In February of 2014 NASA has launched the core observatory of The Global Precipitation Measurement Mission (GPM). Since then, the mission has been providing a wealth of observation data collected by the core observatory along with other satellites belonging to the mission space constellation. One of the most important data products that GPM provides is the Level 4 (L4) rainfall data product called Integrated Multi-satellitE Retrievals for GPM (IMERG). IMERG is constructed using the raw data collected by the Microwave (MW) sensors on board the constellation satellites along with the Infrared (IR) sensors on board geostationary satellites and the advance Dual-frequency Precipitation Radar (DPR) on board the GPM core satellite. The IMERG product is available globally for all interested researchers to use. In this dissertation, I focus on the applicability of IMERG in hydrologic applications, and specifically in flood peak modeling. In order to conduct a comprehensive evaluation of IMERG that is oriented towards hydrologic modeling. I have explored multiple hydrologic models which can be used to produce stream flow estimates using IMERG without the need of parameter calibration based on the model’s inputs. The calibration free capability is essential since model parameter calibration obscures the effect of the errors associated with the rainfall input on the estimated discharges, which in turn will limit our understanding about the distribution of the errors in IMERG over space and time. The two hydrologic models we used in this study are both physically based distributed models and were setup over the domain of the state of Iowa which is located in the United States’ Midwest. I also explored the performance of one of the hydrologic models’ component, which is the runoff-routing component, in order to estimate an additional portion of the errors in the discharge estimates that is not attributed to the model’s input but rather to the hydrologic model itself. A significant portion of my dissertation is concerned with identifying and using accurate methods to evaluate both IMERG and the hydrologic models’ outputs in a hydrologic context that is useful for flood modeling. Several studies have evaluated other satellite rainfall products using methods that vary in complexity. Some studies used the simplest methods of evaluation, such as, mean aerial differences and standard deviation of the differences (additive or multiplicative) compared to a benchmark rainfall product. This is done without taking the spatial dependency of the errors in space into consideration. Other studies modeled the spatial dependency (correlation) between the errors in the rainfall product, however, using Euclidean distance based approaches that do not account for the hydrologic basins’ shape and size. Nevertheless, it is important to realize that hydrologic models will eventually aggregate the rainfall values, along with the errors associated with them, through a stream network that is dichotomous in nature and does not comply with Euclidean distance. Thus, we employed a stream based evaluation framework, called the Spatial Stream Network (SSN) approaches, to characterize the errors in IMERG taking into account the stream distances and the stream connectivity information between evaluation sites. Although previously used in applications such as modeling water temperatures and pollutant transport, to the best of my knowledge this approach has not been used in rainfall product evaluation before this study. The SSN analysis of IMERG allowed me to answer the question, “What is the proper basin scale which is capable of filtering out the correlated errors in IMERG by accumulating the rainfall values through the stream network?” Finally, in order to add value to the current methods of evaluating model simulated stream flows. I proposed a time based evaluation that is capable of detecting peaks in both the observed and simulated flows and estimating the lag time of the simulated peaks. Typically, previous studies have used simple skill scores such as Root Mean Squared Errors (RMSE), correlation coefficient, and Nash-Sutcliff Efficiency (NSE) to evaluate hydrograph performance as a whole, or the difference in time to peak which involves primitive peak detection method (e.g., a moving or a defined time window). In this dissertation I propose a Continuous Wavelet Transform (CWT) based method to evaluate the peak times and shapes produced by the hydrologic model. The method is based on filtering the frequencies in the hydrograph by treating it as a signal and detecting sharp features in both the observed and time series and the phase difference between them. We also emphasized on the importance of the choice of wavelet shape used in the evaluation, and how different wavelet shapes can affect the inference about the time series.

S rychlým rozvojem technologie multispektrálního zobrazování v posledních desetiletích obrázky získané zobrazovacími systémy obsahují nejen barevná pásma RGB v každodenním životě, ale také mají multispektrální barevná pásma a vysoké prostorové rozlišení v multispektrálních obrazových datech. Díky tomu obrázky obsahují bohaté informace o charakteristických cílových oblastech. Fúze obrazu je také důležitou větví v oblasti zpracování obrazu, kde je více obrázků ze stejné oblasti ve stejné výšce sloučeno do jednoho obrazu. Poté se zlepší korelace mezi spektrálními informacemi multispektrálních obrazů. Aby se informace na obrázku neztratily. Tato práce obsahuje popis návrhu a implementace multispektrálního obrazového systému, předzpracování multispektrálních obrazů, fúzi multispektrálních obrazů a analýzu hlavních komponent. Nakonec je představeno hodnocení celého systému.

The thesis deals with addition of pixels outside the image. Lists some methods for inpainting using computers and highlights the pitfalls that appear here. Examines methods for interpolation and approximation of functions in order to find the best method for extrapolating the image beyond its borders. Describes the basics of Wavelet transformation and Multiresolution analysis. It is proposed several methods for replenishment of pixels outside the image. PSNR and SSIM are used to compare achieved results. These methods are explained and compared. Briefly discusses the algorithm OMP, falling within the sparse representation of signals, and used in one of the methods. Also discussed is the development environment of MATLAB as a tool for the implementation of algorithms that practically solves the given problem. The practical part describes the implemented methods for adding pixels outside the image.

