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Root-Free Annihilating Filter Method for Sparse Signal Reconstruction

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Abstract

Traditionally, annihilating filter approach (a.k.a Prony’s approach), universal finite rate of innovation (FRI), and compressed sensing algorithms have been presented to solve the sparse reconstruction problem when the measurement matrix has Fourier bases. However, annihilating filter approach requires computing the polynomial roots of the annihilating filter, and this fact yields an unstable recovery of sparse signal in the high noise environment. In this paper, we present a polynomial root-free annihilating filter approach for reconstructing sparse signals based on the padding of missing measurement values to acquired measurements. The method accomplishes complete reconstruction accuracy of sparse signals in the noiseless environment. Moreover, the superior reconstruction accuracy of the proposed root-free annihilating filter approach, in comparison with the traditional annihilating filter approach and universal FRI, is proved by experimental simulations in the existence of a low signal-to-noise ratio.

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Authors and Affiliations

  1. Department of ECE, Sri Venkateswara College of Engineering (SVCE), Tirupati, 517507, India

    P. Sudhakar Reddy

  2. Department of ECE, National Institute of Technology Karnataka, Surathkal, 575025, India

    B. S. Raghavendra & A. V. Narasimhadhan

Authors
  1. P. Sudhakar Reddy
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  2. B. S. Raghavendra
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  3. A. V. Narasimhadhan
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Correspondence to P. Sudhakar Reddy.

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Sudhakar Reddy, P., Raghavendra, B.S. & Narasimhadhan, A.V. Root-Free Annihilating Filter Method for Sparse Signal Reconstruction. Circuits Syst Signal Process 44, 670–683 (2025). https://doi.org/10.1007/s00034-024-02871-3

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