG codec is currently the most widely used image format. This work deals with the design and implementation of an alternative JPEG codec using proximal algorithms in combination with the fixation of points from the original image to suppression of artifacts created in common JPEG coding. To solve the problem, the prox_TV and then the Douglas-Rachford algorithm were used, for which special functions using l_1-norm for image reconstruction were derived. The results of the proposed solution are very good because they can effectively suppress the artefacts created and the result corresponds to the image with a higher set qualitative factor. The proposed method achieves very good results for both simple images and photos, but in the case of large images (1024 × 1024 px) and larger, a large amount of computing time is required, so the method is more suitable for smaller images.
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Search for a dictionary for audiosignals
Martinek, Václav ; Záviška, Pavel (referee) ; Rajmic, Pavel (advisor)
This thesis should answer what constitutes audio signal. It deals with the dictionary learning based on sparse representations of signals. This thesis describing algorithms, which are important for the creation of learning dictionaries. We find a comparison of signal representation using Fourier transform and learned vocabulary. It describes the creation of a database of musical sounds.
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Search for a dictionary for audiosignals
Martinek, Václav ; Záviška, Pavel (referee) ; Rajmic, Pavel (advisor)
This thesis should answer what constitutes audiosignal. It deals with the dictionary learning based on sparse representations of signals. This thesis describing algorithms, which are important for the creation of learning dictionaries. We find a comparison of signal representation using Fourier transform and learned vocabulary. It describes the creation of a database of musical sounds.
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