Martin Audio WT UB User Manual

Multimedia Applicationsof the Wavelet TransformInauguraldissertation zur Erlangungdes akademischen Grades einesDoktors der Naturwissenschaftender Univ

VI A FEW WORDS...of the presented work. They all contributed to my dissertation with their questions and encouragement,with their implementations and

72 CHAPTER 5DIGITAL AUDIO DENOISINGThe error–minimizing process needs sufficiently many coefficients in each scale to work well;coarser resolution level

5.4 IMPLEMENTATION OF A WAVELET–BASED AUDIO DENOISER 73‘proof by implementation’ of the wavelet–based denoising theory [Jan00] that we discussed inSec

74 CHAPTER 5DIGITAL AUDIO DENOISINGFigure 5.3: Graphical user interface of the wavelet–based audio tool. Audio data can be read from sound-card/file an

5.4 IMPLEMENTATION OF A WAVELET–BASED AUDIO DENOISER 75(a) Add filter dialog box. (b) The noise generator produces white noise.(c) Visualization of the

76 CHAPTER 5DIGITAL AUDIO DENOISING(a) Filter to set all but one wavelet scale parameters to zero.(b) With the dialog box shown in (a), time–scale coe

5.4 IMPLEMENTATION OF A WAVELET–BASED AUDIO DENOISER 77In our example in Figure 5.3, the entire set of actions is surrounded by the difference listene

78 CHAPTER 5DIGITAL AUDIO DENOISING(a) The wavelet denoiser can perform hard or soft thresholding.(b) Display of the time domain before and after appl

5.4 IMPLEMENTATION OF A WAVELET–BASED AUDIO DENOISER 79where is the length of the time series. A similar quantity to Equation (5.5) is calculated for

80 CHAPTER 5DIGITAL AUDIO DENOISINGIn the following chapter, we address the use of wavelet coding for still images for the purpose ofcompression.

Chapter 6Still ImagesReducing a liter of orange juice to a fewgrams of concentrated powder is what lossycompression is about.–St´ephane Mallat6.1 Intr

Ein paar Worte. . ...des Dankes stehen ¨ublicherweise an dieser Stelle. Und auch ich m¨ochte all denen, die mir inirgendeiner Weise bei der Erstellun

82 CHAPTER 6STILL IMAGESThese evaluations help us to provide parameter recommendations for image coding problems. Sec-tion 6.4 generalizes a specific f

6.2 WAVELET–BASED SEMIAUTOMATIC SEGMENTATION 83The search for automatic and reliable computer–based segmentation algorithms yet encounters twomajor pr

84 CHAPTER 6STILL IMAGES(1) the background color is not uniform, (2) the object boundary color is not uniform, (3) a color thatdefines the object bound

6.2 WAVELET–BASED SEMIAUTOMATIC SEGMENTATION 85n /20muser−definedpointsObjectrotate along theending point of the previous rectangleBackgroundFigure 6.

86 CHAPTER 6STILL IMAGESDue to the multiscale analysis of our semiautomatic segmentation algorithms, it is possible to tracknot only ‘sharp’, but also

6.2 WAVELET–BASED SEMIAUTOMATIC SEGMENTATION 87Edge–guided line trace: The user defines a closed polygon that fully encloses the object. Foreach compos

88 CHAPTER 6STILL IMAGESthe column ‘ user interactions’ gives the sum of the interactions per method over the four images.The ‘overall quality’ is the

6.3 EMPIRICAL PARAMETER EVA LUAT I O N F O R IMAGE CODING 896.3 Empirical Parameter Evaluation for Image CodingIn Section 3.3, we have discussed the i

90 CHAPTER 6STILL IMAGES3. complexity of implementation.The rating of the visual quality of the decoded images was based on the peak signal–to–noise r

6.3 EMPIRICAL PARAMETER EVA LUAT I O N F O R IMAGE CODING 91In signal analysis it is extremely difficult to empirically derive general statements as re

VIII EIN PAAR WORTE...nen Spaß gemacht zu haben; Sonja Meyer, Timo M¨uller, Andreas Prassas, Julia Schneider und Till-mann Schulz, die mir geholfen ha

92 CHAPTER 6STILL IMAGES– the compression ratio for circular convolution varies, but most often remains almost con-stant.The explanation for the latte

6.3 EMPIRICAL PARAMETER EVA LUAT I O N F O R IMAGE CODING 93As the visual perception is neither influenced much by the choice of filter nor by the bound

94 CHAPTER 6STILL IMAGES(a) Daub– filter bank: PSNR= . (b) Daub– filter bank: PSNR= .Figure 6.5: Impact of different wavelet filter banks on visual perce

6.3 EMPIRICAL PARAMETER EVA LUAT I O N F O R IMAGE CODING 95the columns ‘circular convolution’ in Table 6.3. We have included them again in order to a

96 CHAPTER 6STILL IMAGESof the transformation and the expansion of disturbing artifacts.2. The coding quality depends on the boundary policy selected,

