SIMG-713 Lecture Schedule
- Probability and
review of the fundamentals of probability and random variables.
- Computations with Random Variables-Functions
- Bernoulli Trials-Repeated
independent trials of an experiment illustrated by modeling of photons striking
a detector array. Modeling of distributions of r photons over n detectors.
- Poisson Distribution-Development of the Poisson distribution from difference equation model and comparison of Poisson and Bernoulli photon count models. Parameters and moments of the Poisson distribution.
- Saturation Effects-Modeling of receptors which saturate after receiving L quanta. Dependence of expected receptor count on quanta flux.
- Detective Quantum Efficiency-Model the ability of a detector to detect a change photon flux against background radiation.
- DQE Model for Saturating Photon Counter-Use the DQE model to characterize the capability of a photon counter with saturation level L to measure the level of background radiation. Define Noise Equivalent Quanta model for this class of detectors.
- Random Process Model-Model of experiments in which the outcomes are sequences of random variables. First and second order moments. Stationary and non-stationary r.p.
- Gaussian Noise Model-Extension of the Poisson model to very large numbers of particles, leading to the normal distribution. Multivariate distribution of independent samples. Concept of white noise.
- Filtered Noise Model-Construction of random processes by filtering of white noise. Use of a discrete FIR filter with discrete white noise input. Characterization of output sequence. Autocorrelation, crosscorrelation and filter parameters.
- Power Spectrum-Definition of power spectrum and its relationship to filter parameters. General discussion of problems with power spectrum measurement.
- Digital Filter Model-Use of a general linear difference equation with constant coefficients driven by white noise as a model of certain random processes.
- Narrowband Noise-Construction of narrowband noise processes by filtering white noise. Properties of narrowband sequences. Estimation of spectrum parameters and their relationship to filter parameters.
- System Function Model-Relationship of the system function to the difference equation model and to the power spectrum of the random process.
- Autoregressive sequences-Properties of autoregressive sequences and estimation of model parameters from a sample function of a random process.
- Model of Signal plus Noise-Model of a signal in random noise, and methods to detect the presence of the signal. Structure of an optimum detector. Receiver Operating Characteristic.
- Estimation of Signal Parameters-How should one measure the value of signal parameters such as frequency, amplitude and phase when a signal of known parametric form is observed in noise? How does one quantify expected performance?
- Detection of Random Signals in Noise-How does one go about detecting the presence of one random process against the background of another random process?
- Modeling of 2D Random Fields-A random field is an array of random numbers which may be statistically related. We discuss special considerations in modeling such fields and their use in image sensor systems.