<p>This thesis describes and evaluates a number of approaches and algorithms for nonuniform correction (NUC) and suppression of fixed pattern noise in a image sequence. The main task for this thesis work was to create a general NUC for infrared focal plane arrays. To create a radiometrically correct NUC, reference based methods using polynomial approximation are used instead of the more common scene based methods which creates a cosmetic NUC.</p><p>The pixels that can not be adjusted to give a correct value for the incomming radiation are defined as dead. Four separate methods of identifying dead pixels are used to find these pixels. Both the scene sequence and calibration data are used in these identifying methods.</p><p>The algorithms and methods have all been tested by using real image sequences. A graphical user interface using the presented algorithms has been created in Matlab to simplify the correction of image sequences. An implementation to convert the corrected values from the images to radiance and temperature is also performed.</p>

Very fast automatic rejection algorithms were developed recently which allow to generate random variates from large classes of unimodal distributions. They require the choice of several design points which decompose the domain of the distribution into small sub-intervals. The optimal choice of these points is an important but unsolved problem. So we present an approach that allows to characterize optimal design points in the asymptotic case (when their number tends to infinity) under mild regularity conditions. We describe a short algorithm to calculate these asymptotically optimal points in practice. Numerical experiments indicate that they are very close to optimal even when only six or seven design points are calculated. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

For generating non-uniform random variates, black-box algorithms are powerful tools that allow drawing samples from large classes of distributions. We give an overview of the design principles of such methods and show that they have advantages compared to specialized algorithms even for standard distributions, e.g., the marginal generation times are fast and depend mainly on the chosen method and not on the distribution. Moreover these methods are suitable for specialized tasks like sampling from truncated distributions and variance reduction techniques. We also present a library called UNU.RAN that provides an interface to a portable implementation of such methods. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Šiame darbe nagrinėjama atsitiktinio dydžio X skirstinio aproksimacijos sudėtiniu Puasono dėsniu netolygūs įverčiai. / In this paper we analyze nonuniform estimates in approximation by the compound Poisson distribution.

This dissertation describes investigations of fully turbulent decelerating hydraulically roughbed flow over gravel and the development of technology to measure turbulence and associated sediment transport in streams. Theory is developed for predicting velocity distributions in simple uniform flow using the asymptotic invariance principle and tested using laboratory and field collected data. A mixed scale is developed that accounts for bed derived turbulent structures throughout the flows depth and is used to parameterize the external boundary’s effect on the flow for the logarithmic and outer layers. The asymptotic invariance principle and similarity analysis is conducted for the equations of motion in the outer region of decelerating flow over gravel to define equilibrium conditions for this class of flows with the velocity scale is the freestream velocity. The combination of time series and time averaged statistical analysis of turbulent flow is used to elucidate the structure of flow under decelerating conditions. Time averaged statistical measures of turbulence confirm results of others for higher Froude number approaching transcritical and time series analysis shows the effects of decelerating flow on turbulence to be frequency dependent. Wireless velocity sensors were developed and found capable of measuring time averaged velocity and able to resolve macroturbulence from time series data. A semi-theoretical model of elastic deformation of cantilever beams under hydraulic forcing was coupled with circuit theory to develop a calibration procedure for the VBS that requires only three measurement points, one of which is at zero velocity. Light based sensors are developed to estimate light attenuation in water for ecological research or estimating sediment concentration in water. A semi-theoretical scaling of light attenuation and sediment properties was developed which predicts light attenuation from sediment properties. The combination of new theory on open channel velocity, turbulent structure and field sensors for measuring turbulence and sediment offers the possibility to extend our laboratory knowledge to realistic flow situations.

Data-dependent triangulation (DDT) based mesh-generation schemes for image representation are studied. A flexible mesh-generation framework and a highly effective mesh-generation method that employs this framework are proposed. The proposed framework is derived from frameworks proposed by Rippa and Garland and Heckbert by making a number of key modifications to facilitate the development of much more effective mesh-generation methods. As the proposed framework has several free parameters, the effects of different choices of these parameters on mesh quality (both in terms of squared error and subjectively) are studied, leading to the recommendation of a particular set of choices for these parameters. A new mesh-generation method is then introduced that employs the proposed framework with these best parameter choices. Experimental results show our proposed mesh-generation method outperforms several competing approaches, namely, the DDT-based incremental scheme proposed by Garland and Heckbert, the COMPRESS scheme proposed by Rippa, and the adaptive thinning scheme proposed by Demaret and Iske. More specifically, in terms of PSNR, our proposed method was found to outperform these three schemes by median margins of 4.1 dB, 10.76 dB, and 0.83 dB, respectively. The subjective qualities of reconstructed images were also found to be correspondingly better. In terms of computational cost, our proposed method was found to be comparable to the schemes proposed by Garland and Heckbert and Rippa. Moreover, our proposed method requires only about 5 to 10% of the time of the scheme proposed by Demaret and Iske. In terms of memory cost, our proposed method was shown to require essentially same amount of memory as the schemes proposed by Garland and Heckbert and Rippa, and orders of magnitude (33 to 800 times) less memory than the scheme proposed by Demaret and Iske. / Graduate

