DIGITAL HOLOGRAPHY AND DIGITAL IMAGE PROCESSING: Principles, Methods, Algorithms

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1 DIGITAL HOLOGRAPHY AND DIGITAL IMAGE PROCESSING: Principles, Methods, Algorithms

2 DIGITAL HOLOGRAPHY AND DIGITAL IMAGE PROCESSING: Principles, Methods, Algorithms by Leonid Yaroslavsky Tel Aviv University, Israel SPRINGER SCIENCE+BUSINESS MEDIA, LLC

3 Library of Congress Cataloging-in-Publication CIP info or: Title: Digital Holography and Digital Image Processing: Principles, Methods, Algorithms Author (s): Leonid Yaroslavsky ISBN ISBN (ebook) DOI / Copyright 2004 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2004 Softcover reprint ofthe hardcover Ist edition 2004 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photo-copying, microfilming, recording, or otherwise, without the prior written permis sion of the publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Permissions forbooks published in the USA: permissions@wkap. corn Permissions for books published in Europe: permissions@wkap.nl Printed on acid-free pa per.

4 TABLE OF CONTENTS 1. INTRODUCTION DIGIT AL HOLOGRAPHY AND EVOLUTION OF IMAGING TECHNIQUES , , '" CONTENTS OF THIS DOOK REFERENCES OPTICAL SIGNALS AND TRANSFORMS MATHEMA TICAL MODELS OF OPTICAL SIGNALS......, Primary definitions and classification Signal space Linear signal space, basis functions and signal representation as expansion over a set ofbasis functions Integral representation of signals SIGNAL TRANSFORMATIONS IMAGING SYSTEMS AND INTEGRAL TRANSFORMS Direct imaging: Convolution integral Imaging in Fourier domain: Holography and diffraction integrals FOURIER TRANS FORM AND ITS DERIVATIVES Properties of integral Fourier Transfonn Special cases ofthe integral Fourier transfonn: integral Cosine, Hartley, Hankel and Mellin transfonns Integral Fresnel and related transfonn Hilbert transfonn IMAGING FROM PROJECTIONS: RADON AND ADEL TRANSFORMS MULTI RESOLUTION IMAGING: W AVELET TRANSFORMS... 61

5 2.7SLIDING WINDOW TRANSFORMS AND "TIME-FREQUENCY" (SPACE-TRANSFORM) SIGNAL REPRESENT A TION Transforms in sliding window (windowed transforms) Sliding window Fourier Transform Sliding window and wavelet transforms as signal sub-band decomposition STOCHASTIC TRANSFORMATIONS AND ST A TISTICAL MODELS Additive, multiplicative, Poisson noise and impulse noise models Speckle noise model References DIGITAL REPRESENT AT ION OF SIGNALS PRINCIPLES OF SIGNAL DIGITIZA TION SIGNAL DISCRETIZA TION AS EXPANSION OVER A SET OF BASIS FUNCTIONS. TYPICAL BASIS FUNCTIONS AND CLASSIFICATION Shift (convolution) basis functions Scale (multiplicative) basis functions Wavelets Discrete bases Optimality ofbases. Karhunen-Loeve, Hotelling and Singular Values Decomposition Transforms Two dimensional and multi dimensional bases SHIFT (CONVOLUTION) BASES FUNCTIONS AND SAMPLING THEOREM D samp ling theorem Sampling 2-D and multi dimensional signals Sampling artifacts: qualitative analysis Sampling artifacts: quantitative analysis MULTI-RESOLUTION SAMPLING UNCONVENTIONAL DIGITAL IMAGING METHODS PRINCIPLES OF SIGNAL SCALAR QUANTIZATION Optimal homogeneous non-uniform quantization

