Simultaneous Least Squares Wavelet Decomposition for Multidimensional Irregularly Spaced Data

Abstract:

The multidimensional Discrete Wavelet Transform (DWT) has been widely used in signal and image processing for regularly sampled data. For irregularly sampled data, however, other techniques should be used including the Least Square Wavelet Decomposition (LSWD). The commonly used level by level (sequential) wavelet decomposition, which calculates the wavelet coefficients in each resolution separately, may result in a gross interpolation error. To overcome this drawback, a different approach called the Simultaneous Least Square Wavelet Decomposition, which computes all wavelet coefficients simultaneously, have been proposed by the authors. In this paper, we extend the simultaneous LSWD approach to the multidimensional case and show that this method has excellent reconstruction property for two dimensional irregularly spaced data.

• Periodical: Applied Mechanics and Materials (Volumes 239-240)
• Pages: 1213-1218
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.239-240.1213
• Online since: December 2012
• Authors: Mehdi Shahbazian, Saeed Shahbazian
• Keywords: Irregular Data, Least Square (LS), Multidimensional, Signal Reconstruction, Wavelet

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