
Decomposition of videosequences 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 lowrank and sparse component. Thanks to the lowrank 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 nonconvex variant, will be employed. Also mentioned will be the multiresolution DMD, which is capable of decomposing the dynamic component based on its velocity.

 

RAW image debayerization using deep neural network
Balušík, Peter ; Myška, Vojtěch (referee) ; Rajmic, Pavel (advisor)
Táto práca sa zaoberá problémom debayerizácie a to konkrétne debayerizáciou pomocou deep image prior. Deep image prior (DIP) je koncept riešenia bežných rekonštrukčných problémov použitím netrénovaných konvolučných neurónových sietí. Jedinou vstupnou informáciou je obrázok, ktorý bol nejakým spôsobom poškodený. Cieľom tejto práce je zistiť, či je DIP použitelná metóda na problémy debayerizácie. Taktiež bola navrhnutá nová debayerizačná metóda založená na DIP a porovnaná s bežnými debayerizačnými metódami. Rôzne mozaikové farebné filtre (CFAs) boli otestované na zistenie plného potenciálu navrhnutej metódy. Číselné porovnanie bolo spravené použitím rôznych metód hodnotenia. Na základne tohto porovnania, zvolená metóda preukázala podobné, v niektorých prípadoch aj lepšie, výsledky ako Malvarova debayerizačná metóda. Vizuálne, navrhovaná metóda ukázala podobné výsledky k najkvalitnejšej metóde v experimentoch – Menonovej debayerizačnej metóde. Dodatočne, spriemerovanie posledných pár obrázkov optimizačného procesu prinieslo pozitívne výsledky vzhľadom na číselné porovnanie. Aj keď navrhovaná metóda priniesla zaujímavé výsledky, ukázalo sa, že je mimoriadne výpočetne náročná v porovnaní s ďaľšími bežnými debayerizačnými metódami.


Alternative JPEG image decoder
Bureš, Jiří ; Štarha, Pavel (referee) ; Rajmic, Pavel (advisor)
This thesis deals with the JPEG image codec, edge detection in images, sparse signal representations and proximal algorithms. First, the operation of the JPEG encoder and decoder and the theory underlying it are described. Then, based on the theoretical knowledge, a new proximal algorithm is constructed and implemented in an existing JPEG algorithm in order to remove block relics in the decoded image. The programming side is solved in Matlab environment. The results are evaluated using MSE, PSNR and SSIM methods.


Increasing bit depth in audio signals
Mrázek, Tomáš ; Mokrý, Ondřej (referee) ; Rajmic, Pavel (advisor)
The task of this bachelor’s thesis is to get acquainted with basic and advanced dequantization methods. It describes basics of declipping with focus on method which uses social sparsity. From this method, an audio dequantization algorithm using social sparsity can be designed and implemented. The resulting program automatically quantize the original file to the required bit depth and then reconstruct it to the closest possible resemblance to the original.


Efficient implementation of methods for the restoration of damaged audio signals
Csiba, Hajnalka ; Rajmic, Pavel (referee) ; Mokrý, Ondřej (advisor)
This bachelor's thesis deals with the restoration of audio signals containing unknown samples at known locations using two algorithms. The first is the Janssen algorithm and the second is a method based on nonnegative matrix factorization. Janssen algorithm is built on the principle of the autoregressive model. The restoration of the samples is performed in such a way that the restored signal matches the predicted model as precisely as possible. The algorithm based on nonnegative matrix factorization is used to decompose the frequency spectrogram of the signal as the product of nonnegative matrices.


Web applications supporting education of JPEG compression
Dziuina, Valeriia ; Záviška, Pavel (referee) ; Rajmic, Pavel (advisor)
This bachelor thesis deals with the problem of lossy compression of image data implemented by the JPEG algorithm. The JPEG algorithm itself is described, as well as the background necessary for its understanding, such as the physical and physiological nature of colour formation, its basic parameters and RGB and YCbCr colour models. The result of this work is three web applications, each of which should demonstrate the flow of certain steps of the algorithm and their influence on the final image. These applications are first aimed at simplifying the understanding of the image data compression process within the JPEG algorithm.


Web applications supporting education of audio signals generation and processing
Tkadlec, Vojtěch ; Schimmel, Jiří (referee) ; Rajmic, Pavel (advisor)
The main goal of the diploma thesis was the creation of 3 web applications for interactive support of studying courses in the area of digital signal processing using the programming language JavaScript, the markup language HTML, and the Web Audio API interface. The topics included additive synthesis, ADSR time envelope, amplitude modulation, and approximation of 1D signals using discrete cosine transform. The written part of the thesis also focuses on the tools used for the practical part of the thesis. For better understanding of the topics, four web applications were created, and a separate web application was created specifically for the topic of ADSR envelope.


Audio signal restoration using the PlugandPlay method
Švento, Michal ; Rajmic, Pavel (referee) ; Mokrý, Ondřej (advisor)
The topic of this thesis is the reconstruction of a digital audio signal that is corrupted in two ways, sample dropout and added noise. The classical approach to solving these problems are convex optimization algorithms, which are based on the sparsity of the audio signal. In this thesis, we try a new PlugandPlay method that embeds a deep network, the denoiser, into conventional algorithms and attempt to solve these two distinct problems using a single algorithm. At the end of the paper, the algorithms are implemented and tested with the most common metrics and these results are evaluated. Modern methods have shown us that they can be more variable in the choice of parameters and offer more balanced solutions.


Web applications supporting education of signal processing fundamentals
Kuře, Dominik ; Ištvánek, Matěj (referee) ; Rajmic, Pavel (advisor)
The main topic of the thesis is the creation of four web applications which are used as learning material for students who are studying the basics of signal processing. The areas on which the thesis focuses on are root mean square and expected value of signals, basic signal operations (amplification, geometric translation, scale change), the effect these operations have on the Fourier series of the given signal and also resampling of a signal using different methods of interpolation (nearest neighbour method, linear interpolation, cubic interpolation and interpolation using the sinc function). These applications are implemented using the TypeScript programming language which is an extension of the JavaScript language which enhances it with static types. Other libraries that are used are the React library which is used for frontend web applications and a library which allows easy to implement but still very detailed manipulation of charts called Chart.js. The first half of the theoretical part of the thesis focuses on those areas of signal processing which are necessary to understand so the applications can be created. The second half focuses on information technologies used for the implementation of said applications. Besides the already mentioned technologies, the text also briefly mentions the basics of HTML and CSS languages as well as the JSX syntax. The practical part describes how the applications were implemented and also serves as documentation for the source code. This part shows the reader how to create differently shaped signals in code (sine, triangle, sawtooth, square with different duty cycles, noise) and how to obtain the Fourier series of each of these signals, how to implement different signal operations, how to interpolate between multiple points using different interpolation formulas and what are some of the methods which can be used to apply cubic interpolation (finite difference method, cardinal spline, Catmull–Rom spline, natural cubic interpolation), what the applications look like and what is their structure.
