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Scale space multiresolution analysis of random signals

Author

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  • Holmström, Lasse
  • Pasanen, Leena
  • Furrer, Reinhard
  • Sain, Stephan R.

Abstract

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.

Suggested Citation

  • Holmström, Lasse & Pasanen, Leena & Furrer, Reinhard & Sain, Stephan R., 2011. "Scale space multiresolution analysis of random signals," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2840-2855, October.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:10:p:2840-2855
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    References listed on IDEAS

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    1. Godtliebsen, Fred & Oigard, Tor Arne, 2005. "A visual display device for significant features in complicated signals," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 317-343, February.
    2. Kolaczyk, Eric D. & Ju, Junchang & Gopal, Sucharita, 2005. "Multiscale, Multigranular Statistical Image Segmentation," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1358-1369, December.
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    Cited by:

    1. Thon, Kevin & Rue, Håvard & Skrøvseth, Stein Olav & Godtliebsen, Fred, 2012. "Bayesian multiscale analysis of images modeled as Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 49-61, January.
    2. Leena Pasanen & Lasse Holmström, 2017. "Scale space multiresolution correlation analysis for time series data," Computational Statistics, Springer, vol. 32(1), pages 197-218, March.
    3. Leena Pasanen & Päivi Laukkanen-Nevala & Ilkka Launonen & Sergey Prusov & Lasse Holmström & Eero Niemelä & Jaakko Erkinaro, 2017. "Extraction of sea temperature in the Barents Sea by a scale space multiresolution method – prospects for Atlantic salmon," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2317-2336, October.

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