6.3 EMPIRICAL PARAMETER EVA LUAT I O N F O R IMAGE CODING 97(a) Mandrill. (b) Brain.(c) Lena. (d) Camera.(e) Goldhill. (f) House.Figure 6.7: Test imag

98 CHAPTER 6STILL IMAGES(a) Mandrill. (b) Brain.(c) Lena. (d) Camera.(e) Goldhill. (f) House.Figure 6.8: Test images with threshold in the time–scale

6.3 EMPIRICAL PARAMETER EVA LUAT I O N F O R IMAGE CODING 99(a) Mandrill. (b) Brain.(c) Lena. (d) Camera.(e) Goldhill. (f) House.Figure 6.9: Test imag

100 CHAPTER 6STILL IMAGES(a) Mandrill. (b) Brain.(c) Lena. (d) Camera.(e) Goldhill. (f) House.Figure 6.10: Test images with threshold in the time–scal

6.3 EMPIRICAL PARAMETER EVA LUAT I O N F O R IMAGE CODING 101(a) Mandrill. (b) Brain.(c) Lena. (d) Camera.(e) Goldhill. (f) House.Figure 6.11: Test im

Table of ContentsList of Figures xixList of Tables xxiiNotation xxiii0 Introduction 1I Wavelet Theory and Practice 51 Wavelets 71.1 Introduction ...

102 CHAPTER 6STILL IMAGESQuality of visual perception — PSNR [dB]zero mirror circular zero mirror circular zero mirror circularWavelet padding padding

6.3 EMPIRICAL PARAMETER EVA LUAT I O N F O R IMAGE CODING 103Discarded information in the time–scale domain due to the threshold — Percentage [ ]zero

104 CHAPTER 6STILL IMAGESAverage image quality — PSNR [dB]zero mirror circular zero mirror circularWavelet padding padding convol. padding padding con

6.3 EMPIRICAL PARAMETER EVA LUAT I O N F O R IMAGE CODING 105Average discarded information — Percentage [ ]zero mirror circular zero mirror circularWa

106 CHAPTER 6STILL IMAGESQuality of visual perception — PSNR [dB]non– non– non–Wavelet standard standard standard standard standard standardMandrill B

6.3 EMPIRICAL PARAMETER EVA LUAT I O N F O R IMAGE CODING 107Average image quality — PSNR [dB]non– non– non– non–standard standard standard standard s

108 CHAPTER 6STILL IMAGES6.4 Regions–of–interest Coding in JPEG2000This section discusses a specific feature of the JPEG2000 coding standard which is b

6.4 REGIONS–OF–INTEREST CODING IN JPEG2000 109Lossy and lossless compression. A lossless modus shall allow to archive, e.g., medical imageswhich do no

110 CHAPTER 6STILL IMAGES5. The subbands are quantized and stored in code blocks.6. The bit layers of the coefficients in the code blocks are entropy–e

6.4 REGIONS–OF–INTEREST CODING IN JPEG2000 111signal according to the assigned segments of equal quality and then encode each quality level withan alg

X TABLE OF CONTENTS1.5 SamplingGridoftheWaveletTransform... 171.6 Multiscale Analysis ... 181.6.1

112 CHAPTER 6STILL IMAGESFigure 6.16: Classification according to perception of distance.6.4.2.3 Shape of Region–of–interest SegmentsThe segments selec

6.4 REGIONS–OF–INTEREST CODING IN JPEG2000 1136.4.2.4 Number of Region–of–interest SegmentsUntil now, we have discussed the special case of a yes/no–b

114 CHAPTER 6STILL IMAGES6.4.3 Qualitative RemarksIn the original meaning of the algorithm, the MAXSHIFT method was intended to ensure that themost im

Chapter 7Hierarchical Video CodingIn research the horizon recedes as we ad-vance, and is no nearer at sixty than it was attwenty. As the power of endu

116 CHAPTER 7HIERARCHICAL VIDEO CODINGkbit/s permits the reception of audio and video in a still poor, but sufficient quality to be able to followthe c

7.2 VIDEO SCALING TECHNIQUES 117Definition 7.1 A color video consists of a sequence of frameswhere each frame is composed of a number of pixels:Here, d

118 CHAPTER 7HIERARCHICAL VIDEO CODING7.2.1 Temporal ScalingTemporal scaling approaches are quite intuitive: They distribute consecutive frames of a v

7.3 QUALITY METRICS FOR VIDEO 119is transformed into the frequency domain. The bits of the DCT coefficients are distributed overseveral layers. This co

120 CHAPTER 7HIERARCHICAL VIDEO CODING[Boc98]. Each scale within the wavelet–transformed domain is accredited to a specific weight whichwas found empir

7.4 EMPIRICAL EVA L UAT I O N O F HIERARCHICAL VIDEO CODING SCHEMES 121where is the error between the distorted frame and the original at time and pos

TABLE OF CONTENTS XI3.4.2 GrowingSpatialRagewithPadding... 493.5 Representation of ‘Synthesis–in–progress’ ...

