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Segmented wavelet transform of images
Kučera, Michal ; Rajmic, Pavel (referee) ; Průša, Zdeněk (advisor)
This master’s thesis is dealing with modification of classical discrete time wavelet transform algorithm to be able to split input image into several segments which could be independently processed. Segmented discrete time wavelet transform is introduced and implemented and the tests shows that it produces the similar values of wavelet coefficients as the classical approach. Complete independent image segment processing is allowed thanks to inverse segmented discrete time wavelet transform. It’s obvious that redundancy calculations appear when the image is processed segment by segment compared to transform the image at once. The redundancy rises with increasing decomposition depth and filter length, however it falls when the segment dimensions are increased. It happens because it is worked with smaller amount of segments which needs to extend. The extension with neighbor samples is the only source of redundancy. The thesis also contains description of two different approaches to signal border extension: firstly complete extension for all decomposition levels before the transformation itself and secondly classical method when the signal is extended in each decomposition step. Both approaches have the same results of image reconstruction, but it distinguishes in calculated wavelet coefficients. Four kinds of signal border extension are compared by using MSE and PSNR. The results of all approaches are similar, however the smooth padding of order 0 and symmetric-padding could be slightly favored against smooth padding of order 1 and zero-padding which shows higher MSE.
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The Z transformation and its application to solutions of difference equations
Hubatová, Michaela ; Opic, Bohumír (advisor) ; Johanis, Michal (referee)
This thesis uses knowledge from the introductory course of complex analysis, especially the theory of Laurent series. It provides basic information about the Z transformation and shows its mathematical applications. The text gives characterizations of exponential type sequences and defines their Z transformation. Presented theorems can be used to determine images of exponential type sequences and to find preimages of functions holomorphic at the point infinity. These theorems are given with proofs and illustrated with examples. Also some methods of the inverse tranformation are mentioned and a list of preimages of chosen rational functions holomorphic at infinity is included. In the last chapter the Z transformation is applied to solve linear difference equations. Powered by TCPDF (www.tcpdf.org)
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Segmented wavelet transform of images
Kučera, Michal ; Rajmic, Pavel (referee) ; Průša, Zdeněk (advisor)
This master’s thesis is dealing with modification of classical discrete time wavelet transform algorithm to be able to split input image into several segments which could be independently processed. Segmented discrete time wavelet transform is introduced and implemented and the tests shows that it produces the similar values of wavelet coefficients as the classical approach. Complete independent image segment processing is allowed thanks to inverse segmented discrete time wavelet transform. It’s obvious that redundancy calculations appear when the image is processed segment by segment compared to transform the image at once. The redundancy rises with increasing decomposition depth and filter length, however it falls when the segment dimensions are increased. It happens because it is worked with smaller amount of segments which needs to extend. The extension with neighbor samples is the only source of redundancy. The thesis also contains description of two different approaches to signal border extension: firstly complete extension for all decomposition levels before the transformation itself and secondly classical method when the signal is extended in each decomposition step. Both approaches have the same results of image reconstruction, but it distinguishes in calculated wavelet coefficients. Four kinds of signal border extension are compared by using MSE and PSNR. The results of all approaches are similar, however the smooth padding of order 0 and symmetric-padding could be slightly favored against smooth padding of order 1 and zero-padding which shows higher MSE.
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