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Regularization techniques based on the least squares method
Kubínová, Marie ; Hnětynková, Iveta (advisor)
Title: Regularization Techniques Based on the Least Squares Method Author: Marie Michenková Department: Department of Numerical Mathematics Supervisor: RNDr. Iveta Hnětynková, Ph.D. Abstract: In this thesis we consider a linear inverse problem Ax ≈ b, where A is a linear operator with smoothing property and b represents an observation vector polluted by unknown noise. It was shown in [Hnětynková, Plešinger, Strakoš, 2009] that high-frequency noise reveals during the Golub-Kahan iterative bidiagonalization in the left bidiagonalization vectors. We propose a method that identifies the iteration with maximal noise revealing and reduces a portion of high-frequency noise in the data by subtracting the corresponding (properly scaled) left bidiagonalization vector from b. This method is tested for different types of noise. Further, Hnětynková, Plešinger, and Strakoš provided an estimator of the noise level in the data. We propose a modification of this estimator based on the knowledge of the point of noise revealing. Keywords: ill-posed problems, regularization, Golub-Kahan iterative bidiagonalization, noise revealing, noise estimate, denoising 1
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Regularizační metody založené na metodách nejmenších čtverců
Michenková, Marie ; Hnětynková, Iveta (advisor) ; Zítko, Jan (referee)
Title: Regularization Techniques Based on the Least Squares Method Author: Marie Michenková Department: Department of Numerical Mathematics Supervisor: RNDr. Iveta Hnětynková, Ph.D. Abstract: In this thesis we consider a linear inverse problem Ax ≈ b, where A is a linear operator with smoothing property and b represents an observation vector polluted by unknown noise. It was shown in [Hnětynková, Plešinger, Strakoš, 2009] that high-frequency noise reveals during the Golub-Kahan iterative bidiagonalization in the left bidiagonalization vectors. We propose a method that identifies the iteration with maximal noise revealing and reduces a portion of high-frequency noise in the data by subtracting the corresponding (properly scaled) left bidiagonalization vector from b. This method is tested for different types of noise. Further, Hnětynková, Plešinger, and Strakoš provided an estimator of the noise level in the data. We propose a modification of this estimator based on the knowledge of the point of noise revealing. Keywords: ill-posed problems, regularization, Golub-Kahan iterative bidiagonalization, noise revealing, noise estimate, denoising 1
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Audio noise reduction using deep neural networks
Talár, Ondřej ; Galáž, Zoltán (referee) ; Harár, Pavol (advisor)
The thesis focuses on the use of deep recurrent neural network, architecture Long Short-Term Memory for robust denoising of audio signal. LSTM is currently very attractive due to its characteristics to remember previous weights, or edit them not only according to the used algorithms, but also by examining changes in neighboring cells. The work describes the selection of the initial dataset and used noise along with the creation of optimal test data. For creation of the training network is selected KERAS framework for Python and are explored and discussed possible candidates for viable solutions.
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Odstranění rozmazání pomocí dvou snímků s různou délkou expozice
Sabo, Jozef ; Šroubek, Filip (advisor) ; Horáček, Jan (referee)
In the presented work we study methods of image deblurring using two images of the same scene with different exposure times, focusing on two main approach categories, the so called deconvolution and non-deconvolution methods. We present theoretical backgrounds on both categories and evaluate their limitations and advantages. We dedicate one section to a comparison of both method categories on test data (images) for which we use a MATLAB implementation of the methods. We also compare the effectiveness of said methods against the results of a selected single- image de-noising algorithm. We do not focus at computational efficiency of algorithms and work with grayscale images only.
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Odstranění rozmazání pomocí dvou snímků s různou délkou expozice
Sabo, Jozef ; Šroubek, Filip (advisor) ; Horáček, Jan (referee)
In the presented work we study the methods of image deblurring using two images of the same scene with different exposure times, focusing on two main approach categories, so called deconvolution and non-deconvolution methods. We present theoretical backgrounds on both categories and evaluate their limitations and advantages. We dedicate one section to compare both method categories on test data (images) for which we our MATLAB implementation of the methods. We also compare the effectiveness of said methods against the results of a selected single-image de-noising algorithm. We do not focus at computational efficiency of algorithms and work with single-channel images only.
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Methods of acquisition and processing of images based on sparse representations
Talár, Ondřej ; Mach, Václav (referee) ; Rajmic, Pavel (advisor)
Thesis deals with the reconstruction possibilities provided by the sparse representation of signals. This representation reduces the signal to a mere vector of elements which indicate the signal portion in the dictionary array. It outlined the problems with the quantized signal and recalled modulation type, involving a quantization and its ways. The solution is selected Douglas-Rachford algorithm that allows us to approximate on to the set of all acceptable solutions. At the end is demonstrated problem solution and several tests for presentation of created program.
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Static image enhancement using wavelet transform
Candrák, Matúš ; Rajmic, Pavel (referee) ; Smékal, Zdeněk (advisor)
In tomography and ultrasound signal processing, there is the noise build-up into the processing. Bachelor's thesis deals with static images highlighting, with denoising using wavelet transformation and edge detection with basic operators. This work describes some types of wavelts used for denoising of image and basic operators for edge detection in the image. The last part deals with a particular application for image processing, which was created in MATLAB.
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Polygonal Models Smoothing
Svěchovský, Radek ; Švub, Miroslav (referee) ; Kršek, Přemysl (advisor)
Object digitizing or 3D model transformation into surface representation brings defects in the form of noise. This thesis analyses the well-known approaches to the noise elimination from polygonal models. The reader will be concerned with the fundamental principles of smoothing and foremost the results of the comparison of different methods including Laplace method, algorithm Laplace-HC, Taubin's low-pass filter and bilateral filter.
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Applications of sparse data representations
Navrátilová, Barbora ; Veselý, Vítězslav (referee) ; Rajmic, Pavel (advisor)
The goal of this thesis is to demonstrate practical application of sparse data representation in the processing of sparse signals. For solving several example problems - denoising, dequantization, and sparse signal decomposition - convex optimization was used. The solutions were implemented in the Matlab environment. For each of the problems, there are two solutions - one for one-dimensional, and one for two-dimensional signal.
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