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Minimum-Energy Wavelet Frames on Local Fields

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Abstract

To overcome the computational complexity, numerical instability and the complication of change of bases problem, we introduce the concept of minimum-energy wavelet frame on local fields of positive characteristic and present its equivalent characterizations in terms of their wavelet masks. Besides, in view of polyphase representation of the wavelet masks, we give a necessary and sufficient condition for the existence of minimum-energy wavelet frames on local fields. At last, we present the decomposition and reconstruction formulae of minimum-energy wavelet frame for \(L^2(K)\).

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Acknowledgements

This work is supported by NBHM, Department of Atomic Energy, Government of India (Grant No. 2/48(8)/2016/NBHM(R.P)/R&D II/13924).

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Authors and Affiliations

  1. Department of Mathematics, University of Kashmir, South Campus, Anantnag, Jammu and Kashmir, 192101, India

    Firdous A. Shah

  2. Department of Mathematics, University of Texas-Pan, American, Edinburg, TX, 78539, USA

    Lokenath Debnath

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  1. Firdous A. Shah
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  2. Lokenath Debnath
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Correspondence to Firdous A. Shah.

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Shah, F.A., Debnath, L. Minimum-Energy Wavelet Frames on Local Fields. Int. J. Appl. Comput. Math 3, 3455–3469 (2017). https://doi.org/10.1007/s40819-017-0310-z

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  • DOI: https://doi.org/10.1007/s40819-017-0310-z

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