Название: Optimal Signal Processing Under Uncertainty
Автор: Edward R. Dougherty
Издательство: Society of Photo Optical
ISBN: 1510619291
Год: 2018
Страниц: 308
Язык: английский
Формат: pdf (true)
Размер: 20.2 MB

Whereas modern science concerns the mathematical modeling of phenomena, essentially a passive activity, modern engineering involves determining operations to actively alter phenomena to effect desired changes of behavior. It begins with a scientific (mathematical) model and applies mathematical methods to derive a suitable intervention for the given objective. Since one would prefer the best possible intervention, engineering inevitably becomes optimization and, since all but very simple systems must account for randomness, modern engineering might be defined as the study of optimal operators on random processes.

The design of optimal operators takes different forms depending on the random process constituting the scientific model and the operator class of interest. The operators might be linear filters, morphological filters, controllers, classifiers, or cluster operators, each having numerous domains of application. The underlying random process might be a random signal/image for filtering, a Markov process for control, a feature-label distribution for classification, or a random point set for clustering. 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 criterion, an optimal operator found. For the classical Wiener filter, the model is a pair of jointly distributed wide-sense stationary random signals, the objective is to estimate a desired signal from an observed signal via a linear filter, and the cost function to be minimized is the mean-square error between the filtered observation and the desired signal.