Multiscale, Statistical Anomaly Detection Analysis andAlgorithms for Linearized Inverse Scattering Problems

Authors:
Eric L. Miller;Alan S. Willsky
Affiliations:
The Communications and Digital Signal Processing Center, Department of Electrical and Computer Engineering, 235 Forsyth, Northeastern University, 360 Huntington Ave., Boston, MA 02115;Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Venue:
Multidimensional Systems and Signal Processing
Year:
1997

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Abstract

Inthis paper we explore the utility of multiscale and statisticaltechniques for detecting and characterizing the structure oflocalized anomalies in a medium based upon observations of scatteredenergy obtained at the boundaries of the region of interest.Wavelet transform techniques are used to provide an efficientand physically meaningful method for modeling the non-anomalousstructure of the medium under investigation. We employ decision-theoreticmethods both to analyze a variety of difficulties associatedwith the anomaly detection problem and as the basis for an algorithmto perform anomaly detection and estimation. These methods allowfor a quantitative evaluation of the manner in which the performanceof the algorithms is impacted by the amplitudes, spatial sizes,and positions of anomalous areas in the overall region of interest.Given the insight provided by this work, we formulate and analyzean algorithm for determining the number, location, and magnitudesassociated with a set of anomaly structures. This approach isbased upon the use of a Generalized, M-ary Likelihood Ratio Testto successively subdivide the region as a means of localizinganomalous areas in both space and scale. Examples of our multiscaleinversion algorithm are presented using the Born approximationof an electrical conductivity problem formulated so as to illustratemany of the features associated with similar detection problemsarising in fields such as geophysical prospecting, ultrasonicimaging, and medical imaging.