Digital Holography and Digital Image Processing

Abstract

1. Introduction -- 1.1 Digital holography and evolution of imaging techniques -- 1.2 Contents of this book -- 2. Optical signals and transforms -- 2.1 Mathematical models of optical signals -- 2.2 Signal transformations -- 2.3 Imaging systems and integral transforms -- 2.4 Fourier transform and its derivatives -- 2.5 Imaging from projections: Radon and Abel transforms -- 2.6 Multi resolution imaging: Wavelet transforms -- 2.7 Sliding window transforms and "time-frequency" (space-transform) signal representation -- 2.8 Stochastic transformations and statistical models -- 3. Digital representation of signals -- 3.1 Principles of signal digitization -- 3.2 Signal discretization as expansion over a set of basis functions: Typical basis functions and classification -- 3.3 Shift (convolution) bases functions and sampling theorem -- 3.4 Multi-resolution sampling -- 3.5 Unconventional digital imaging methods -- 3.6 Principles of signal scalar quantization -- 3.7 Basics of signal coding and data compression -- 4. Digital representation of signal transformations -- 4.1 The principles -- 4.2 Discrete representation of colvolution integral: Digital filters -- 4.3 Discrete representation of Fourier integral transform -- 4.4 Discrete representation of Fresnel integral transform -- 5. Methods and algorithms of digital filtering -- 5.1 Filtering in signal domain -- 5.2 Filtering in transform domain -- 5.3 Combined algorithms for computing DFT and DCT of real valued signals -- 6. Fast algorithms -- 6.1 The principle of fast Fourier transforms -- 6.2 Matrix techniques in fast transforms -- 6.3 Transforms and their fast algorithms in matrix representation -- 6.4 Pruned algorithms -- 6.5 Quantized DFT -- 7. Statistical methods and algorithms -- 7.1 Measuring signal statistical characteristics -- 7.2 Digital statistical models and Monte Carlo methods -- 7.3 Statistical (Monte Carlo) simulation: Case study: Speckle noise phenomena in coherent imaging and digital holography -- 8. Sensor signal perfecting, image restoration, reconstruction and enhancement -- 8.1 Mathematical models of imaging systems -- 8.2 Linear filters for image restoration -- 8.3 Sliding window transform domain adaptive signal restoration -- 8.4 Multi-component image restoration -- 8.5 Filtering impulse noise -- 8.6 Methods for correcting gray scale nonlinear distortions -- 8.7 Image reconstruction -- 8.8 Image enhancement -- 9. Image resampling and geometrical transformations -- 9.1 Principles of image resampling -- 9.2 Nearest neighbor, linear and spline interpolation methods -- 9.3 Algorithms of discrete sinc-interpolation -- 9.4 Application examples -- 10. Signal parameter estimation and measurement: Object localization -- 10.1 Problem formulation: Optimal statistical estimates -- 10.2 Localization of an object in the presence of additive white Gaussian noise -- 10.3 Performance of the optimal localization device -- 10.4 Localization of an object in the presence of additive correlated Gaussian noise -- 10.5 Optimal localization in color and multi component images -- 10.6 Object localization in the presence of multiple nonoverlapping non-target objects -- 11. Target location in clutter -- 11.1 Problem formulation -- 11.2 Localization of precisely known objects: Spatially homogeneous optimality criterion -- 11.3 Localization of inexactly known object: Spatially homogeneous criterion -- 11.4 Localization methods for spatially inhomogeneous criteria -- 11.5 Object localization and image blur -- 11.6 Object localization and edge detection: Selection of reference objects for target tracking -- 11.7 Optimal adaptive correlator and optical correlators -- 11.8 Target locating in color and multi component images -- 12. Nonlinear filters in signal/image processing -- 12.1 Classification principles -- 12.2 Filter classification tables -- 12.3 Practical examples -- 13. Computer generated holograms -- 13.1 Mathematical models -- 13.2 Methods for encoding and recording computer generated holograms -- 13.3 Reconstruction of computer generated holograms.