NON-LINEAR N-TERM APPROXIMATION BY NON-STATIONARY BIORTHOGONALWAVELET SYSTEMS BASED ON EXPONENTIAL B-SPLINES
Yeon Ju Lee, Amos Ron, Jungho Yoon · 한국산업응용수학회 학술대회 논문집 · 2009
In this study, we are interested in non-linear N-term approximation by wavelet sums for a wide class of acoustic emission signals. Since the differential operators associated with polynomialbased stationary wavelets make all the poles at the origin in frequency domain, they do not consider the spectral features of signals. To overcome this drawback, the non-stationary biorthogonal wavelet systems based on the exponential B-spline are selected such that they can be tuned to the spectral characteristic of a given signal, yielding better approximation and sparser representation than classical wavelets at the strictly the same computational costs. This study is first concerned with constructing an algorithm for choosing thresholding values corresponding the given number N. Next, we discuss the approximation order of the suggested N-term approximation method. In order to illustrate our construction and results, we present some numerical examples, which confirms its powerful properties for the accuracy and sparse representation.