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Sparse Signal Recovery via Convex Optimization
Novosadová, Michaela
We propose recovering 1D piecewice linear signal using a sparsity-based method consisting of two steps. The first step is signal segmentation via optimization algorithms solving sparsity based model. Second step consists of applying an ordinary mean square method on each detected segment of the signal. We show results of our experiments on two types of the signal.
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Modern restoration of audio containing missing portions
Skyva, Pavel ; Mangová, Marie (referee) ; Rajmic, Pavel (advisor)
This bachelor thesis deals with modern method of audio signal restoration. The reconstruction is primarily based on sparse signal representations. In thesis is described the way of searching sparse coefficients using proximal Douglas-Rachford algorithm and following computation of reconstructed signal using this coefficients. The algorithm of reconstruction is implemented in the MATLAB software with toolbox LTFAT included. Results of the reconstruction are compared using objective evaluation method Signal-to-Noise ratio (SNR).
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Methods for increasing bit-depth in images
Záviška, Pavel ; Koldovský, Zbyněk (referee) ; Rajmic, Pavel (advisor)
The goal of this bachelor thesis is the application of an issue of sparse representations on the task of increasing bit-depth in images. Standard methods for bit-depth expansion are described, subsequently a method using sparse representation of an image signal is introduced. Methods are programmed in the Matlab enviroment. The results of the methods implemented are compared by using PSNR, SSIM objective indexes and subjectively using an online questionnaire.
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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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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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Restoration of overexposed digital image
Zonygová, Kristýna ; Veselý, Vítězslav (referee) ; Rajmic, Pavel (advisor)
The Bachelor thesis deals with the recovery of overexposed grayscale images based on sparse signal representation. For image conversion to another representation wavelet transform was used. In this representation, the solution of convex optimization which demand on relax signal sparse and restored pixels values was searched for. In this case, the proximal Douglas-Rachford algorithm was applied which uses two proximal operators. The implementation was carried out in numerical computing enviroment MATLAB using the Wavelet Toolbox software. The PSNR (peak signal-to-noise ratio) was utilized to evaluate success rate of proposed method. The method was tested on 5 random images and compared to results of image manipulation software Adobe Photoshop Lightroom CC.
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Restoration of overexposed digital image
Zonygová, Kristýna ; Veselý, Vítězslav (referee) ; Rajmic, Pavel (advisor)
The Bachelor thesis deals with the recovery of overexposed grayscale images based on sparse signal representation. For image conversion to another representation wavelet transform was used. In this representation, the solution of convex optimization which demand on relax signal sparse and restored pixels values was searched for. In this case, the proximal Douglas-Rachford algorithm was applied which uses two proximal operators. The implementation was carried out in numerical computing enviroment MATLAB using the Wavelet Toolbox software. The PSNR (peak signal-to-noise ratio) was utilized to evaluate success rate of proposed method. The method was tested on 5 random images and compared to results of image manipulation software Adobe Photoshop Lightroom CC.
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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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Sparse Signal Recovery via Convex Optimization
Novosadová, Michaela
We propose recovering 1D piecewice linear signal using a sparsity-based method consisting of two steps. The first step is signal segmentation via optimization algorithms solving sparsity based model. Second step consists of applying an ordinary mean square method on each detected segment of the signal. We show results of our experiments on two types of the signal.
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Modern restoration of audio containing missing portions
Skyva, Pavel ; Mangová, Marie (referee) ; Rajmic, Pavel (advisor)
This bachelor thesis deals with modern method of audio signal restoration. The reconstruction is primarily based on sparse signal representations. In thesis is described the way of searching sparse coefficients using proximal Douglas-Rachford algorithm and following computation of reconstructed signal using this coefficients. The algorithm of reconstruction is implemented in the MATLAB software with toolbox LTFAT included. Results of the reconstruction are compared using objective evaluation method Signal-to-Noise ratio (SNR).
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