Yes / PICARD is a space-based observatory hosting the Solar Diameter Imager and Surface Mapper (SODISM) telescope, which has continuously observed the Sun from July 2010 and up to March 2014. In order to study the fine structure of the solar surface, it is helpful to apply techniques that enhance the images so as to improve the visibility of solar features such as sunspots or faculae. The objective of this work is to develop an innovative technique to enhance the quality of the SODISM images in the five wavelengths monitored by the telescope at 215.0 nm, 393.37 nm, 535.7 nm, 607.1 nm and 782.2 nm. An enhancement technique using interpolation of the high-frequency sub-bands obtained by Discrete Wavelet Transforms (DWT) and the input image is applied to the SODISM images. The input images are decomposed by the DWT as well as Stationary Wavelet Transform (SWT) into four separate sub-bands in horizontal and vertical directions namely, low-low (LL), low-high (LH), high-low (HL) and high–high (HH) frequencies. The DWT high frequency sub-bands are interpolated by a factor 2. The estimated high frequency sub-bands (edges) are enhanced by introducing an intermediate stage using a stationary Wavelet Transform (SWT), and then all these sub-bands and input image are combined and interpolated with half of the interpolation factor α/2, used to interpolate the high-frequency sub-bands, in order to reach the required size for IDWT processing. Quantitative and visual results show the superiority of the proposed technique over a bicubic image resolution enhancement technique. In addition, filling factors for sunspots are calculated from SODISM images and results are presented in this work.

This thesis deals with wavelet analysis of sleep electroencephalogram to sleep stages scoring. The theoretical part of the thesis deals with the theory of EEG signal creation and analysis. The polysomnography (PSG) is also described. This is the method for simultaneous measuring the different electrical signals; main of them are electroencephalogram (EEG), electromyogram (EMG) and electrooculogram (EOG). This method is used to diagnose sleep failure. Therefore sleep, sleep stages and sleep disorders are also described in the present study. In practical part, some results of application of discrete wavelet transform (DWT) for decomposing the sleep EEGs using mother wavelet Daubechies 2 „db2“ are shown and the level of the seven. The classification of the resulting data was used feedforward neural network with backpropagation errors.