Start being greedy: sparse covariance learning algorithms in signal processing

Esa Ollila1
  • 1

    Department of Information and Communications Engineering, Aalto University, Finland
    [esa.ollila@aalto.fi]

Keywords: Sparsity – Robustness – Orthogonal matching pursuit – Elliptical distributions – Geodesic convexity – source localization – mMTC

Matching pursuit (MP) [Mallat and Zhang, 1993] and orthogonal matching pursuit (OMP) [Pati et al., 1993] are well-established greedy sparse signal processing algorithms, widely adopted across various domains. These techniques are extended to the multiple measurement vectors (MMV) model where a set of independent multiple measurement vectors are assumed to have the same sparsity basis. In this talk, we present the covariance learning (orthogonal) matching pursuit (CLMP and CLOMP) algorithms [Ollila, 2024, Marata et al., 2024] for a Gaussian MMV model where the main aim is to solve the unknown power of active sources and the additive noise variance. The proposed CL algorithms demonstrate superior performance compared to classical sparse reconstruction techniques, particularly in low SNR or coherent dictionary scenarios. Robust extensions of the algorithms are also introduced. Applications in source localization using sensor arrays and device activity detection in massive machine-type communications (mMTC) illustrate the effectiveness of the proposed approaches.

References

  • Mallat and Zhang [1993] Stéphane G Mallat and Zhifeng Zhang. Matching pursuits with time-frequency dictionaries. IEEE Transactions on signal processing, 41(12):3397–3415, 1993.
  • Marata et al. [2024] Leatile Marata, Esa Ollila, and Hirley Alves. Activity detection for massive random access using covariance-based matching pursuit. IEEE Transactions on Vehicular Technology (conditionally accepted), 2024. arXiv preprint arXiv:2405.02741.
  • Ollila [2024] Esa Ollila. Matching pursuit covariance learning. In 2024 32nd European Signal Processing Conference (EUSIPCO), pages 2447–2451. IEEE, 2024.
  • Pati et al. [1993] Yagyensh Chandra Pati, Ramin Rezaiifar, and Perinkulam Sambamurthy Krishnaprasad. Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition. In Proceedings of 27th Asilomar conference on signals, systems and computers, pages 40–44. IEEE, 1993.