Wavelet Analysis in Turbulence

The objective of this thesis is to study wavelets and their role in turbulence applications. Under scrutiny in the thesis is the intermittency in turbulence models. Wavelets are used as a mathematical tool to study the intermittent activities that turbulence models produce. The first section generally introduces wavelets and wavelet transforms as a mathematical tool. Moreover, the basic properties of turbulence are discussed and classical methods for modeling turbulent flows are explained. Wavelets are implemented to model the turbulence as well as to analyze turbulent signals. The model studied here is the GOY (Gledzer 1973, Ohkitani & Yamada 1989) shell model of turbulence, which is a popular model for explaining intermittency based on the cascade of kinetic energy. The goal is to introduce better quantification method for intermittency obtained in a shell model. Wavelets are localized in both space (time) and scale, therefore, they are suitable candidates for the study of singular bursts, that interrupt the calm periods of an energy flow through various scales. The study concerns two questions, namely the frequency of the occurrence as well as the intensity of the singular bursts at various Reynolds numbers. The results gave an insight that singularities become more local as Reynolds number increases. The singularities become more local also when the shell number is increased at certain Reynolds number. The study revealed that the singular bursts are more frequent at Re ~ 107 than other cases with lower Re. The intermittency of bursts for the cases with Re ~ 106 and Re ~ 105 was similar, but for the case with Re ~ 104 bursts occured after long waiting time in a different fashion so that it could not be scaled with higher Re.

Selecting Wavelet Filter for Compression of Spectra from Multispectral Images

The problem of selecting anappropriate wavelet filter is always present in signal compression based on thewavelet transform. In this report, we propose a method to select a wavelet filter from a predefined set of filters for the compression of spectra from a multispectral image. The wavelet filter selection is based on the Learning Vector Quantization (LVQ). In the training phase for the test images, the best wavelet filter for each spectrum has been found by a careful compression-decompression evaluation. Certain spectral features are used in characterizing the pixel spectra. The LVQ is used to form the best wavelet filter class for different types of spectra from multispectral images. When a new image is to be compressed, a set of spectra from that image is selected, the spectra are classified by the trained LVQand the filter associated to the largest class is selected for the compression of every spectrum from the multispectral image. The results show, that almost inevery case our method finds the most suitable wavelet filter from the pre-defined set for the compression.

Multispectral image compression using the wavelet transform

Multispectral images contain information from several spectral wavelengths and currently multispectral images are widely used in remote sensing and they are becoming more common in the field of computer vision and in industrial applications. Typically, one multispectral image in remote sensing may occupy hundreds of megabytes of disk space and several this kind of images may be received from a single measurement. This study considers the compression of multispectral images. The lossy compression is based on the wavelet transform and we compare the suitability of different waveletfilters for the compression. A method for selecting a wavelet filter for the compression and reconstruction of multispectral images is developed. The performance of the multidimensional wavelet transform based compression is compared to other compression methods like PCA, ICA, SPIHT, and DCT/JPEG. The quality of the compression and reconstruction is measured by quantitative measures like signal-to-noise ratio. In addition, we have developed a qualitative measure, which combines the information from the spatial and spectral dimensions of a multispectral image and which also accounts for the visual quality of the bands from the multispectral images.

Distance Transforms on Gray-Level Surfaces

This thesis studies gray-level distance transforms, particularly the Distance Transform on Curved Space (DTOCS). The transform is produced by calculating distances on a gray-level surface. The DTOCS is improved by definingmore accurate local distances, and developing a faster transformation algorithm. The Optimal DTOCS enhances the locally Euclidean Weighted DTOCS (WDTOCS) with local distance coefficients, which minimize the maximum error from the Euclideandistance in the image plane, and produce more accurate global distance values.Convergence properties of the traditional mask operation, or sequential localtransformation, and the ordered propagation approach are analyzed, and compared to the new efficient priority pixel queue algorithm. The Route DTOCS algorithmdeveloped in this work can be used to find and visualize shortest routes between two points, or two point sets, along a varying height surface. In a digital image, there can be several paths sharing the same minimal length, and the Route DTOCS visualizes them all. A single optimal path can be extracted from the route set using a simple backtracking algorithm. A new extension of the priority pixel queue algorithm produces the nearest neighbor transform, or Voronoi or Dirichlet tessellation, simultaneously with the distance map. The transformation divides the image into regions so that each pixel belongs to the region surrounding the reference point, which is nearest according to the distance definition used. Applications and application ideas for the DTOCS and its extensions are presented, including obstacle avoidance, image compression and surface roughness evaluation.