122 CHAPTER 7HIERARCHICAL VIDEO CODINGFour different spatial video scaling algorithms were used: The algorithms to are based on thediscrete cosine tra

7.4 EMPIRICAL EVA L UAT I O N O F HIERARCHICAL VIDEO CODING SCHEMES 123soft flickering of the luminance, probably produced by the auto focus of the cam

124 CHAPTER 7HIERARCHICAL VIDEO CODING(a) : Pyramid encoding. (b) : Layered DCT frequencies.(c) : Bit layering. (d) : Layered wavelet–transformed coef

7.4 EMPIRICAL EVA L UAT I O N O F HIERARCHICAL VIDEO CODING SCHEMES 125Video Sequence subject. rating DIST PSNR [dB]Mainzelm¨annchen 4.50 2.63 64.7War

126 CHAPTER 7HIERARCHICAL VIDEO CODINGPSNR is negative. The same holds true for the DIST metric. The two chrominance parts of the DISTmetric, DISTUand

7.5 LAYERED WAVELET CODING POLICIES 127convincingly better than the output of the PSNR, we conclude that it is not worth the cost of imple-mentation a

128 CHAPTER 7HIERARCHICAL VIDEO CODINGsynthesized first, and if there is still a capacity for further synthesis, the high–pass filtered blocks aresucces

7.5 LAYERED WAVELET CODING POLICIES 129is exactly as high as the low–pass filtered part, the mixed policy is identical to the blockwise policy1.The vis

130 CHAPTER 7HIERARCHICAL VIDEO CODING7.5.3 ResultsAs explained above, our evaluation results on the performance of the ‘clever’ video metrics suggest

7.5 LAYERED WAVELET CODING POLICIES 131which ‘smear’ the incomplete signal information into neighboring locations. (cf. also the results inSection 6.3

XII TABLE OF CONTENTS6.2.1 Fundamentals ... 826.2.2 A Wavelet–based Algorithm . . ... 846.2.3 Impl

132 CHAPTER 7HIERARCHICAL VIDEO CODING(a) Original frame. (b) Wavelet–transformed.(c) Policy 1: blockwise synthesis. (d) Policy 2: maximum absolute co

7.5 LAYERED WAVELET CODING POLICIES 133and MPEG usually use run length and Huffman encoding in order to compress the DCT–transformedcoefficients. Since

134 CHAPTER 7HIERARCHICAL VIDEO CODINGNumber of Runs (16 bit)Percentage of synthesized coefficients18.75% 12.5% 6.25%Wavelet policy 2 policy 3 policy 2

7.6 HIERARCHICAL VIDEO CODING WITH MOTION–JPEG2000 135quantized time–scale coefficients for the run length encoding presented above, we have implemente

136 CHAPTER 7HIERARCHICAL VIDEO CODINGwas set to pixels. We used two home videos for our tests: The sequence Mannheim showspeople walking around on th

7.6 HIERARCHICAL VIDEO CODING WITH MOTION–JPEG2000 137number of layers received by the client ( ), andquantization factors applied to the enhancement

138 CHAPTER 7HIERARCHICAL VIDEO CODINGLayers Quantization Frames Data Duration Average Average PSNRtransmitted factors received received[number] [byte

7.6 HIERARCHICAL VIDEO CODING WITH MOTION–JPEG2000 139Layers Quantization Frames Data Duration Average Average PSNRtransmitted factors received receiv

140 CHAPTER 7HIERARCHICAL VIDEO CODINGFurthermore, we have evaluated different strategies to subdivide a video stream into several qualitylayers. Our

Part IIIInteractive Learning Tools for SignalProcessing Algorithms

TABLE OF CONTENTS XIII7.4.4 Conclusion ... 1267.5 LayeredWaveletCodingPolicies... 1277.5.1 La

Chapter 8Didactic ConceptThis luke warmness arises [...] partly fromthe incredulity of mankind, who do not trulybelieve in anything new until they hav

144 CHAPTER 8DIDACTIC CONCEPTanalyze the frequencies in a given signal and (b) why this is done. It is this deep understanding of theunderlying concep

8.2 THE LEARNING CYCLE IN DISTANCE EDUCATION 145resembles a flip–book, whereby the more complex a topic is, the more frames of still images it willinvo

146 CHAPTER 8DIDACTIC CONCEPT8.2.2 ConstructionThis is the phase of acquisition of problem–solving competence. The learner shall make use of his/herne

Chapter 9Java Applets Illustrating MathematicalTransformationsWe shall not cease from exploration. And theend of all our exploring will be to arrive w

148 CHAPTER 9JAVA APPLETS ILLUSTRATING MATHEMATICAL TRANSFORMATIONSThe Java applets are used for synchronous teaching within a lecture or seminar as w

9.2 STILL IMAGE SEGMENTATION 149more sophisticated: It combines smoothing (with a Gaussian filter) and edge detection. Canny requiresthe standard devia

150 CHAPTER 9JAVA APPLETS ILLUSTRATING MATHEMATICAL TRANSFORMATIONSAn image for the segmentation task can be selected from a pool of grayscale images.

