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On Homotopy Continuation for Speech Restoration.

Darian M Onchis1, Pedro Real2

  • 1Faculty of Mathematics, University of Vienna, Vienna, Austria.

Computational Topology in Image Context : 6Th International Workshop, CTIC 2016, Marseille, France, June 15-17, 2016, Proceedings. CTIC (Conference) (6Th : 2016 : Marseille, France)
|May 27, 2017
PubMed
Summary
This summary is machine-generated.

This study recovers corrupted speech using a homotopy-based method and compressed sensing. The technique effectively reconstructs audio signals even with missing data in noisy conditions.

Keywords:
Basis pursuitGabor framesHomotopy continuationNumerical algorithmSpeech restorationℓ1 regularization

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Area of Science:

  • Signal Processing
  • Audio Engineering
  • Applied Mathematics

Background:

  • Speech recordings are susceptible to data loss and corruption due to noisy environments and acquisition device limitations.
  • Compressed sensing offers a framework for signal recovery from undersampled data, but requires robust algorithms for practical applications.
  • Gabor frames are utilized in signal processing for their time-frequency localization properties, relevant in audio analysis.

Purpose of the Study:

  • To develop and evaluate a novel method for reconstructing speech signals from incomplete or corrupted samples.
  • To apply a homotopy-based approach within a compressed sensing framework for enhanced audio recovery.
  • To assess the efficacy of the proposed method across diverse speech recordings under simulated noisy conditions.

Main Methods:

  • A homotopy continuation algorithm is integrated with the basis pursuit denoising method.
  • The acquisition model is based on compressed sensing using Gabor frames.
  • The method is tested on various real-world speech recordings with simulated data corruption and noise.

Main Results:

  • The homotopy-based method successfully recovered approximations of the original speech recordings.
  • The basis pursuit denoising approach, combined with homotopy, demonstrated effectiveness in handling missing and corrupted samples.
  • The proposed technique showed robustness in reconstructing speech signals from noisy environments.

Conclusions:

  • The homotopy-based method provides a viable solution for speech recovery in challenging acoustic environments.
  • This approach offers a significant advancement in signal processing for audio restoration from corrupted data.
  • The study validates the use of compressed sensing with Gabor frames and homotopy continuation for practical speech signal reconstruction.