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      Projection-based wavelet denoising [lecture notes]

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      Author(s)
      Çetin, A. Enis
      Tofighi M.
      Date
      2015
      Source Title
      IEEE Signal Processing Magazine
      Print ISSN
      1053-5888
      Publisher
      Institute of Electrical and Electronics Engineers Inc.
      Volume
      32
      Issue
      5
      Pages
      120 - 124
      Language
      English
      Type
      Article
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      Abstract
      In this lecture note, we describe a wavelet domain denoising method consisting of making orthogonal projections of wavelet (subbands) signals of the noisy signal onto an upside down pyramid-shaped region in a multidimensional space. Each horizontal slice of the upside down pyramid is a diamond shaped region and it is called an -ball. The upside down pyramid is called the epigraph set of the -norm cost function. We show that the method leads to soft-thresholding as in standard wavelet denoising methods. Orthogonal projection operations automatically determine the soft-threshold values of the wavelet signals. © 2015 IEEE.
      Keywords
      Cost functions
      Denoising methods
      Horizontal slices
      Multi-dimensional space
      Orthogonal projection
      Soft threshold
      Soft thresholding
      Wavelet denoising
      Wavelet denoising method
      Wavelet analysis
      Permalink
      http://hdl.handle.net/11693/21081
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/MSP.2015.2440051
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      • Department of Electrical and Electronics Engineering 3702
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