HANDBOOK OF ASTRONOMICAL DATA ANALYSIS
TABLE OF CONTENTS 1 INTRODUCTION TO APPLICATIONS AND METHODS INTRODUCTION TRANSFORMATION AND DATA REPRESENTATION FOURIER ANALYSIS TIME-FREQUENCY REPRESENTATION TIME-SCALE REPRESENTATION: THE WAVELET TRANSFORM THE RADON TRANSFORM MATHEMATICAL MORPHOLOGY EDGE DETECTION FIRST ORDER DERIVATIVE EDGE DETECTION SECOND ORDER DERIVATIVE EDGE DETECTION SEGMENTATION PATTERN RECOGNITION CHAPTER SUMMARY 2 FILTERING MULTISCALE TRANSFORMS THE A TROUS ISOTROPIC WAVELET TRANSFORM MULTISCALE TRANSFORMS COMPARED TO OTHER DATA TRANS- FORMS CHOICE OF MULTISCALE TRANSFORM THE MULTIRESOLUTION SUPPORT SIGNI?CANT WAVELET COE?CIENTS DE?NITION NOISE MODELING AUTOMATIC ESTIMATION OF GAUSSIAN NOISE FILTERING AND WAVELET COE?CIENT THRESHOLDING THRESHOLDING ITERATIVE FILTERING EXPERIMENTS ITERATIVE FILTERING WITH A SMOOTHNESS CONSTRAINT HAAR WAVELET TRANSFORM AND POISSON NOISE HAAR WAVELET TRANSFORM POISSON NOISE AND HAAR WAVELET COE?CIENTS 3 DECONVOLUTION THE DECONVOLUTION PROBLEM LINEAR REGULARIZED METHODS LEAST SQUARES SOLUTION TIKHONOV REGULARIZATION GENERALIZATION CLEAN BAYESIAN METHODOLOGY MAXIMUM LIKELIHOOD WITH GAUSSIAN NOISE GAUSSIAN BAYES MODEL MAXIMUM LIKELIHOOD WITH POISSON NOISE POISSON BAYES MODEL MAXIMUM ENTROPY METHOD OTHER REGULARIZATION MODELS ITERATIVE REGULARIZED METHODS CONSTRAINTS JANSSON-VAN CITTERT METHOD OTHER ITERATIVE METHODS WAVELET-BASED DECONVOLUTION WAVELET-VAGUELETTE DECOMPOSITION REGULARIZATION FROM THE MULTIRESOLUTION SUPPORT WAVELET CLEAN MULTISCALE ENTROPY DECONVOLUTION AND RESOLUTION SUPER-RESOLUTION GERCHBERG-SAXON PAPOULIS METHOD DECONVOLUTION WITH INTERPOLATION UNDERSAMPLED POINT SPREAD FUNCTION MULTISCALE SUPPORT CONSTRAINT 310 CONCLUSIONS AND CHAPTER SUMMARY 4 DETECTION FROM IMAGES TO CATALOGS MULTISCALE VISION MODEL MULTISCALE VISION MODEL DE?NITION FROM WAVELET COE?CIENTS TO OBJECT IDENTI?CATION PARTIAL RECONSTRUCTION EXAMPLES APPLICATION TO ISOCAM DATA CALIBRATION DETECTION AND DECONVOLUTION CONCLUSION 5 IMAGE COMPRESSION LOSSY IMAGE COMPRESSION METHODS THE PRINCIPLE COMPRESSION WITH PYRAMIDAL MEDIAN TRANSFORM PMT AND IMAGE COMPRESSION COMPRESSION PACKAGES REMARKS ON THESE METHODS COMPARISON QUALITY ASSESSMENT VISUAL QUALITY FIRST ALADIN PROJECT STUDY SECOND ALADIN PROJECT STUDY COMPUTATION TIME LOSSLESS IMAGE COMPRESSION THE LIFTING SCHEME LARGE IMAGES: COMPRESSION AND VISUALIZATION LARGE IMAGE VISUALIZATION ENVIRONMENT: LIVE DECOMPRESSION BY SCALE AND BY REGION THE SAO-DS9 LIVE IMPLEMENTATION 6 MULTICHANNEL DATA THE WAVELET-KARHUNEN-LO`EVE TRANSFORM CORRELATION MATRIX AND NOISE MODELING SCALE AND KARHUNEN-LO`EVE TRANSFORM THE WT-KLT TRANSFORM THE WT-KLT RECONSTRUCTION ALGORITHM NOISE MODELING IN THE WT-KLT SPACE MULTICHANNEL DATA FILTERING RECONSTRUCTION FROM A SUBSET OF EIGENVECTORS WT-KLT COE?CIENT THRESHOLDING EXAMPLE: ASTRONOMICAL SOURCE DETECTION THE HAAR-MULTICHANNEL TRANSFORM INDEPENDENT COMPONENT ANALYSIS 7 AN ENTROPIC TOUR OF ASTRONOMICAL DATA ANALYSIS THE CONCEPT OF ENTROPY SIGNAL AND NOISE INFORMATION MULTISCALE ENTROPY FILTERING FILTERING THE REGULARIZATION PARAMETER USE OF A MODEL THE MULTISCALE ENTROPY FILTERING ALGORITHM OPTIMIZATION DECONVOLUTION THE PARAMETERS BACKGROUND FLUCTUATION ANALYSIS RELEVANT INFORMATION IN AN IMAGE MULTISCALE ENTROPY AND OPTIMAL COMPRESSIBILITY 710 CONCLUSIONS AND CHAPTER SUMMARY 8 ASTRONOMICAL CATALOG ANALYSIS TWO-POINT CORRELATION FUNCTION DETERMINING THE 2-POINT CORRELATION FUNCTION ERROR ANALYSIS CORRELATION LENGTH DETERMINATION CREATION OF RANDOM CATALOGS FRACTAL ANALYSIS THE HAUSDOR?AND MINKOWSKI MEASURES THE HAUSDOR?AND MINKOWSKI DIMENSIONS MULTIFRACTALITY GENERALIZED FRACTAL DIMENSION WAVELET AND MULTIFRACTALITY SPANNING TREES AND GRAPH CLUSTERING VORONOI TESSELLATION AND PERCOLATION MODEL-BASED CLUSTERING MODELING OF SIGNAL AND NOISE APPLICATION TO THRESHOLDING WAVELET ANALYSIS NEAREST NEIGHBOR CLUTTER REMOVAL 9 MULTIPLE RESOLUTION IN DATA STORAGE AND RETRIEVAL WAVELETS IN DATABASE MANAGEMENT FAST CLUSTER ANALYSIS NEAREST NEIGHBOR FINDING ON GRAPHS CLUSTER-BASED USER INTERFACES IMAGES FROM DATA MATRIX SEQUENCING FILTERING HYPERTEXT CLUSTERING DOCUMENT-TERM DATA 10 TOWARDS THE VIRTUAL OBSERVATORY 101 DATA AND INFORMATION 102 THE INFORMATION HANDLING CHALLENGES FACING US REFERENCES