9.3 ONE–DIMENSIONAL DISCRETE COSINE TRANSFORM 151value this applet very highly since image segmentation is a very complex topic, not easy to understan

XIV TABLE OF CONTENTS9.3.2 LearningGoal ... 1529.3.3 Implementation... 1539.4 Two–dimensio

152 CHAPTER 9JAVA APPLETS ILLUSTRATING MATHEMATICAL TRANSFORMATIONS9.3.1 Technical BasisThe JPEG standard [PM93] defines that an image be subdivided in

9.3 ONE–DIMENSIONAL DISCRETE COSINE TRANSFORM 153(a) Block ofgrayscale values.1101201301401501601701801900 1 2 3 4 5 6 7data(b) Discrete functionof hi

154 CHAPTER 9JAVA APPLETS ILLUSTRATING MATHEMATICAL TRANSFORMATIONSFigure 9.4: GUI of the DCT applet. In step 1, the user is asked to choose a (blue,

9.4 TWO–DIMENSIONAL DISCRETE COSINE TRANSFORM 1559.4 Two–dimensional Discrete Cosine TransformOur applet on the two–dimensional discrete cosine transf

156 CHAPTER 9JAVA APPLETS ILLUSTRATING MATHEMATICAL TRANSFORMATIONSto help the user understand how the one–dimensional and the two–dimensional DCTs ar

9.5 WAVELET TRANSFORM:MULTISCALE ANALYSIS AND CONVOLUTION 157Figure 9.6: GUI of the 2D–DCT applet. The left hand side shows the selected target image

158 CHAPTER 9JAVA APPLETS ILLUSTRATING MATHEMATICAL TRANSFORMATIONS9.5.1 Technical BasisThe technical basis of multiscale analysis and convolution–bas

9.5 WAVELET TRANSFORM:MULTISCALE ANALYSIS AND CONVOLUTION 159(a) Multiscale analysis with different scale parameters (i.e., dilation).(b) Multiscale a

160 CHAPTER 9JAVA APPLETS ILLUSTRATING MATHEMATICAL TRANSFORMATIONSregard to either the Haar filter bank, or the Daubechies–2 filter bank [Sch01a]. Sinc

9.6 WAVELET TRANSFORM AND JPEG2000 ON STILL IMAGES 1619.6.3 ImplementationOur wavelet transform applet [Ess01] has two different modes:convolution mod

TABLE OF CONTENTS XVIV Appendix 181A Original Documents of the Evaluation 183A.1 Computer–based Learning Setting . . . ... 183A.1

162 CHAPTER 9JAVA APPLETS ILLUSTRATING MATHEMATICAL TRANSFORMATIONS(a) Parameter definition.(b) Transform visualization.Figure 9.9: The two windows of

9.6 WAVELET TRANSFORM AND JPEG2000 ON STILL IMAGES 163of parameters and visualization into the following fields: source image, analysis,andsynthesis.Th

164 CHAPTER 9JAVA APPLETS ILLUSTRATING MATHEMATICAL TRANSFORMATIONS

Chapter 10Empirical Evaluation of Interactive Mediain TeachingTeaching should be such that what is offeredis perceived as a valuable gift and not as a

166 CHAPTER 10 EMPIRICAL EVA LUAT I ON O F Interactive Media in Teaching10.2 Test SetupOnly students enrolled in computer science were selected to par

10.2 TEST SETUP 167instructions on how to use the two applets on the discrete cosine transform. Figure 10.1 shows photostaken during the evaluation.(a

168 CHAPTER 10 EMPIRICAL EVA LUAT I ON O F Interactive Media in Teaching10.2.2 HypothesesThe large number of participants allowed us to test two impor

10.3 RESULTS 169. Test of hypothesis :– Lecture: One group of students attended a traditional–minute lecture.– Exploration: The students in this compu

170 CHAPTER 10 EMPIRICAL EVA LUAT I ON O F Interactive Media in TeachingAnalysis of Variance: Not all data are significant for the explanation of a fac

10.3 RESULTS 171Setting mean std. dev.Lecture 28 6.8929 3.2385c’t–article 19 5.8684 2.5919Years of total computer usage –version 21 6.0952 2.1072Scrip

Dekan: Professor Dr. Herbert Popp, Universit¨at MannheimReferent: Professor Dr. Wolfgang Effelsberg, Universit¨at MannheimKorreferent: Professor Dr. G

XVI TABLE OF CONTENTS

172 CHAPTER 10 EMPIRICAL EVA LUAT I ON O F Interactive Media in TeachingTable 10.2 details the five most important entries of Table 10.1 on the differe

10.3 RESULTS 173In the evaluation of traditional learning versus computer–based learning, therefore, we have concen-trated on the three settings lectu

174 CHAPTER 10 EMPIRICAL EVA LUAT I ON O F Interactive Media in Teachingsetting also significantly (i.e., ) influences the students’ knowledge gain, and