Wavelet Filter Parameterization for Compression of Spectral Images

Vaatimus kuvatiedon tiivistämisestä on tullut entistä ilmeisemmäksi viimeisen kymmenen vuoden aikana kuvatietoon perustuvien sovellutusten myötä. Nykyisin kiinnitetään erityistä huomiota spektrikuviin, joiden tallettaminen ja siirto vaativat runsaasti levytilaa ja kaistaa. Aallokemuunnos on osoittautunut hyväksi ratkaisuksi häviöllisessä tiedontiivistämisessä. Sen toteutus alikaistakoodauksessa perustuu aallokesuodattimiin ja ongelmana on sopivan aallokesuodattimen valinta erilaisille tiivistettäville kuville. Tässä työssä esitetään katsaus tiivistysmenetelmiin, jotka perustuvat aallokemuunnokseen. Ortogonaalisten suodattimien määritys parametrisoimalla on työn painopisteenä. Työssä todetaan myös kahden erilaisen lähestymistavan samanlaisuus algebrallisten yhtälöiden avulla. Kokeellinen osa sisältää joukon testejä, joilla perustellaan parametrisoinnin tarvetta. Erilaisille kuville tarvitaan erilaisia suodattimia sekä erilaiset tiivistyskertoimet saavutetaan eri suodattimilla. Lopuksi toteutetaan spektrikuvien tiivistys aallokemuunnoksen avulla.

New Distance Transforms for Gray Level Image Compression

This thesis deals with distance transforms which are a fundamental issue in image processing and computer vision. In this thesis, two new distance transforms for gray level images are presented. As a new application for distance transforms, they are applied to gray level image compression. The new distance transforms are both new extensions of the well known distance transform algorithm developed by Rosenfeld, Pfaltz and Lay. With some modification their algorithm which calculates a distance transform on binary images with a chosen kernel has been made to calculate a chessboard like distance transform with integer numbers (DTOCS) and a real value distance transform (EDTOCS) on gray level images. Both distance transforms, the DTOCS and EDTOCS, require only two passes over the graylevel image and are extremely simple to implement. Only two image buffers are needed: The original gray level image and the binary image which defines the region(s) of calculation. No other image buffers are needed even if more than one iteration round is performed. For large neighborhoods and complicated images the two pass distance algorithm has to be applied to the image more than once, typically 3 10 times. Different types of kernels can be adopted. It is important to notice that no other existing transform calculates the same kind of distance map as the DTOCS. All the other gray weighted distance function, GRAYMAT etc. algorithms find the minimum path joining two points by the smallest sum of gray levels or weighting the distance values directly by the gray levels in some manner. The DTOCS does not weight them that way. The DTOCS gives a weighted version of the chessboard distance map. The weights are not constant, but gray value differences of the original image. The difference between the DTOCS map and other distance transforms for gray level images is shown. The difference between the DTOCS and EDTOCS is that the EDTOCS calculates these gray level differences in a different way. It propagates local Euclidean distances inside a kernel. Analytical derivations of some results concerning the DTOCS and the EDTOCS are presented. Commonly distance transforms are used for feature extraction in pattern recognition and learning. Their use in image compression is very rare. This thesis introduces a new application area for distance transforms. Three new image compression algorithms based on the DTOCS and one based on the EDTOCS are presented. Control points, i.e. points that are considered fundamental for the reconstruction of the image, are selected from the gray level image using the DTOCS and the EDTOCS. The first group of methods select the maximas of the distance image to new control points and the second group of methods compare the DTOCS distance to binary image chessboard distance. The effect of applying threshold masks of different sizes along the threshold boundaries is studied. The time complexity of the compression algorithms is analyzed both analytically and experimentally. It is shown that the time complexity of the algorithms is independent of the number of control points, i.e. the compression ratio. Also a new morphological image decompression scheme is presented, the 8 kernels' method. Several decompressed images are presented. The best results are obtained using the Delaunay triangulation. The obtained image quality equals that of the DCT images with a 4 x 4

On convergence of transforms based on parabolic scaling

This thesis studies properties of transforms based on parabolic scaling, like Curvelet-, Contourlet-, Shearlet- and Hart-Smith-transform. Essentially, two di erent questions are considered: How these transforms can characterize H older regularity and how non-linear approximation of a piecewise smooth function converges. In study of Hölder regularities, several theorems that relate regularity of a function f : R2 → R to decay properties of its transform are presented. Of particular interest is the case where a function has lower regularity along some line segment than elsewhere. Theorems that give estimates for direction and location of this line, and regularity of the function are presented. Numerical demonstrations suggest also that similar theorems would hold for more general shape of segment of low regularity. Theorems related to uniform and pointwise Hölder regularity are presented as well. Although none of the theorems presented give full characterization of regularity, the su cient and necessary conditions are very similar. Another theme of the thesis is the study of convergence of non-linear M ─term approximation of functions that have discontinuous on some curves and otherwise are smooth. With particular smoothness assumptions, it is well known that squared L2 approximation error is O(M-2(logM)3) for curvelet, shearlet or contourlet bases. Here it is shown that assuming higher smoothness properties, the log-factor can be removed, even if the function still is discontinuous.

