Noise reduction using wavelet cycle spinning: analysis of useful periodicities in the z-transform domain

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• 作者：Miguel A. Rodriguez-Hernandez ; José L. San Emeterio
• 关键词：Wavelets ; Cycle spinning ; Periodicities ; Signal denoising ; Ultrasonics ; Z ; transform
• 刊名：Signal, Image and Video Processing
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：10
• 期：3
• 页码：519-526
• 全文大小：564 KB
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• 作者单位：Miguel A. Rodriguez-Hernandez (1)
  José L. San Emeterio (2)
  
  1. ITACA, Universitat Politécnica de Valéncia, Valencia, Spain
  2. Sensors and Ultrasonic Systems Department, ITEFI, CSIC, Madrid, Spain
  
• 刊物类别：Engineering
• 刊物主题：Signal,Image and Speech Processing
  Image Processing and Computer Vision
  Computer Imaging, Vision, Pattern Recognition and Graphics
  Multimedia Information Systems
  
• 出版者：Springer London
• ISSN：1863-1711

文摘

Cycle spinning (CS) and a’trous algorithms are different implementations of the undecimated wavelet transform (UWT). Both algorithms can be used for UWT and even though the resulting wavelet coefficients are different, they keep a correspondence. This paper describes an analysis of the CS algorithm performed in the z-transform domain, showing the similarities and differences with the a’trous implementation. CS generates more wavelet coefficients than a’trous, but the number of significative and different coefficients is the same in both cases because of the occurrence of a periodic repetition in CS coefficients. Mathematical expressions for the relationship between CS and a’trous coefficients and for CS coefficient periodicities are provided in the z-transform domain. In some wavelet denoising applications, periodicities (present in the coefficients of the CS procedure) can also be found in the performance measure of the processed signals. In particular, in ultrasonic CS denoising applications, periodicities have been appreciated in the signal-to-noise ratio (SNR) of the ultrasonic denoised signals. These periodicities can be used to optimize the number of CS coefficients for an efficient implementation. Two examples showing the periodicities in the SNR are included. A selection of several reduced sets of CS wavelet coefficients has been utilized in the examples, and the SNRs resulting after denoising are analyzed. Keywords Wavelets Cycle spinning Periodicities Signal denoising Ultrasonics Z-transform