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Applications of wavelet transform in Mathematica and Sage
Novotný, Radek ; Trzos, Michal (referee) ; Rajmic, Pavel (advisor)
This thesis focuses on image processing using wavelet transform. The usage of wavelet transform is analysed especially for image compression and image noise reduction purposes. The analysis describes in detail aspects and application of the following wavelet transform methods: CWT, DWT, DTWT, 2D DWT. The thesis further explains the meaning of the mother wavelet and studies certain specific kinds of wavelets, kinds of thresholding and its purposes and also touches on the JPEG2000 standard. Mathematica and Sage software packages were used to design algorithms for image compression and image noise reduction, utilising relevant wavelet transform findings. The concluding part of the thesis compares the two software packages and results obtained using different algorithms.
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ECG signal filtering in the wavelet domain
Zedníček, Vlastimil ; Vítek, Martin (referee) ; Smital, Lukáš (advisor)
The aim of this work is introduction with the method of filtering the signal using wavelet transform. Our task was to use a redundant wavelet transform for filtering ECG signals. First we met with wavelet filtering. In the practical part, we implemented a filter based on redundant DTWT in Matlab. The results were evaluated based on the achieved signal / noise ratio. The proposed filter, we tested the CSE database, and we tried to optimize the filter parameters and the degree of decomposition of wavelet transform, the bank decomposition and reconstruction filters, thresholding methods and threshold setting. The results were evaluated based on the achieved signal / noise ratio. as a last resort, we compared the results obtained with the results of different filtering methods
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ECG Signal Wavelet Filtering
Zahradník, Radek ; Kozumplík, Jiří (referee) ; Smital, Lukáš (advisor)
The aim of this work is introduction to problems about the wavelet transform and then to use this transformation to filter ECG signal disturbed with myopotentials. The first part of this thesis contains basic information about the measurement, waveform and disturbance of ECG signal. The next part describes the method of wavelet transform and its use for the signal filtering The last part describes the practical part of work, where the results of filtering with different filter settings are evaluated, especially the various types of thresholding. At the end of this part is a comparison of results from wavelet and linear filter.
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Image Inpainting Methods
Kovacs, Jan ; Špiřík, Jan (referee) ; Průša, Zdeněk (advisor)
This thesis deals with an overview of modern Image Inpainting Methods. There are several best-known methods selected and described in the theoretical part of this work. Each of the selected methods is described and evaluated according to the informations available in literature. Among the methods that were selected and subsequently described in this work are Image Inpainting, Fragment-Based Image Completion, Exemplar-Based Image Inpainting, Gradient-Based Image Completion by Solving Poisson Equation and Inpainting by Flexible Haar-Wavelet Shrinkage. The MATLAB implementation of the Framelet-Based Image Inpainting algorithm forms practical part of the thesis. The Framelet transform was created for the purposes of the algorithm. The user interaction provides GUI, which was also implemented in MATLAB. The GUI allows setting input images, algorithm parameters and interaction with the output. The user is always informed about the current state of the computation, and the current result of image completion is shown to him. Moreover, it was created a tool that allows the user to define the areas to be supplemented, using the mouse. Finally, the algorithm performance is evaluated and compared using both Framelet and Contourlet transform.
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Image Inpainting Methods
Kovacs, Jan ; Špiřík, Jan (referee) ; Průša, Zdeněk (advisor)
This thesis deals with an overview of modern Image Inpainting Methods. There are several best-known methods selected and described in the theoretical part of this work. Each of the selected methods is described and evaluated according to the informations available in literature. Among the methods that were selected and subsequently described in this work are Image Inpainting, Fragment-Based Image Completion, Exemplar-Based Image Inpainting, Gradient-Based Image Completion by Solving Poisson Equation and Inpainting by Flexible Haar-Wavelet Shrinkage. The MATLAB implementation of the Framelet-Based Image Inpainting algorithm forms practical part of the thesis. The Framelet transform was created for the purposes of the algorithm. The user interaction provides GUI, which was also implemented in MATLAB. The GUI allows setting input images, algorithm parameters and interaction with the output. The user is always informed about the current state of the computation, and the current result of image completion is shown to him. Moreover, it was created a tool that allows the user to define the areas to be supplemented, using the mouse. Finally, the algorithm performance is evaluated and compared using both Framelet and Contourlet transform.
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ECG signal filtering in the wavelet domain
Zedníček, Vlastimil ; Vítek, Martin (referee) ; Smital, Lukáš (advisor)
The aim of this work is introduction with the method of filtering the signal using wavelet transform. Our task was to use a redundant wavelet transform for filtering ECG signals. First we met with wavelet filtering. In the practical part, we implemented a filter based on redundant DTWT in Matlab. The results were evaluated based on the achieved signal / noise ratio. The proposed filter, we tested the CSE database, and we tried to optimize the filter parameters and the degree of decomposition of wavelet transform, the bank decomposition and reconstruction filters, thresholding methods and threshold setting. The results were evaluated based on the achieved signal / noise ratio. as a last resort, we compared the results obtained with the results of different filtering methods
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ECG Signal Wavelet Filtering
Zahradník, Radek ; Kozumplík, Jiří (referee) ; Smital, Lukáš (advisor)
The aim of this work is introduction to problems about the wavelet transform and then to use this transformation to filter ECG signal disturbed with myopotentials. The first part of this thesis contains basic information about the measurement, waveform and disturbance of ECG signal. The next part describes the method of wavelet transform and its use for the signal filtering The last part describes the practical part of work, where the results of filtering with different filter settings are evaluated, especially the various types of thresholding. At the end of this part is a comparison of results from wavelet and linear filter.
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|
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Applications of wavelet transform in Mathematica and Sage
Novotný, Radek ; Trzos, Michal (referee) ; Rajmic, Pavel (advisor)
This thesis focuses on image processing using wavelet transform. The usage of wavelet transform is analysed especially for image compression and image noise reduction purposes. The analysis describes in detail aspects and application of the following wavelet transform methods: CWT, DWT, DTWT, 2D DWT. The thesis further explains the meaning of the mother wavelet and studies certain specific kinds of wavelets, kinds of thresholding and its purposes and also touches on the JPEG2000 standard. Mathematica and Sage software packages were used to design algorithms for image compression and image noise reduction, utilising relevant wavelet transform findings. The concluding part of the thesis compares the two software packages and results obtained using different algorithms.
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|
|
Applications of wavelet transform in Mathematica and Sage
Novotný, Radek ; Trzos, Michal (referee) ; Rajmic, Pavel (advisor)
This thesis focuses on image processing using wavelet transform. The usage of wavelet transform is analysed especially for image compression and image noise reduction purposes. The analysis describes in detail aspects and application of the following wavelet transform methods: CWT, DWT, DTWT, 2D DWT. The thesis further explains the meaning of the mother wavelet and studies certain specific kinds of wavelets, kinds of thresholding and its purposes and also touches on the JPEG2000 standard. Mathematica and Sage software packages were used to design algorithms for image compression and image noise reduction, utilising relevant wavelet transform findings. The concluding part of the thesis compares the two software packages and results obtained using different algorithms.
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