Acoustical Imaging and Point Processes II: Exact Solution
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 a point process is embedded. A point process is a random set of points (random both in number and positions) in an appropriate state space. Examples of acoustical imaging problems involving point processes (in the static case) may be found in non destructive evaluation (including acoustical emission), underwater surveillance (e.g., bearing estimation), medical imaging (e.g., detection of echogenic nodules in breast tissues), etc.
At a much earlier symposium in the present series, a paper  with the same general title was presented, where several problems were considered but with approximate solutions. In particular, the point-process aspect of the problems was treated by a complex, but approximate, solution methodology. In this paper, the same problems are considered, but with exact solutions. Here the point-process aspect of the problems is treated by a relatively simple, but exact, solution methodology. A brief discussion of this methodology is given and numerical test examples based upon synthetic data are presented.
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