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Scale space multiresolution analysis of random signals. (English) Zbl 1218.62067

Summary: A method to capture the scale-dependent features in a random signal is proposed with the main focus on images and spatial fields defined on a regular grid. A technique based on scale space smoothing is used. However, while the usual scale space analysis approach is to suppress detail by increasing smoothing progressively, the proposed method instead considers differences of smooths at neighboring scales. A random signal can then be represented as a sum of such differences, a kind of a multiresolution analysis, each difference representing details relevant at a particular scale or resolution. Bayesian analysis is used to infer which details are credible and which are just artifacts of random variation. The applicability of the method is demonstrated using noisy digital images as well as global temperature change fields produced by numerical climate prediction models.

MSC:

62H35 Image analysis in multivariate analysis
62F15 Bayesian inference
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
62M40 Random fields; image analysis
62P12 Applications of statistics to environmental and related topics
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