18-751/FALL 1999/CHEN

n         Review of probability concepts

n         Random variables and random vectors.  Multivariate Gaussian

n         Random processes

n         Common random processes: Gaussian processes, Markov processes, Poisson processes, etc.

n         Random fields.  Markov random fields.  Application to image processing.

n         Moment analysis: correlation and covariance, Karhunen-Loeve transform

n         Frequency-domain descriptions.  Power density spectrum.  White noise.

n         Linear systems applied to random processes

n         Estimation: Maximum likelihood, minimum-variance estimate

n         Bayes estimation: MAP, mean-square, and linear mean-square

n         Optimal filtering: Linear prediction, Wiener and Kalman filtering.