The main focus of this work is to describe and implement a method to analyze sympathovagal balance. The theoretical part begins with electrocardiogram origin and measurement followed by heart rate variability explanation and a method of tachogram creation. The chapter is finished by description of wavelet transform as a means for tachogram processing and obtaining the sympato-vagal balance coeficient. Practical part of work focuses on developing a solution in Matlab for this problem. The R detector, tachogram creation and wavelet transform processing scripts with sympato-vagal balance assesment are fully described along with an example of their outputs. The work is finished with a conclusion of the findings and the assessment of sympato-vagal balance form them, which is unfortunately not so simple.

This thesis deals with detection of the retinal nerve fiber layer in gray level retinal images taken by fundus camera. The first part describes a physiology of human eye and glaucoma disease. Then, the use of wavelet transform and algorithm of texture analysis applied for texture analysis. Next chapters describe theory of texture analysis named „Gray level run length matrices“ and its application for detection of the nerve fiber layer. Applications of this method are described for three types of retinal tissues and for whole image. The last chapter describes gray levels around optic disc and results obtained from parameters from GLRL matrices.

This diploma thesis deals with digital image lossy compression. Lossy compression in general inserts some kind of distorsion to the resulting image. The distorsion should not be interupting or even noticable in the better case. For image analysis there is used process called transformation and for choosing relevant coefficients process called coding. Evaluation of image quallity can be done by objective or subjective method. There is encoder introduced and realized in this work. Encoder utilizes two-dimension wavelet transform and SPIHT algortihm for coefficient coding. It was made use of accelerated method of wavelet transform computation by lifting scheme. Coder can proccess color information of images using modificated original SPIHT algorithm. For implementation the JAVA programming language was employed. The object-oriented design principes was made use of and thus the program is easy to extended. At demonstaration pictures there are shown effectiveness and characteristic way of distorsion of the proposed coder at high compression rates.

The aim of this masters thesis is design and implement an appropriate method for highlighting MR images and the identification of rough edges to provide for division of controlled areas. To this purpose is possible to use the Wavelet analysis. For the simulation environment I using MATLAB entviroment, where introduce the comparison for different types of de-noising and too for different mother wavelets. These methods will be implemented on various MR images of termoromandibular joint.

This master’s thesis is dealing with modification of classical discrete time wavelet transform algorithm to be able to split input image into several segments which could be independently processed. Segmented discrete time wavelet transform is introduced and implemented and the tests shows that it produces the similar values of wavelet coefficients as the classical approach. Complete independent image segment processing is allowed thanks to inverse segmented discrete time wavelet transform. It’s obvious that redundancy calculations appear when the image is processed segment by segment compared to transform the image at once. The redundancy rises with increasing decomposition depth and filter length, however it falls when the segment dimensions are increased. It happens because it is worked with smaller amount of segments which needs to extend. The extension with neighbor samples is the only source of redundancy. The thesis also contains description of two different approaches to signal border extension: firstly complete extension for all decomposition levels before the transformation itself and secondly classical method when the signal is extended in each decomposition step. Both approaches have the same results of image reconstruction, but it distinguishes in calculated wavelet coefficients. Four kinds of signal border extension are compared by using MSE and PSNR. The results of all approaches are similar, however the smooth padding of order 0 and symmetric-padding could be slightly favored against smooth padding of order 1 and zero-padding which shows higher MSE.

This diploma thesis deals with the problem of using an objective quality assessment methods in image data compression. Lossy compression always introduces some kind of distortion into the processed data causing degradation in the quality of the image. The intensity of this distortion can be measured using subjective or objective methods. To be able to optimize compression algorithms the objective criteria are used. In this work the SSIM index as a useful tool for describing the quality of compressed images has been presented. Lossy compression scheme is realized using the wavelet transform and SPIHT algorithm. The modification of this algorithm using partitioning of the wavelet coefficients into the separate tree-preserving blocks followed by independent coding, which is especially suitable for parallel processing, was implemented. For the given compression ratio the traditional problem is being solved – how to allocate available bits among the spatial blocks to achieve the highest possible image quality. The possible approaches to achieve this solution were discussed. As a result, some methods for bit allocation based on MSSIM index were proposed. To test the effectivity of these methods the MATLAB environment was used.

The thesis deals with possibilities of using wavelet transform in applications dealing with noise reduction, primarily in the field of ECG signals denoising. We assess the impact of the various filtration parameters setting as the thresholding wavelet coefficients method, thresholds level setting and the selection of decomposition and reconstruction filter banks.. Our results are compared with the results of linear filtering. The results of wavelet Wieners filtration with pilot estimation are described below. Mainly, we tested a combination of decomposition and reconstruction filter banks. All the filtration methods described here are tested on real ECG records with additive myopotential noise character and are implemented in the Matlab environment.