Triangle mesh models of images are studied. Through exploration, a computational framework for mesh generation based on data-dependent triangulations (DDTs) and two specific mesh-generation methods derived from this framework are proposed. In earlier work, Yang et al. proposed a highly-effective technique for generating triangle-mesh models of images, known as the error diffusion (ED) method. Unfortunately, the ED method, which chooses triangulation connectivity via a Delaunay triangulation, typically yields triangulations in which many (triangulation) edges crosscut image edges (i.e., discontinuities in the image), leading to increased approximation error. In this thesis, we propose a computational framework for mesh generation that modifies the ED method to use DDTs in conjunction with the Lawson local optimization procedure (LOP) and has several free parameters. Based on experimentation, we recommend two particular choices for these parameters, yielding two specific mesh-generation methods, known as MED1 and MED2, which make different trade offs between approximation quality and computational cost. Through the use of DDTs and the LOP, triangulation connectivity can be chosen optimally so as to minimize approximation error. As part of our work, two novel optimality criteria for the LOP are proposed, both of which are shown to outperform other well known criteria from the literature. Through experimental results, our MED1 and MED2 methods are shown to yield image approximations of substantially higher quality than those obtained with the ED method, at a relatively modest computational cost. For example, in terms of peak-signal-to-noise ratio, our MED1 and MED2 methods outperform the ED method, on average, by 3.26 and 3.81 dB, respectively. / Graduate

In this paper we study the error behavior of the well known fast Fourier transform for nonequispaced data (NFFT) with respect to the L2-norm. We compare the arising errors for different window functions and show that the accuracy of the algorithm can be significantly improved by modifying the shape of the window function. Based on the considered error estimates for different window functions we are able to state an easy and efficient method to tune the involved parameters automatically. The numerical examples show that the optimal parameters depend on the given Fourier coefficients, which are assumed not to be of a random structure or roughly of the same magnitude but rather subject to a certain decrease.

Sampling and reconstruction is used as a fundamental signal processing operation since the history of signal theory. Classically uniform sampling is treated so that the resulting mathematics is simple. However there are various instances that nonuniform sampling and reconstruction of signals from their nonuniform samples are required. There exist two broad classes of reconstruction methods. They are the reconstruction according to a deterministic, and according to a stochastic model. In this thesis, the most fundamental aspects of nonuniform sampling and reconstruction, according to a deterministic model, is analyzed, implemented and tested by considering specific nonuniform reconstruction algorithms. Accuracy of reconstruction, computational efficiency and noise stability are the three criteria that nonuniform reconstruction algorithms are tested for. Specifically, four classical closed form interpolation algorithms proposed by Yen are discussed and implemented. These algorithms are tested, according to the proposed criteria, in a variety of conditions in order to identify their performances for reconstruction quality and robustness to noise and signal conditions. Furthermore, a filter bank approach is discussed for the interpolation from nonuniform samples in a computationally efficient manner. This approach is implemented and the efficiency as well as resulting filter characteristics is observed. In addition to Yen&#039 / s classical algorithms, a trade off algorithm, which claims to find an optimal balance between reconstruction accuracy and noise stability is analyzed and simulated for comparison between all discussed interpolators. At the end of the stability tests, Yen&#039 / s third algorithm, known as the classical recurrent nonuniform sampling, is found to be superior over the remaining interpolators, from both an accuracy and stability point of view.

There exists a vast literature on nonuniform random variate generators. Most of these generators are especially designed for a particular distribution. However in pratice only a few of these are available to practioners. Moreover for problems as (e.g.) sampling from the truncated normal distribution or sampling from fairly uncommon distributions there are often no algorithms available. In the last decade so called universal methods have been developed for these cases. The resulting algorithms are fast and have properties that make them attractive even for standard distributions. In this contribution we describe the concept of Automatic random variate generation where these methods are used to produce a single piece of code in a high level programming language. Using a web-based front-end to such a program this is an easy-to-use source for researchers and programmers for high quality generators for a large class of distributions. Using our UNURAN library we have implemented such a system, which is accessable at <a href="http://statistik.wu-wien.ac.at/anuran" target="_blank">http://statistik.wu-wien.ac.at/anuran</a>. / Series: Preprint Series / Department of Applied Statistics and Data Processing