6 3.6.2 Quantization in digital holography BASICS OF SIGNAL CODING AND DATA COMPRESSION I.l Signal rate distortion funetion, entropy and statistical eoding Image eompression methods: a review DIGITAL REPRESENTATION OF SIGNAL TRANSFORMATIONS THE PRINCIPLES DISCRETE REPRESENT ATION OF CONVOLUTION INTEGRAL. DIGITAL FILTERS DISCRETE REPRESENT A TION OF FOURIER INTEGRAL TRANS FORM Diserete Fourier Transforms Properties of Diserete Fourier Transforms Diserete eosine and sine transforms Lapped Transforms DlSCRETE REPRESENT A TION OF FRESNEL INTEGRAL TRANSFORM I Diserete Fresnel Transform Properties of Diserete Fresnel Transforms References METHODS AND ALGORITHMS OF DIGITAL FILTERING FILTERING IN SIGNAL DOMAIN Transversal and reeursive filtering Separable, easeade, parabel and parabel reeursive filtering Reeursive algorithms ofsliding window DFT and DCTlDeST Border proeessing in digital filtering FILTERING IN TRANSFORM DOMAIN DFT and eyelie eonvolution. Border proeessing Signal eonvolution in the DCT domain

7 5.3 COMBINED ALGORITHMS FOR COMPUTING DFT AND DCT OF REAL V ALUED SIGNALS Combined algorithms for computing DFT of signals with real sampies... '" Combined algorithm for computing the DCT via FFT References FAST ALGORITHMS THE PRINCIPLE OF FAST FOURIER TRANSFORMS MATRIX TECHNIQUES IN FAST TRANSFORMS TRANSFORMS AND THEIR FAST ALGORITHMS IN MATRIX REPRESENT AT ION Walsh-Hadamard transform Walsh-Paley Transform and Bit Reversal Permutation Walsh Transform and Binary-to-Gray Code and Hadamard Permutations Haar Transform Discrete Fourier Transform DCT and DcST PRUNED ALGORITHMS QUANTIZED DFT REFERENCES STATISTICAL METHODS AND ALGORITHMS MEASURING SIGNAL STATISTICAL CHARACTERISTICS Measuring probability distribution and its moments and order statistics Measuring signal corre1ation functions and spectra Measuring parameters of random interferences in sensor and imaging systems..., DIGITAL STATISTICAL MODELS AND MONTE CARLO METHODS

8 7.2.1 Principles of generating pseudo-random numbers. Generating independent uniformly distributed pseudo-random numbers Generating pseudo-random numbers with special statistical properties Generating pseudo-random images Generating correlated phase masks. Kinoform and programmed diffuser holograms STATISTICAL (MONTE CARLO) SIMULATION. CASE STUDY: SPECKLE NOISE PHENOMENA IN COHERENT IMAGING AND DIGITAL HOLOGRAPHY Computer model Simulation results References SENSOR SIGNAL PERFECTING, IMAGE RESTORA TION, RECONSTRUCTION AND ENHANCEMENT MATHEMATICAL MODELS OF IMAGING SYSTEMS LINEAR FILTERS FOR IMAGE RESTORATION Transform domain MSE optimal scalar Wiener Filters Empirical Wiener filters for image denoising Image deblurring, inverse filters and aperture correction SLIDING WINDOW TRANS FORM DOMAIN ADAPTIVE SIGNAL RESTORA TION Local adaptive filtering Sliding window transform domain DCT filtering Hybrid DCT/wavelet filtering MUL TI-COMPONENT IMAGE RESTORA TION FILTERING IMPULSE NOISE METHODS FOR CORRECTING GRAY SCALE NONLINEAR DISTORTIONS IMAGE RECONSTRUCTION