10.3 RESULTS 175(see Section A.2.2). An expected result of to for the follow–up test is thus very highin either setting. However, the mean program rat

176 CHAPTER 10 EMPIRICAL EVA LUAT I ON O F Interactive Media in TeachingSource Dependent variable Sig.( )–Exploration, –version, c’t–articlePreliminar

10.3 RESULTS 177Dependent Variable Setting mean std. dev. Confidence Intervallower border upper border( )–Exploration, –version, c’t–articleMean rating

178 CHAPTER 10 EMPIRICAL EVA LUAT I ON O F Interactive Media in Teachingprograms produces better results, though with a percentage of (see Table 10.5

Chapter 11Conclusion and Outlook‘Where shall I begin, please your Majesty?’he asked. ‘Begin at the beginning,’ the Kingsaid, gravely, ‘and go on till

180 CHAPTER 11 CONCLUSION AND OUTLOOKClearly, our evaluation of parameter settings could be extended in many directions. With the inclusionof differen

Part IVAppendix

List of Figures1.1 Samplewavelets ... 121.2 The Mexican hat wavelet and two of its dilates and translates, including

Appendix AOriginal Documents of the EvaluationEs muss z.B. das Geh¨or mit dem Gesicht,die Sprache mit der Hand stets verbundenwerden, indem man den Wi

184 CHAPTER AORIGINAL DOCUMENTS OF THE EVA L UAT I O NA.1.1 Setting: ExplorationLiebe Studierende!In diesem Semester werden die Lernmodule zur Bildver

A.1 COMPUTER–BASED LEARNING SETTING 185A.1.2 Setting: ScriptLiebe Studierende!In diesem Semester werden die Lernmodule zur Bildverarbeitung mit Hilfed

186 CHAPTER AORIGINAL DOCUMENTS OF THE EVA L UAT I O NZur Bearbeitung der LernmoduleIm Rahmen der Unterrichtsforschung zeigte sich, dass verschiedeneB

A.1 COMPUTER–BASED LEARNING SETTING 187LeitfragenBitte denken Sie daran auch die Hilfefunktionen der Lernmodule bei derBeantwortung der Fragen zu benu

188 CHAPTER AORIGINAL DOCUMENTS OF THE EVA L UAT I O NA.1.3 Setting: –VersionLiebe Studierende!In diesem Semester werden die Lernmodule zur Bildverarb

A.1 COMPUTER–BASED LEARNING SETTING 189A.1.4 Setting: c’t–ArticleLiebe Studierende!In diesem Semester werden die Lernmodule zur Bildverarbeitung mit H

190 CHAPTER AORIGINAL DOCUMENTS OF THE EVA L UAT I O NFigure A.1: c’t–Article.

A.2 KNOWLEDGE TESTS 191A.2 Knowledge TestsA.2.1 Preliminary TestLiebe Studierende,Die nachfolgenden Frageb¨ogen dienen der Erfassung zentraler Aspekte

XVIII LIST OF FIGURES3.8 The lifting scheme ... 544.1 Digital signal processing system ... 59

192 CHAPTER AORIGINAL DOCUMENTS OF THE EVA L UAT I O NVorkenntnisse1. Welche Note haben Sie in der Klausur ‘Praktische Informatik 1’ erzielt?Note:Ich

A.2 KNOWLEDGE TESTS 193A.2.2 Follow–up TestLiebe Studierende,Die nachfolgenden Fragen sollen Ihre aktuelle Stimmung, f¨ur den Lernprozessrelevante Sel

194 CHAPTER AORIGINAL DOCUMENTS OF THE EVA L UAT I O NInstruktion:Im folgenden m¨ochten wir mehr dar¨uber erfahren, wie Sie sich bez¨uglich IhrerLeist

A.2 KNOWLEDGE TESTS 195Instruktion:Bitte beurteilen Sie die Lernmodule, mit denen Sie hier gearbeitet haben,insgesamt anhand der nachfolgenden Aussage

196 CHAPTER AORIGINAL DOCUMENTS OF THE EVA L UAT I O NInstruktion:Bitte beantworten Sie die nachfolgenden Fragen. Arbeiten Sie unbedingt ohnefremde Hi

A.2 KNOWLEDGE TESTS 1978. Wir bezeichnen die St¨arke einer Frequenz¨anderung als Amplitude. Wieverhalten sich die Amplituden der drei Signale zueinand

198 CHAPTER AORIGINAL DOCUMENTS OF THE EVA L UAT I O NA.2.3 Sample SolutionsSample Solution of Preliminary Knowledge Test1. Gerade Parit¨at bedeutet,

A.2 KNOWLEDGE TESTS 199Sample Solution of Follow–up Knowledge Test1. Bild mit deutlichen Kanten f¨ur Kopf, Brille, etc.2. Scharfe¨Uberg¨ange zwischen

200 CHAPTER AORIGINAL DOCUMENTS OF THE EVA L UAT I O NA.3 Quotations of the StudentsThe following quotations have been found in the follow–up test (se

