Acoustical Imaging and Point Processes
There are many situations in acoustical imaging (active or passive) where the possible sources or scatterers to be detected or discriminated against are points, or, more generally, are represented by models in which some kind of point process is embedded. A point process is a random set of points (random both in number and positions) in some kind of state space. Examples of imaging problems involving point processes may be found in nondestructive evaluation (including acoustic emission), underwater surveillance (e.g., bearing estimation), medical imaging (e.g., in the case where the detection of echogenic nodules in breast tissue is desired), etc. In this paper, we will address the problem of estimating the average local density of points in some appropriate state space, given a set of measured signals. This density function or a suitable slice or projection of it constitutes the image. Most earlier treatments of this problem involve either 1) an approach that is exact for a single-point model, but which involves an inaccurate ad hoc extension to the many-point case, or 2) an approximate approach involving linear estimators with or without the use of an underlying many-point model. Neither of these approaches can yield algorithms that can resolve two point sources that are too close to be resolvable according to conventional optical criteria. We present here a third approach, based on a many-point model, where the estimation procedure is sufficiently accurate to preserve the essential “pointyness” of the model. Our estimation procedure involves the solution of a hierarchy of integro-differ-ential equations, appropriately truncated, in which the independent variable is a parameter defining the a priori density bias. Computational examples will be presented and discussed.
KeywordsAcoustic Emission Point Process Acoustical Imaging Truncation Approximation Assumed Source
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- Ruelle, D., 1969, Statistical Mechanics-Rigorous Results, Chap. 4, Benjamin, NY.Google Scholar