Speech Compressive Sampling Using Approximate Message Passing and a Markov Chain Prior.

Area of Science:

• Signal Processing
• Information Theory
• Speech Technology

Background:

• Compressive sampling (CS) enables efficient signal recovery with fewer samples than traditional methods.
• Speech signals pose challenges for CS due to their lack of sparsity in standard bases.
• Existing CS methods struggle with effective speech signal reconstruction.

Purpose of the Study:

• To develop an advanced method for reconstructing speech signals from compressive samples.
• To address the sparsity limitations of speech signals in compressive sampling.
• To enhance the quality and accuracy of speech signal recovery using CS.

Main Methods:

• A novel approach combining Approximate Message Passing (AMP) with Markov chains is proposed.
• The method exploits interdependencies among Modified Discrete Cosine Transform (MDCT) coefficients of speech signals.
• A turbo framework iteratively applies AMP and belief propagation, incorporating a constraint to ensure stability.

Main Results:

• The new method significantly improves signal-to-noise ratio (SNR) compared to traditional CS techniques.
• Higher Perceptual Evaluation of Speech Quality (PESQ) scores were achieved, indicating enhanced speech quality.
• The reconstructed speech spectrogram shows better energy distribution similarity to the original signal.
• Comparable speech enhancement performance to state-of-the-art methods was demonstrated.

Conclusions:

• The proposed AMP and Markov chain-based turbo framework effectively reconstructs speech signals from CS samples.
• This method overcomes sparsity limitations, offering superior performance in SNR and PESQ.
• The technique provides a robust and efficient solution for speech signal recovery in CS applications.