Wet Oxidation of Concentrated Wastewaters: Process Combination and Reaction Kinetic Modeling

The accumulation of aqueous pollutants is becoming a global problem. The search for suitable methods and/or combinations of water treatment processes is a task that can slow down and stop the process of water pollution. In this work, the method of wet oxidation was considered as an appropriate technique for the elimination of the impurities present in paper mill process waters. It has been shown that, when combined with traditional wastewater treatment processes, wet oxidation offers many advantages. The combination of coagulation and wet oxidation offers a new opportunity for the improvement of the quality of wastewater designated for discharge or recycling. First of all, the utilization of coagulated sludge via wet oxidation provides a conditioning process for the sludge, i.e. dewatering, which is rather difficult to carry out with untreated waste. Secondly, Fe2(SO4)3, which is employed earlier as a coagulant, transforms the conventional wet oxidation process into a catalytic one. The use of coagulation as the post-treatment for wet oxidation can offer the possibility of the brown hue that usually accompanies the partial oxidation to be reduced. As a result, the supernatant is less colored and also contains a rather low amount of Fe ions to beconsidered for recycling inside mills. The thickened part that consists of metal ions is then recycled back to the wet oxidation system. It was also observed that wet oxidation is favorable for the degradation of pitch substances (LWEs) and lignin that are present in the process waters of paper mills. Rather low operating temperatures are needed for wet oxidation in order to destruct LWEs. The oxidation in the alkaline media provides not only the faster elimination of pitch and lignin but also significantly improves the biodegradable characteristics of wastewater that contains lignin and pitch substances. During the course of the kinetic studies, a model, which can predict the enhancements of the biodegradability of wastewater, was elaborated. The model includes lumped concentrations suchas the chemical oxygen demand and biochemical oxygen demand and reflects a generalized reaction network of oxidative transformations. Later developments incorporated a new lump, the immediately available biochemical oxygen demand, which increased the fidelity of the predictions made by the model. Since changes in biodegradability occur simultaneously with the destruction of LWEs, an attempt was made to combine these two facts for modeling purposes.

Lossless compression of hyperspectral images

Technological progress has made a huge amount of data available at increasing spatial and spectral resolutions. Therefore, the compression of hyperspectral data is an area of active research. In somefields, the original quality of a hyperspectral image cannot be compromised andin these cases, lossless compression is mandatory. The main goal of this thesisis to provide improved methods for the lossless compression of hyperspectral images. Both prediction- and transform-based methods are studied. Two kinds of prediction based methods are being studied. In the first method the spectra of a hyperspectral image are first clustered and and an optimized linear predictor is calculated for each cluster. In the second prediction method linear prediction coefficients are not fixed but are recalculated for each pixel. A parallel implementation of the above-mentioned linear prediction method is also presented. Also,two transform-based methods are being presented. Vector Quantization (VQ) was used together with a new coding of the residual image. In addition we have developed a new back end for a compression method utilizing Principal Component Analysis (PCA) and Integer Wavelet Transform (IWT). The performance of the compressionmethods are compared to that of other compression methods. The results show that the proposed linear prediction methods outperform the previous methods. In addition, a novel fast exact nearest-neighbor search method is developed. The search method is used to speed up the Linde-Buzo-Gray (LBG) clustering method.

Studying the recent situation of information and communication technology industry

Globaalinen liiketoimintaympäristö on muutoksessa. Uudet teknologiat muuttavat toimintaympäristöä ja talouden säännöt muuttuvat nopeasti. Uusia liiketoimintamalleja tarvitaan. Tutkimuksen tavoitteena oli analysoida tieto- ja viestintäteollisuuden (ICT-teollisuus) nykytilannetta strategisesta ja kilpailuanalyyttisestä näkökulmasta, sekä luoda kuva ICT-teollisuudesta ja sen suurista pelureista Euroopassa ja USA:ssa. Tutkimus analysoi viittä suurta ICT-alan yritystä. Tutkimus oli luonteeltaan sekä kvalitatiivinen että kvantitatiivinen. Yrityksiä analysoitiin käyttäen numeerista ja laadullista materiaalia. Tutkimus perustui kirjallisuuteen, artikkeleihin, tutkimusraportteihin, yritysten internet-kotisivuihin ja vuosikertomuksiin. Tutkimuksen tuloksena voitiin löytää sekä yhtäläisyyksiä että eroavaisuuksia yritysten liiketoimintamallien ja taloudellisen menestymisen väliltä.

