Optimal signal processing under uncertainty / Edward R. Dougherty.

Format:

Book

Author/Creator:

Dougherty, Edward R., author.

Contributor:

Society of Photo-Optical Instrumentation Engineers, publisher.

Series:

SPIE monograph ; PM287.

SPIE digital library

SPIE Press monograph ; PM287

Language:

English

Subjects (All):

Signal processing--Mathematics.

Signal processing.

Mathematical optimization.

Genre:

Electronic books.

Physical Description:

1 online resource (308 pages).

Place of Publication:

Bellingham, Washington, USA : SPIE Press, [2018]

System Details:

Mode of access: World Wide Web.

text file

Summary:

"The design of optimal operators takes different forms depending on the random process constituting the scientific model and the operator class of interest. In all cases, operator class and random process must be united in a criterion (cost function) that characterizes the operational objective and, relative to the cost function, an optimal operator found. A common difficulty is uncertainty in the parameters of the scientific model. Then, in addition to optimization relative to the original cost function, optimization must take into account uncertainty relative to an uncertainty class of random processes. If there is a prior distribution (or posterior distribution if data are employed) governing likelihood in the uncertainty class, then one can choose an operator minimizing the expected cost over the uncertainty class. A critical point is that the prior distribution is not on the parameters of the operator model, but on the uncertainty relative to the parameters of the scientific model. The basic principle embodied in the book is to express the optimal operator under the joint probability space formed from the joint internal and external uncertainty in the same form as the optimal operator for a known model by replacing the mathematical structures forming the standard optimal operator with corresponding structures, called effective characteristics, that incorporate model uncertainty. For instance, in Wiener filtering the power spectra might be uncertain and be replaced by effective power spectra in the representation of the Wiener filter"-- Provided by publisher.

Contents:

Preface

Acknowledgments

1. Random functions: 1.1. Moments; 1.2. Calculus; 1.3. Three fundamental processes; 1.4. Stationarity; 1.5. Linear systems

2. Canonical expansions: 2.1. Fourier representation and projections; 2.2. Constructing canonical expansions; 2.3. Orthonormal coordinate functions; 2.4. Derivation from a covariance expansion; 2.5. Integral canonical expansions; 2.6. Expansions of WS stationary processes

3. Optimal filtering: 3.1. Optimal mean-square-error filters; 3.2. Optimal finite-observation linear filters; 3.3. Optimal linear filters for random vectors; 3.4. Recursive linear filters; 3.5. Optimal infinite-observation linear filters; 3.6. Optimal filtering via canonical expansions; 3.7. Optimal morphological bandpass filters; 3.8. General schema for optimal design

4. Optimal robust filtering: 4.1. Intrinsically Bayesian robust filters; 4.2. Optimal Bayesian filters; 4.3. Model-constrained Bayesian robust filters; 4.4. Robustness via integral canonical expansions; 4.5. Minimax robust filters; 4.6. IBR Kalman filtering; 4.7. IBR Kalman-Bucy filtering

5. Optimal experimental design: 5.1. Mean objective cost of uncertainty; 5.2. Experimental design for IBR linear filtering; 5.3. IBR Karhunen-Loève compression; 5.4. Markovian regulatory networks; 5.5. Complexity reduction; 5.6. Sequential experimental design; 5.7. Design with inexact measurements; 5.8. General MOCU-based experimental design

6. Optimal classification: 6.1. Bayes classifier; 6.2. Optimal Bayesian classifier; 6.3. Classification rules; 6.4. OBC in the discrete and Gaussian models; 6.5. Consistency; 6.6. Optimal sampling via experimental design; 6.7. Prior construction; 6.8. Epistemology

7. Optimal clustering: 7.1. Clustering; 7.2. Bayes clusterer; 7.3. Separable point processes; 7.4. Intrinsically Bayesian robust clusterer

References

Index.

Notes:

"SPIE Digital Library."--Website.

Includes bibliographical references and index.

Title from PDF title page (SPIE eBooks Website, viewed 2018-07-06).

Other Format:

Print version

ISBN:

9781510619302

1510619305

OCLC:

1044639004

Access Restriction:

Restricted for use by site license.