Bibliography[Abo99] Gregory D. Abowd. Classroom 2000: An experiment with the instrumentation of aliving educational environment. IBM Systems Journal,

LIST OF FIGURES XIX6.17 Two examples of a pre–defined shape of a region–of–interest ... 1126.18 Region–of–interest mask with three quality le

202 BIBLIOGRAPHY[B¨om00] Florian B¨omers. Wavelets in Real–Time Digital Audio Processing: Analysis and Sam-ple Implementations. Master’s thesis, Unive

BIBLIOGRAPHY 203[DJ94] David L. Donoho and Iain M. Johnstone. Ideal spatial adaptation by wavelet shrinkage.Biometrika, 81(3):425–455, 1994.[DJ95] Dav

204 BIBLIOGRAPHY[GFBV97] Javier Garcia-Frias, Dan Benyamin, and John D. Villasenor. Rate Distortion OptimalParameter Choice in a Wavelet Image Communi

BIBLIOGRAPHY 205[HFH01] Holger Horz, Stefan Fries, and Manfred Hofer. St¨arken und Schw¨achen eines Tele-seminars zum Thema ‘Distance Learning’. In H.

206 BIBLIOGRAPHY[JB99] Maarten Jansen and A. Bultheel. Multiple wavelet threshold estimation by generalizedcross validation for images with correlated

BIBLIOGRAPHY 207[LGOB95] M. Lang, H. Guo, J.E. Odegard, and C.S. Burrus. Nonlinear processing of a shift in-variant DWT for noise reduction. SPIE, Mat

208 BIBLIOGRAPHY[Mey93] Yves Meyer. Wavelets: Algorithms and Applications. SIAM, Philadelphia, PA, 1993.[MFSW97] Michael Merz, Konrad Froitzheim, Pete

BIBLIOGRAPHY 209[RF85] A.R. Robertson and J.F. Fisher. Color Vision, Representation and Reproduction. InK.B. Benson, editor, Television Engineering Ha

210 BIBLIOGRAPHY[SE01] Claudia Schremmer and Christoph Esser. Simulation of the Wavelet Transformon Still Images. http://www-mm.informatik.uni-mannhei

BIBLIOGRAPHY 211[SPB 98] Sylvain Sardy, Donald B. Percival, Andrew G. Bruce, Hong-Ye Gao, and Werner Stuet-zle. Wavelet Shrinkage for Unequally Spaced

XX LIST OF FIGURES

212 BIBLIOGRAPHY[VIR01] Cooperation Project ‘Virtuelle Hochschule Oberrhein’ VIROR. Universities Freiburg,Heidelberg, Karlsruhe, and Mannheim. http://

List of Tables1.1 Relations between signals and spaces in multiscale analysis . ... 243.1 The number of possible iterations on the approxima

XXII LIST OF TABLES7.2 Correlation between the human visual perception and the PSNR, respectively theDIST metric and its sub–parts ...

NotationSetsIntegersReal numbersComplex numbersBanach space of all absolute integrable functions:Hilbert space of all square integrable functions:Set

XXIV NOTATIONSignalsContinuous time signalCoefficients in Fourier seriesConvolution of andif and else1Indicator function on the intervalWaveletweighted

Chapter 0IntroductionWanting is not enough; desiring only makesyou reach the target.–OvidMotivationIn recent years, the processing of multimedia data

If we knew what we were doing,it would not be called research, would it?— Albert Einstein

2CHAPTER 0INTRODUCTIONCompression. Compression demands efficient coding schemes to keep the data stream ofa digital medium as compact as possible. This

3OutlineThis dissertation is divided into three major parts. The first part reviews the theory of wavelets and thedyadic wavelet transform and thus pro

4CHAPTER 0INTRODUCTION

Part IWavelet Theory and Practice

Chapter 1WaveletsMy dream is to solve problems, with or with-out wavelets.– Bruno Torresani1.1 IntroductionThis chapter introduces the concept of the

8CHAPTER 1WAVELETS2 are inspired by [Mal98] [LMR98] [Ste00] [Dau92] [Boc98], and [Hub98]. Chapter 3 presents ourown contribution to the discussion of

1.3 THE WAVELET TRANSFORM 9multiscale analysis and to calculate the transform filters recursively. The idea to not extract the filtercoefficients from th

10 CHAPTER 1WAVELETSThe constant designates the admissibility constant [LMR98]. Approaching gets critical.To guarantee that Equation (1.1) is accompli

1.3 THE WAVELET TRANSFORM 11accomplishes the admissibility condition (1.1) [LMR98]. The Mexican Hat owes its name to its shape(see Figure 1.1 (b)). It

12 CHAPTER 1WAVELETS-1-0.500.51-1 -0.5 0 0.5 1 1.5 2(a) Haar wavelet.-0.6-0.4-0.200.20.40.60.811.2-8 -6 -4 -2 0 2 4 6 8(b) Mexican Hat.-0.4-0.3-0.2-0.

