Theory of Remote Image Formation

by Richard E. Blahut

• ISBN13: 9780521553735
• ISBN10: 0521553733
• Format: Hardcover
• Copyright: 2005-01-10
• Publisher: Cambridge University Press

Summary

In many applications, images, such as ultrasonic or X-ray signals, are recorded and then analyzed with digital or optical processors in order to extract information. Such processing requires the development of algorithms of great precision and sophistication. This book presents a unified treatment of the mathematical methods that underpin the various algorithms used in remote image formation. The author begins with a review of transform and filter theory. He then discusses two- and three-dimensional Fourier transform theory, the ambiguity function, image construction and reconstruction, tomography, baseband surveillance systems, and passive systems (where the signal source might be an earthquake or a galaxy). Information-theoretic methods in image formation are also covered, as are phase errors and phase noise. Throughout the book, practical applications illustrate theoretical concepts, and there are many homework problems. The book is aimed at graduate students of electrical engineering and computer science, and practitioners in industry.

Table of Contents

Preface	xiii
Acknowledgments	xvi
Introduction	1	(28)
Remote image-formation systems	1	(3)
The history of image formation	4	(4)
Radar and sonar systems	8	(6)
Imaging by projections	14	(2)
Passband and complex baseband waveforms	16	(2)
Temporal and spatial coherence	18	(2)
Monodirectional waves	20	(3)
Wavefront diffraction	23	(3)
Deterministic and random models	26	(3)
Signals in one dimension	29	(38)
The one-dimensional Fourier transform	29	(5)
Transforms of some useful functions	34	(4)
The dirichlet functions	38	(5)
Passband signals and passband filters	43	(2)
Baseband and passband sampling	45	(3)
Signal space	48	(6)
The matched filter	54	(5)
Resolution and apodization	59	(8)
Signals in two dimensions	67	(44)
The two-dimensional Fourier transform	67	(4)
Transforms of some useful functions	71	(9)
Circularly symmetric functions	80	(5)
The projection-slice theorem	85	(3)
Hankel transforms	88	(2)
Two-dimensional pulse arrays	90	(2)
Sampling in two dimensions	92	(8)
Two-dimensional signals and filters	100	(2)
Resolution and apodization	102	(9)
Optical imaging systems	111	(42)
Scalar diffraction	112	(3)
The Huygens--Fresnel principle	115	(3)
Fresnel and Fraunhofer approximations	118	(3)
The geometrical optics approximation	121	(2)
The ideal lens	123	(9)
Noncoherent imaging	132	(4)
Optical filtering	136	(3)
Phase-contrast imaging	139	(2)
Wavefront reconstruction	141	(12)
Antenna systems	153	(33)
Aperture and pattern	154	(7)
Reciprocity	161	(2)
Antenna arrays	163	(9)
Focused antennas and arrays	172	(1)
Nondiffracting beams	173	(1)
Interferometry	174	(2)
Vector diffraction	176	(3)
Scanning antenna patterns	179	(1)
Wideband radiation patterns	180	(6)
The ambiguity function	186	(35)
Theory of the ambiguity function	186	(7)
Properties of the ambiguity function	193	(3)
Shape and resolution parameters	196	(3)
Ambiguity function of a pulse train	199	(4)
Ambiguity function of a Costas pulse	203	(5)
The cross-ambiguity function	208	(2)
The sample cross-ambiguity function	210	(11)
Radar imaging systems	221	(33)
The received signal	221	(7)
The imaging equation	228	(3)
Imaging resolution	231	(2)
Focusing and motion compensation	233	(4)
Structure of typical imaging systems	237	(5)
Computing the cross-ambiguity function	242	(5)
Dual aperture imaging	247	(7)
Diffraction imaging systems	254	(33)
The three-dimensional Fourier transform	254	(2)
Transforms of some useful functions	256	(6)
Diffraction by three-dimensional objects	262	(3)
Observation from diffraction data	265	(2)
X-ray diffraction by arrays	267	(5)
Diffraction imaging	272	(1)
Model formation from diffraction data	273	(5)
Diffraction from fiber arrays	278	(2)
Diffraction from excited arrays	280	(7)
Construction and reconstruction of images	287	(34)
Deconvolution and deblurring	288	(5)
Deconvolution of nonnegative images	293	(3)
Blind image deconvolution	296	(6)
Phase retrieval	302	(5)
Optical imaging from point events	307	(4)
Coded aperture imaging	311	(10)
Tomography	321	(40)
Projection tomography	322	(8)
Fourier and algebraic reconstruction	330	(5)
Merging of multiple images	335	(2)
Diffraction tomography	337	(6)
Diffusion tomography	343	(3)
Coherent and noncoherent radar tomography	346	(3)
Emission tomography from magnetic excitation	349	(3)
Emission tomography from decay events	352	(1)
Coherence tomography	353	(8)
Likelihood and information methods	361	(47)
Likelihood functions and decision rules	362	(5)
The maximum-likelihood principle	367	(1)
Alternating maximization	368	(8)
Other principles of inference	376	(3)
Nonnegativity constraints and discrimination	379	(6)
Likelihood methods in blind image deconvolution	385	(2)
Likelihood methods in photon imaging	387	(3)
Radar imaging of diffuse reflectors	390	(5)
Regularization	395	(2)
Notions of equivalence	397	(3)
The Dempster--Laird--Rubin method	400	(8)
Radar search systems	408	(47)
The radar range equation	408	(2)
Coherent detection of pulses in noise	410	(4)
The Neyman--Pearson theorem	414	(5)
Rayleigh and ricean probability distributions	419	(4)
Noncoherent detection of pulses in noise	423	(2)
Detection under unknown parameters	425	(6)
Clutter	431	(3)
Detection of moving objects	434	(4)
Coherent estimation of pulse parameters	438	(5)
Noncoherent estimation of pulse parameters	443	(12)
Passive and baseband surveillance systems	455	(26)
Radio astronomy	456	(5)
Estimation of direction	461	(5)
Passive location of emitters	466	(4)
Magnetic anomaly detection	470	(3)
Estimation of differential parameters	473	(2)
Detection of unknown waveforms	475	(1)
Lidar surveillance	476	(5)
Data combination and tracking	481	(18)
Noncoherent integration	482	(3)
Sequential detection	485	(1)
Multitarget sorting	486	(4)
The assignment problem	490	(5)
Multilateration	495	(4)
Phase noise and phase distortion	499	(14)
Quadratic-phase errors	500	(3)
Phase noise and coherence	503	(2)
Phase noise and the Fourier transform	505	(1)
Phase noise and the matched filter	506	(3)
Phase noise and the ambiguity function	509	(2)
Effect of phase distortion	511	(1)
Array errors	511	(2)
References	513	(16)
Index	529