RegularizedAutoregression

This is an accompanying repository for the article Regularized autoregressive modeling and its application to audio signal reconstruction, which is to be submitted to IEEE Transactions on Audio, Speech, and Language Processing.

Autoregressive (AR) modeling is invaluable in signal processing, in particular in speech and audio fields. Attempts in the literature can be found that regularize or constrain either the time-domain signal values or the AR coefficients, which is done for various reasons, including the incorporation of prior information or numerical stabilization. Although these attempts are appealing, an encompassing and generic modeling framework is still missing. We propose such a framework and the related optimization problem and algorithm. We discuss the computational demands of the algorithm and explore the effects of various improvements on its convergence speed. In the experimental part, we demonstrate the usefulness of our approach on the audio declipping and dequantization problems. We compare its performance against state-of-the-art methods and demonstrate the competitiveness of the proposed method in declipping musical signals, and its superiority in declipping speech. The evaluation includes a heuristic algorithm of generalized linear prediction (GLP), a strong competitor which has only been presented as a patent and is new in the scientific community.

The submitted manuscript is available at arXiv.

Accompanying webpage with examples for listening is available through GitHub pages.

Contents of the repository

The repository contains MATLAB implementation of all the methods and experiments described in the article.

It is organized as follows:

Subfolders

• dequantization toolbox – clone of the repository audio_dequantization
• docs – source files for the accompanying webpage
• results – numerical results of the experiments presented in the paper, as well as the scripts used to plot the results
• signals – music audio signals used in the experiments which do not use the full set from survey toolbox
• speech – speech signals used in the experiments
• survey toolbox – clone of selected parts of the repository declipping2020_codes, which is used for comparison of the proposed method with the state-of-the-art optimization-based audio declipping methods
• utils – all the functions implementing the proposed framework and functions used by the plotting scripts in results

Scripts

• acceleration_test.m tests different acceleration options for the DRA and ACS
• consistency_test.m analyzes the results in terms of performance and consistency; note that this code cannot be run without first running survey_test.m and generating all the declipped waveforms
• demo.m is a demonstrative script which runs a single instance of the declipping experiment using GLP and the proposed ACS approach
• demo_quant.m is a demonstrative script which runs a single instance of the dequantization experiment using the proposed ACS approach
• demo_speech.m is a demonstrative script which runs a single instance of the speech declipping experiment using the proposed ACS approach
• dequantization_test.m performs the dequantization experiment from the article Audio Dequantization Using (Co)Sparse (Non)Convex Methods using the proposed ACS approach
• iteration_tradeoff.m tests the proposed method for different combinations of the ACS (outer) and DRA (inner) iterations
• main_csl1_speech.m, main_Social_Sparsity_speech.m, main_spade_speech.m are minor modifications of the sripts from survey toolbox for the sake of the speech experiment
• oracle_test.m tests the inpainting / declipping using Janssen algorithm or GLP and compares the progression of AR coefficients to the coefficients of the ground truth signal
• speech_test.m performs the speech declipping experiment inspired by the article A Survey and an Extensive Evaluation of Popular Audio Declipping Methods using the proposed ACS approach and GLP
• speech_test_add_metrics.mcomputes the STOI, MOS and NSIM metrics for the declipped speech signals; note that this code cannot be run without first running speech_test.m, main_csl1_speech.m, main_Social_Sparsity_speech.m, and main_spade_speech.m to generate all the declipped waveforms
• survey_test.m performs the declipping experiment from the article A Survey and an Extensive Evaluation of Popular Audio Declipping Methods using the proposed ACS approach and GLP
• survey_test_add_CR.m performs the post-processing of the results from survey_test.m as described in the article Audio Declipping Performance Enhancement via Crossfading; note that this code cannot be run without first running survey_test.m to generate all the declipped waveforms

Dependencies

The codes were tested in MATLAB R2025a. They depend on the following toolboxes:

• Parallel Computing Toolbox,
• Signal Processing Toolbox,
• Statistics and Machine Learning Toolbox,
• The Large Time-Frequency Analysis Toolbox (LTFAT).

Acknowledgment

Special thank you goes to:

1. the authors of the declipping survey [1], the follow-up article [2] and the dequantization contribution [3] for sharing publically the code and numerical results, which allowed to build on their work,
2. the authors of [4] and the Audio Inpainting Toolbox for sharing the implementation of the basic Janssen algorithm,
3. İlker Bayram for sharing the codes for [5].

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[1] P. Záviška, P. Rajmic, A. Ozerov and L. Rencker, “A Survey and an Extensive Evaluation of Popular Audio Declipping Methods,” IEEE Journal of Selected Topics in Signal Processing, vol. 15, no. 1, pp. 5–24, 2021, doi: 10.1109/JSTSP.2020.3042071.

[2] P. Záviška, P. Rajmic and O. Mokrý, “Audio declipping performance enhancement via crossfading,” Signal Processing, vol. 192, 2022, doi: 10.1016/j.sigpro.2021.108365.

[3] P. Záviška, P. Rajmic and O. Mokrý, “Audio Dequantization Using (Co)Sparse (Non)Convex Methods,” 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Toronto, ON, Canada, 2021, pp. 701–705, doi: 10.1109/ICASSP39728.2021.9414637.

[4] A. Adler, V. Emiya, M. G. Jafari, M. Elad, R. Gribonval and M. D. Plumbley, “Audio Inpainting,” IEEE Transactions on Audio, Speech, and Language Processing, vol. 20, no. 3, pp. 922-932, 2012, doi: 10.1109/TASL.2011.2168211.

[5] İ. Bayram, “Proximal Mappings Involving Almost Structured Matrices,” IEEE Signal Processing Letters, vol. 22, no. 12, pp. 2264-2268, 2015, doi: 10.1109/LSP.2015.2476381.