Myynnin raportoinnin kehittäminen kassajärjestelmähankkeen yhteydessä

Raportointi liittyy kiinteänä osana yrityksen jokapäiväiseen toimintaan. Raportoinnin sisältö ja muoto vaihtelevat organisaatiotasosta riippuen päivittäisen toiminnan tarkkailusta kuukausittaiseen tulosraportointiin. Raportointi voidaan toteuttaa operatiivisten järjestelmien kautta tai nykyisin entistä suositumpana vaihtoehtona on keskitetty raportointi. Uuden raportointijärjestelmän hankintaprojekti on usein koko yritystä koskeva investointi. Jos raportointijärjestelmällä on tarkoitus raportoida sekä operatiivista toimintaa että johdon tarpeita, on sen mukauduttava moneen tarkoitukseen. Aluksi on tärkeää määritellä tietotarpeet ja tavoitteet projektille unohtamatta riskien- ja projektinhallintaa sekä investointilaskelmia. Jos raportoidaan myös yrityksen ulkopuolelle, tulee ottaa huomioon mahdolliset säädökset sekä tietoturvallisuusnäkökulmat. Myös yrityksen toimintatapoja ja – prosesseja on syytä tarkastella kriittisesti ennen järjestelmähankintaa jolloin voidaan havaita uusia raportointikohteita, tai toimintatapoja voidaan uudelleen organisoida parhaan toimintatavan saavuttamiseksi. Raportointijärjestelmää hankittaessa turvaudutaan usein ulkopuoliseen ohjelmistotoimittajaan, joka integroi ja räätälöi järjestelmän yrityksen omiin tarpeisiin soveltuvaksi. Raportointijärjestelmän hankintaprojekti ei lopu käyttöönottoon vaan projektin alussa on huomioitava myös järjestelmän huomattavasti pisin elinkaari eli käyttö ja ylläpito. Raportointi-, kuten ei moni muukaan tietojärjestelmä, ole ikinä valmis sillä tarpeet ja toimintatavat muuttuvat ajan kuluessa ja käyttäjien tietoisuus lisääntyy.

Prediction in transformed images

The study is related to lossless compression of greyscale images. The goal of the study was to combine two techniques of lossless image compression, i.e. Integer Wavelet Transform and Differential Pulse Code Modulation to attain better compression ratio. This is an experimental study, where we implemented Integer Wavelet Transform, Differential Pulse Code Modulation and an optimized predictor model using Genetic Algorithm. This study gives encouraging results for greyscale images. We achieved a better compression ration in term of entropy for experiments involving quadrant of transformed image and using optimized predictor coefficients from Genetic Algorithm. In an other set of experiments involving whole image, results are encouraging and opens up many areas for further research work like implementing Integer Wavelet Transform on multiple levels and finding optimized predictor at local levels.

Development of phase retrieval algorithm and techniques for optical spectrum analysis

Coherent anti-Stokes Raman scattering is the powerful method of laser spectroscopy in which significant successes are achieved. However, the non-linear nature of CARS complicates the analysis of the received spectra. The objective of this Thesis is to develop a new phase retrieval algorithm for CARS. It utilizes the maximum entropy method and the new wavelet approach for spectroscopic background correction of a phase function. The method was developed to be easily automated and used on a large number of spectra of different substances.. The algorithm was successfully tested on experimental data.

Wavelets in real-time paper web analysis

Online paper web analysis relies on traversing scanners that criss-cross on top of a rapidly moving paper web. The sensors embedded in the scanners measure many important quality variables of paper, such as basis weight, caliper and porosity. Most of these quantities are varying a lot and the measurements are noisy at many different scales. The zigzagging nature of scanning makes it difficult to separate machine direction (MD) and cross direction (CD) variability from one another. For improving the 2D resolution of the quality variables above, the paper quality control team at the Department of Mathematics and Physics at LUT has implemented efficient Kalman filtering based methods that currently use 2D Fourier series. Fourier series are global and therefore resolve local spatial detail on the paper web rather poorly. The target of the current thesis is to study alternative wavelet based representations as candidates to replace the Fourier basis for a higher resolution spatial reconstruction of these quality variables. The accuracy of wavelet compressed 2D web fields will be compared with corresponding truncated Fourier series based fields.