Digital Holography and Digital Image Processing:: Principles, Methods, Algorithms Book

1	Introduction	1
1.1	Digital Holography and Evolution of Imaging Techniques	1
1.2	Contents of this Book	5
2	Optical Signals and Transforms	11
2.1	Mathematical Models of Optical Signals	11
2.2	Signal Transformations	24
2.3	Imaging Systems and Integral Transforms	27
2.4	Fourier Transform and its Derivatives	39
2.5	Imaging from Projections: Radon and Abel Transforms	57
2.6	Multi Resolution Imaging: Wavelet Transforms	61
2.7	Sliding Window Transforms and "Time-Frequency" (Space-Transform) Signal Representation	63
2.8	Stochastic Transformations and Statistical Models	67
3	Digital Representation of Signals	79
3.1	Principles of Signal Digitization	79
3.2	Signal Discretization as Expansion Over a Set of Basis Functions. Typical Basis Functions and Classification	80
3.3	Shift (Convolution) Bases Functions and Sampling Theorem	106
3.4	Multi-Resolution Sampling	129
3.5	Unconventional Digital Imaging Methods	131
3.6	Principles of Signal Scalar Quantization	133
3.7	Basics of Signal Coding and Data Compression	147
4	Digital Representation of Signal Transformations	161
4.1	The Principles	161
4.2	Discrete Representation of Convolution Integral. Digital Filters	170
4.3	Discrete Representation of Fourier Integral Transform	170
4.4	Discrete Representation of Fresnel Integral Transform	199
5	Methods and Algorithms of Digital Filtering	211
5.1	Filtering in Signal Domain	211
5.2	Filtering in Transform Domain	226
5.3	Combined Algorithms for Computing DFT and DCT of Real Valued Signals	231
6	Fast Algorithms	239
6.1	The Principle of Fast Fourier Transforms	239
6.2	Matrix Techniques in Fast Transforms	243
6.3	Transforms and their Fast Algorithms in Matrix Representation	249
6.4	Pruned Algorithms	264
6.5	Quantized DFT	269
7	Statistical Methods and Algorithms	275
7.1	Measuring Signal Statistical Characteristics	275
7.2	Digital Statistical Models and Monte Carlo Methods	291
7.3	Statistical (Monte Carlo) Simulation. Case Study: Speckle Noise Phenomena in Coherent Imaging and Digital Holography	305
8	Sensor Signal Perfecting, Image Restoration, Reconstruction and Enhancement	313
8.1	Mathematical Models of Imaging Systems	313
8.2	Linear Filters for Image Restoration	315
8.3	Sliding Window Transform Domain Adaptive Signal Restoration	328
8.4	Multi-Component Image Restoration	340
8.5	Filtering Impulse Noise	343
8.6	Methods for Correcting Gray Scale Nonlinear Distortions	348
8.7	Image Reconstruction	353
8.8	Image Enhancement	361
9	Image Resampling and Geometrical Transformations	373
9.1	Principles of Image Resampling	373
9.2	Nearest Neighbor, Linear and Spline Interpolation Methods	376
9.3	Algorithms of Discrete Sinc-Interpolation	380
9.4	Application examples	395
10	Signal Parameter Estimation and Measurement. Object Localization	411
10.1	Problem Formulation. Optimal Statistical Estimates	411
10.2	Localization of an Object in the Presence of Additive White Gaussian Noise	414
10.3	Performance of the Optimal Localization Device	421
10.4	Localization of an Object in the Presence of Additive Correlated Gaussian Noise	443
10.5	Optimal Localization in Color and Multi Component Images	449
10.6	Object Localization in the Presence of Multiple Nonoverlappning Non-Target Objects	454
11	Target Location in Clutter	461
11.1	Problem Formulation	461
11.2	Localization of Precisely Known Objects: Spatially Homogeneous Optimality Criterion	465
11.3	Localization of Inexactly Known Object: Spatially Homogeneous Criterion	474
11.4	Localization Methods for Spatially Inhomogeneous Criteria	478
11.5	Object Localization and Image Blur	483
11.6	Object Localization and Edge Detection. Selection of Reference Objects for Target Tracking	485
11.7	Optimal Adaptive Correlator and Optical Correlators	490
11.8	Target Locating in Color and Multi Component Images	499
12	Nonlinear Filters in Signal/Image Processing	509
12.1	Classification Principles	510
12.2	Filter Classification Tables	519
12.3	Practical Examples	527
13	Computer Generated Holograms	541
13.1	Mathematical Models	541
13.2	Methods for Encoding and Recording Computer Generated Holograms	548
13.3	Reconstruction of Computer Generated Holograms	565