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Decomposition of video-sequences into components with different dynamics
Gebrtová, Karolína ; Druckmüller, Miloslav (referee) ; Rajmic, Pavel (advisor)
The thesis is focused on the decomposition of video sequences, primarily on background and dynamic component separation, where the background remains the same and only small parts are in motion. Such a video is represented by a low-rank and sparse component. Thanks to the low-rank structure, the background can be separated using a median filter and dynamic mode decomposition. Furthermore, the robust principal component analysis, formulated as an optimization problem and its non-convex variant, will be employed. Also mentioned will be the multiresolution DMD, which is capable of decomposing the dynamic component based on its velocity.
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Computational methods in single molecule localization microscopy
Ovesný, Martin ; Hagen, Guy Michael (advisor) ; Plášek, Jaromír (referee) ; Fliegel, Karel (referee)
Computational methods in single molecule localization microscopy Abstract Fluorescence microscopy is one of the chief tools used in biomedical research as it is a non invasive, non destructive, and highly specific imaging method. Unfortunately, an optical microscope is a diffraction limited system. Maximum achievable spatial resolution is approximately 250 nm laterally and 500 nm axially. Since most of the structures in cells researchers are interested in are smaller than that, increasing resolution is of prime importance. In recent years, several methods for imaging beyond the diffraction barrier have been developed. One of them is single molecule localization microscopy, a powerful method reported to resolve details as small as 5 nm. This approach to fluorescence microscopy is very computationally intensive. Developing methods to analyze single molecule data and to obtain super-resolution images are the topics of this thesis. In localization microscopy, a super-resolution image is reconstructed from a long sequence of conventional images of sparsely distributed single photoswitchable molecules that need to be sys- tematically localized with sub-diffraction precision. We designed, implemented, and experimentally verified a set of methods for automated processing, analysis and visualization of data acquired...
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Separation of dynamic and static structures in a series of images
Gebrtová, Karolína ; Kosová, Petra (referee) ; Rajmic, Pavel (advisor)
This bachelor thesis is focused on the separation of static and dynamic structures of video. While the major part of the video background remains static, a few moving particles can be observed. Such video can be represented by a low-rank and a sparse component. Using a low-rank structure, the background can be separated by applying either the median filter or the dynamic mode decomposition. Furthermore, the thesis includes the robust principal component analysis which can be perceived as an optimization problem. In addition, the thesis is enhanced by result visualization methods.
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Restoration of signals with limited instantaneous value using a psychoacoustic model
Beňo, Tomáš ; Rajmic, Pavel (referee) ; Záviška, Pavel (advisor)
The master's thesis deals with the restoration of audio signals that have been damaged by clipping. Used methods are based on sparse representations of signals. The introduction of the thesis explains the issue of clipping and mentions the list of already existing methods that solve declipping, which are followed by the thesis. In the next chapter, the necessary theory of sparse representations and the proximal algorithms is described, including specific representatives from the category of convex optimization problems. The thesis contains declipping algorithm implemented in Matlab software environment. Chosen method for solving the task uses the Condat algorithm or Generic proximal algorithm for convex optimization and solves minimization of sum of three convex functions. The result of the thesis is five versions of algorithm and three of them have implemented psychoacoustic model for results improvement. For each version has been found optimal setting of parameters. The restoration quality results are evaluated using objective measurements like SDR and PEMO-Q and also using subjective listening test.
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Modern methods for restoration of degraded audiosignals
Mokrý, Ondřej ; Koldovský,, Zbyněk (referee) ; Rajmic, Pavel (advisor)
The master's thesis deals with the problem of restoring a block of missing samples in a digital audio signal. This problem is formulated as an optimization task, which seeks the sparsest time-frequency representation of a signal within the set of feasible reconstructed signals. Several particular formulations are discussed, namely the analyzing and the synthesizing model, both for convex and non-convex approaches. Suitable algorithms are proposed for solving these formulations, and in the convex case, the method is further enhanced by various procedures to compensate for the energy drop in the inpainted signal segment. The proposed algorithms are tested on real recordings, and their performance is shown to be competitive with the state-of-the-art.
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Image Bit-Depth Expansion Method Based On Sparse
Representations
Záviška, Pavel
In this paper, a method for restoration of low bit-depth images based on sparse representations is presented. Proposed method is independent on the transform used, however for the purposes of experiments, Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) are used. The experiments show that our method enhances the visual quality of low bit-depth images and performs better, in terms of PSNR, than basic bit-depth expansion methods.
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Restoration of signals after passing through the limiter with the use of psychoacoustic model
Kramář, Denis ; Rajmic, Pavel (referee) ; Záviška, Pavel (advisor)
This bachelor thesis deals with the use of sparse representaions for the purpose of restoration clipping-damaged audiosignal. First, a theory of limiter and signal limiting itself is discussed. Subsequently, some of present methods based on sparse representations theory are given. The theory of sparse representations is discussed in following chapture. After that is here described a psychoacoustic model and it's use for declipping. At the end of theoretical part, two methods dealing with this problem are introduced. First is based on synthesis model of signal using Douglas-Rachford algorithm. Second is based on analysis signal model using Chambolle-Pock algorithm. In the next part is their implementation in the Matlab environment. Finally, the result achieved by both algorithms are evaluated.
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Reconstruction of signal modified by fade-in/fade-out
Bača, Petr ; Kiska, Tomáš (referee) ; Rajmic, Pavel (advisor)
This thesis contains the theory needed to solve the special problem of bit-depth expansion. The goal is to reconstruct the signal which suffered from application of the fade-in, fade-out effect. The theory includes information of analog to digital conversion and the theory of sparse representations. Thesis formulates the task of bit-depth expansion and advices the algorithm to solve it. Furthermore, the realization of the issue is discussed and the results are given.
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Restoration of degraded audiosignals using sparse representations
Mokrý, Ondřej ; Veselý, Vítězslav (referee) ; Rajmic, Pavel (advisor)
This bachelor thesis is focused on the problem of inpainting a segment of missing samples in an audiosignal. The signal is represented as sparse vector using discrete Gabor transform. The problem of inpainting missing samples while preserving the sparsity of the representation is formulated as an optimisation task, which is then solved using Douglas-Rachford algorithm. In contrast with the state-of-the-art approaches, the algorithm is extended by proposing method for compensating the energy decrease which occurs in the restored signal.
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Audio restoration based on sparse signal representations
Záviška, Pavel ; Průša, Zdeněk (referee) ; Rajmic, Pavel (advisor)
This Master's Thesis deals with the issue of audio clipping and the application of sparse represenations model for the task of declipping. First, a general theory of clipping is described, followed by a brief overview of existing methods and a description of the general theory concerning sparse representations of signals and bases, respectively frames. Subsequently, two methods solving declipping problem based on sparse representations are intruduced. The first method uses the Generic proximal algorithm for convex optimization, the second one uses the Douglas-Rachford algorithm. The above mentioned methods have been programmed in the Matlab environment. The results of the declipping methods are evaluated according to SNR, PEMO-Q and also by subjective listening tests.
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