## Random processes for image and signal processingPart of the SPIE/IEEE Series on Imaging Science and Engineering. This book provides a framework for understanding the ensemble of temporal, spatial, and higher-dimensional processes in science and engineering that vary randomly in observations. Suitable as a text for undergraduate and graduate students with a strong background in probability and as a graduate text in image processing courses. |

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### Contents

Probability Theory | 1 |

Exercises for Chapter 1107 | 107 |

Random Processes | 115 |

Copyright | |

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### Common terms and phrases

according to Eq algorithm applied assume autocorrelation Bessel inequality binary Boolean model Borel canonical expansion canonical representation Chapman-Kolmogorov equations components compression conditional expectation consider convergence coordinate functions covariance function covariance matrix defined denote derivative deterministic differentiation discrete distributed with mean eigenvalues error Example exists expression finite Fourier coefficients gamma distribution given grain Hence Huffman code identically distributed image processing inequality inner product space interval joint density Karhunen-Loeve expansion large numbers linear estimator linearly independent Markov chain maximum-likelihood estimator mean-square minimized moment-generating function normally distributed optimal filter optimal linear filter orthogonal orthonormal system output parameter pixel Poisson points Poisson process possessing probability distribution function pseudoinverse random function random function X(t random process random set random vector realization recursive respectively Show signal stationary random steady-state distribution subspace Suppose Theorem transform uncorrelated values variance a2 white noise yields zero-mean random