1.3 THE WAVELET TRANSFORM 131.3.3 Integral Wavelet TransformDefinition 1.2 The integral wavelet transform of a function with regard to the admissiblewa

14 CHAPTER 1WAVELETS1.3.4 Wavelet BasesA wavelet transform decomposes a signal into coefficients for a corresponding wavelet .Asallwavelets ‘live’ in,

1.4 TIME–FREQUENCY RESOLUTION 15Regarding the Fourier transform of the time–scaled signal ,wegetThis means that the amount of localization gained in t

16 CHAPTER 1WAVELETSand its center frequency is . The frequency spread around isand is independent of and . Consequently, the Heisenberg box of the tr

1.5 SAMPLING GRID OF THE WAVELET TRANSFORM 17around isThe energy spread of a wavelet atom is thus centered at and of size along time andalong frequenc

18 CHAPTER 1WAVELETSTheorem 1.1 says that even the translation parameter in the definition of the dyadic wavelet transform(1.6) can be restricted furth

1.6 MULTISCALE ANALYSIS 19Figure 1.5: Multiscale analysis. The image is subdivided into approximations and details. While the approx-imation contains

20 CHAPTER 1WAVELETSIn order for the multiscale approach to approximate a given function with arbitrary preci-sion, four conditions are sufficient that

1.6 MULTISCALE ANALYSIS 21is called the scaling function. It is the counterpart to the wavelets which we will define later in thissection. The explicit

AbstractThis dissertation investigates novel applications of the wavelet transform in the analysis and compres-sion of audio, still images, and video.

22 CHAPTER 1WAVELETSOn the double fine scale, would need three representatives, i.e.,Here, the filter coefficients are: and else. See also Figure 1.6(b).

1.6 MULTISCALE ANALYSIS 23is referred to as detail information of level . These details are exactly the information that is lostduring approximation.

24 CHAPTER 1WAVELETSwhere the coefficients of the filter mask for the wavelet are calculated asAs we have stated conditions for the scaling function and

1.6 MULTISCALE ANALYSIS 25function defines the approximation at the ‘stopping level’. It thus defines the resolution of the coarsestapproximation. Witho

26 CHAPTER 1WAVELETStimefrequencyFigure 1.8: Tiling the time–scale domain for the dyadic wavelet transform. The iteration has been carried outthree ti

1.7 TRANSFORMATION BASED ON THE HAAR WAVELET 27philosophy and nature of a wavelet transform, as it contains an intrinsically intuitive interpretation.

28 CHAPTER 1WAVELETSoriginal signaltimeamplitude1234mean=approximationdetail(a) Graphical illustration, level .original signaltimeamplitude1234approxi

1.7 TRANSFORMATION BASED ON THE HAAR WAVELET 29By simply shifting the factor from the analysis filters to the synthesis filters, the filters used in thea

30 CHAPTER 1WAVELETS

Chapter 2Filter BanksAnd since geometry is the right foundation ofall painting, I have decided to teach its rudi-ments and principles to all youngster

II ABSTRACT

32 CHAPTER 2FILTER BANKSwhere the sinc function is defined as sinc . For the sake of simplicity, we set .Thenfor, the Fourier transform of can be repre

2.2 IDEAL FILTERS 33The application of an ideal low–pass filter to a function means multiplication of and inthe frequency space, which corresponds to c

34 CHAPTER 2FILTER BANKSfrequency-1/2 -1/4 1/21/4(a) Ideal low–pass filter.frequency-1/2 -1/4 1/21/4(b) Ideal high–pass filter.Figure 2.1: Ideal filters.

2.3 TWO–CHANNEL FILTER BANK 35where (see Equation (2.6))high high(2.10)The complete signalcan now be completely described as the sum of its low–pass a

36 CHAPTER 2FILTER BANKS0h 0hh1 h12222+fffflowhighanalysis filter bank synthesis filter bank(a)Idealfilterbank.22+analysis filter bank synthesis filter

2.4 DESIGN OF ANALYSIS AND SYNTHESIS FILTERS 37. Multiplication and addition of two –transforms and are given byFrom the arbitrary filter bank in Figur

38 CHAPTER 2FILTER BANKSFor simplification, the conditions (2.13) and (2.14) can be written in matrix form. With the settingin the above equations, we

2.4 DESIGN OF ANALYSIS AND SYNTHESIS FILTERS 39This finally makes explicit the required relationship between andfor perfect reconstruction. Due to the

40 CHAPTER 2FILTER BANKSA check of the conditions on perfect reconstruction reveals that Equation (2.13) is satisfied:The second condition (2.14) is no

Chapter 3Practical Considerations for the Use ofWaveletsOne man’s hack is another man’s thesis.–SeanLevy3.1 IntroductionThe previous sections concentr

KurzfassungDie vorliegende Dissertation untersucht neue Einsatzm¨oglichkeiten der Wavelet–Transformation f¨urdie Analyse und Kompression der multimedi

42 CHAPTER 3PRACTICAL CONSIDERATIONS FOR THE USE OF WAVELETStension into multiple dimensions.Two– and three–dimensional wavelet filter design is an act

