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Signal Reconstruction from Blind Compressive Measurements Using Procrustes Method

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Abstract

The reconstruction of signals from their blind compressed measurements is a highly ill-posed problem because the representing basis is unknown. This paper proposes an alternating optimization method to estimate the signal from a given set of blind compressive measurement vectors. The representing coefficients, representing basis (sparsifying basis), and the updated estimate of the signals are identified iteratively. The representing basis is identified using the orthogonal Procrustes method. The signal estimate is updated using \(\ell _1\)-trend filtering. The high computational intensity of the proposed method compared to other existing methods limits its application to non-real-time signal estimation. The proposed method reconstructs the signal uniquely up to a lower error bound.

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Data Availability

The codes and the synthetic data generated for the current study are available from the corresponding author on request. A working example of the code for speech signal is given in the GITHUB repository. The link to the repository is https://github.com/veenanarayanan28/BCS-using-Orthogonal-Procrustes-method.

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Author notes

  1. Veena Narayanan and G. Abhilash have contributed equally to this work.

Authors and Affiliations

  1. Department of Electronics and Communication Engineering, National Institute of Technology Calicut, Kozhikode, Kerala, 673601, India

    Veena Narayanan & G. Abhilash

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  1. Veena Narayanan
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  2. G. Abhilash
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Correspondence to Veena Narayanan.

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Narayanan, V., Abhilash, G. Signal Reconstruction from Blind Compressive Measurements Using Procrustes Method. Circuits Syst Signal Process 42, 2941–2958 (2023). https://doi.org/10.1007/s00034-022-02246-6

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  • DOI: https://doi.org/10.1007/s00034-022-02246-6

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