9 8.8 IMAGE ENHANCEMENT Image enhaneement as an image proeessing task. Classifieation of image enhaneement methods Gray level histogram modifieation methods Image speetra modifieation methods Using color, stereo and dynamieal vision for image enhaneement References IMAGE RESAMPLING AND GEOMETRICAL TRANSFORMATIONS PRINCIPLES OF IMAGE RESAMPLING NEAREST NEIGHBOR, LINEAR AND SPLINE INTERPOLATION METHODS ALGORITHMS OF DISCRETE SINC-INTERPOLA TION Diserete sine-interpolation by zero padding signal OFT speetrum OFT based diserete sine-interpolation algorithm for signal arbitrary translation DCT based diserete sine-interpolation algorithm for signal arbitrary translation Sliding window adaptive diserete sine-interpolation algorithms Application examples Signal and image resizing and loealization with sub-pixel aeeuraey Fast algorithm for image rotation with diserete-sine-interpolation Signal differentiating and filtered back projeetion method for tomographie reeonstruetion Signal integrating and reeonstrueting surfaees from their slope Polar-to-Cartesian eoordinate eonversion, interpolation of OFT speetra ofprojeetions and the direet Fourier method ofimage reeonstruetion from projeetions References

10 10. SIGNAL PARAMETER ESTIMATION AND MEASUREMENT. OBJECT LOCALIZATION PROBLEM FORMULA TION. OPTIMAL ST A TISTICAL ESTIMA TES LOCALIZATION OF AN OBJECT IN THE PRESENCE OF ADDITIVE WHITE GAUSSIAN NOISE Optimallocalization device. Correlator and matched filter Computer and optical implementations ofthe matched filter correlator Performance of optimal estimators: normal and anomalous localization errors PERFORMANCE OF THE OPTIMAL LOCALIZA TION DEVICE Distribution density and variance ofnormal errors Illustrative examples Localization accuracy for non-optimallocalization devices Localization reliability. Probability ofanomalous localization errors LOCALIZATION OF AN OBJECT IN TUE PRESENCE OF ADDITIVE CORRELATED GAUSSIAN NOISE Localization of a target object in the presence of non-white (correlated) additive Gaussian noise Localization accuracy ofthe optimal filter OPTIMAL LOCALIZA TION IN COLOR AND MULTI COMPONENT IMAGES Optimallocalization device Localization accuracy and reliability Optimallocalization in multi component images with correlated noise OBJECT LOCALIZATION IN THE PRESENCE OF MULTIPLE NONOVERLAPPNING NON-TARGET OBJECTS References

11 11. TARGET LOCATION IN CLUTTER PROBLEM FORMULA TION LOCALIZATION OF PRECISELY KNOWN OBJECTS: SPATIALLY HOMOGENEOUS OPTIMALITY CRITERION Optimal adaptive correlator Implementation issues, practical recommendations and illustrative examples LOCALIZATION OF INEXACTLY KNOWN OBJECT: SPATIALLY HOMOGENEOUS CRITERION LOCALIZATION METHODS FOR SPATIALLY INHOMOGENEOUS CRITERIA OBJECT LOCALIZA TION AND IMAGE BLUR OBJECT LOCALIZATION AND EDGE DETECTION. SELECTION OF REFERENCE OBJECTS FOR TARGET TRACKING OPTIMAL ADAPTIVE CORRELATOR AND OPTICAL CORRELATORS Optical correlators with improved discrimination capability Computer and optical implementations ofthe optimal adaptive correlator TARGET LOCA TING IN COLOR AND MULTI COMPONENT IMAGES Theoretical framework Separable component-wise implementations ofthe optimal adaptive multi-component correlator References NON LINEAR FILTERS IN SIGNAL/IMAGE PROCESSING CLASIFICATION PRINCIPLES Main assumptions and definitions

12 Typical signal attributes Estimation operations Neighborhood building operations FILTER CLASSIFICATION TABLES Transferential filters Iterative filtering Multiple branch parallel, cascade and recursive filters Miscellaneous new filters PRACTICAL EXAMPLES Image denoising Image enhancement Image segmentation and edge detection Implementation issues References COMPUTER GENERATED HOLOGRAMS MATHEMATICAL MODELS METHODS FOR ENCODING AND RECORDING COMPUTER GENERATED HOLOGRAMS RECONSTRUCTION OF COMPUTER GENERATED HOLOGRAMS '" References

Digital Image Processing

Digital Image Processing Third Edition Rafael C. Gonzalez University of Tennessee Richard E. Woods MedData Interactive PEARSON Prentice Hall Pearson Education International Contents Preface xv Acknowledgments