3.2 WAVELETS IN MULTIPLE DIMENSIONS 43Equation (3.1) indicates that the two–dimensional wavelet analysis splits an image into sub–parts ofdifferent sc

44 CHAPTER 3PRACTICAL CONSIDERATIONS FOR THE USE OF WAVELETSV x VW x WW x VV x W11111111(a) Start of iteration; idea. (b) Start of iteration; visu-ali

3.3 SIGNAL BOUNDARY 45(3.4)thus in seven summands after the second iteration step. In this nonstandard decomposition, the mixedtermsand of the first it

46 CHAPTER 3PRACTICAL CONSIDERATIONS FOR THE USE OF WAVELETSabd23456781signaldetailapproximationa b d1234wavelet domaincc(a) Circular Convolution.2345

3.4 ‘PAINTING’ THE TIME–SCALE DOMAIN 47by each iteration step, see Figure 3.2 (b). Though the amount of storage space required can be cal-culated in a

48 CHAPTER 3PRACTICAL CONSIDERATIONS FOR THE USE OF WAVELETSSince the multiresolution aspect of the wavelet transform allows a direct interpretation o

3.4 ‘PAINTING’ THE TIME–SCALE DOMAIN 49the visual representation and the second for the calculation of the coding process.3.4.2 Growing Spatial Rage w

50 CHAPTER 3PRACTICAL CONSIDERATIONS FOR THE USE OF WAVELETS(a) All coefficients in thetime–scale domain with zeropadding.(b) All coefficients in thetim

3.5 REPRESENTATION OF ‘SYNTHESIS–IN–PROGRESS’51(a) Analysis reversal. (b) Growing spatial resolu-tion.(c) Interpolation, block wise.(d) Interpolation,

IV KURZFASSUNG

52 CHAPTER 3PRACTICAL CONSIDERATIONS FOR THE USE OF WAVELETSGrowing spatial resolution ‘draws’ only the purely low–pass filtered approximation. When th

3.6 LIFTING 53aaad0,2k0,2k+20,2k+11,kFigure 3.7: Lifting scheme: prediction for the odd coefficients as difference from the linear approximation.Let us

54 CHAPTER 3PRACTICAL CONSIDERATIONS FOR THE USE OF WAVELETSaaaaaaaddj,2k+1 j,2k+2j,2k j,2k+2...1/4 1/4-1/2 -1/2 -1/2 -1/21/4 1/4j,2kj+

3.6 LIFTING 55Daub–5/3 Analysis and Synthesis Filter CoefficientsAnalysis Filter Synthesis Filteri low–pass high–pass low–pass high–pass6/8 1 1 6/82/8

56 CHAPTER 3PRACTICAL CONSIDERATIONS FOR THE USE OF WAVELETS

Part IIApplication of Wavelets in Multimedia

Chapter 4Multimedia FundamentalsThe real danger is not that computers will be-gin to think like men, but that men will beginto think like computers.–S

60 CHAPTER 4MULTIMEDIA FUNDAMENTALSideally works to minimize the perceptible loss of quality; this goes along with analysis of the signaland maintenan

4.2 DATA COMPRESSION 61successive frames are searched for similar objects. The storage of the affine transformation,which maps an object inonto plus th

A few words. . ...ofacknowledgment usually are placed at this location. And I also wish to express my gratitude toall those who contributed to the fo

62 CHAPTER 4MULTIMEDIA FUNDAMENTALSthe encoding is performed only once, and plenty of time is available, but the decoding is time–critical(e.g., a vid

4.3 NYQUIST SAMPLING RAT E 63Equation (4.1) states that the spectrum of the sampled signal is the sum of the spectra of the continuoussignal repeated

64 CHAPTER 4MULTIMEDIA FUNDAMENTALS

Chapter 5Digital Audio DenoisingIt would be possible to describe everythingscientifically, but it would make no sense;it would be without meaning, as i

66 CHAPTER 5DIGITAL AUDIO DENOISINGon wavelet thresholding and noise reduction, Section 5.3 provides the theory of wavelet–based audiodenoising. Our o

5.2 STANDARD DENOISING TECHNIQUES 67Detection. The detection procedure will estimate the value of the noise , in other words itdecides which samples a

68 CHAPTER 5DIGITAL AUDIO DENOISINGlikelihood estimation. In the scope of this work, we do not detail the function . See [GR98] for moredetails.Most m

5.3 NOISE REDUCTION WITH WAVELETS 695.3.2 Orthogonal Wavelet Transform and ThresholdingIf the wavelet transform is orthogonal and I,thenETI. This mean

70 CHAPTER 5DIGITAL AUDIO DENOISING0 200 400 600 800 1000 1200 1400 1600 1800 2000−2024681012(a) Original ‘clean’ audio signal in the time do-main.0 2

5.3 NOISE REDUCTION WITH WAVELETS 71(a) Hard thresholding. (b) Soft thresholding. (c) Shrinkage.Figure 5.2: Hard and soft thresholding, and shrinkage.