Abstract
A technique for the restoration of low resonance component and high resonance component of K independently measured signals is presented. The definition of low and high resonance component is given by the Rational Dilatation Wavelet Transform (RADWT), a particular kind of finite frame that provides sparse representation of functions with different oscillations persistence. It is assumed that the signals are measured simultaneously on several independent channels and in each channel the underlying signal is the sum of two components: the low resonance component and the high resonance component, both sharing some common characteristic between the channels. Components restoration is performed by means of the lasso-type penalty and backfitting algorithm. Numerical experiments show the performance of the proposed method in different synthetic scenarios highlighting the advantage of estimating the two components separately rather than together.
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Notes
- 1.
A collection of functions \(\{w_i\}\) of \(L_2(R)\) forms a frame if exist two constants \(c_l\) and \(c_r\) such that \(c_l\Vert f\Vert ^2 \le \sum _{i} <f, w_i>^2 \le c_r \Vert f\Vert ^2\) for all \(f \in L_2(R)\). The frame is tight if \(c_l=c_r\).
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De Canditiis, D., De Feis, I. (2020). Low and High Resonance Components Restoration in Multichannel Data. In: La Rocca, M., Liseo, B., Salmaso, L. (eds) Nonparametric Statistics. ISNPS 2018. Springer Proceedings in Mathematics & Statistics, vol 339. Springer, Cham. https://doi.org/10.1007/978-3-030-57306-5_16
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DOI: https://doi.org/10.1007/978-3-030-57306-5_16
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