Abstract
Clipping, or saturation, is a common nonlinear distortion in signal processing. Recently, declipping techniques have been proposed based on sparse decomposition of the clipped signals on a fixed dictionary, with additional constraints on the amplitude of the clipped samples. Here we propose a dictionary learning approach, where the dictionary is directly learned from the clipped measurements. We propose a soft-consistency metric that minimizes the distance to a convex feasibility set, and takes into account our knowledge about the clipping process. We then propose a gradient descent-based dictionary learning algorithm that minimizes the proposed metric, and is thus consistent with the clipping measurement. Experiments show that the proposed algorithm outperforms other dictionary learning algorithms applied to clipped signals. We also show that learning the dictionary directly from the clipped signals outperforms consistent sparse coding with a fixed dictionary.
L. Rencker—The research leading to these results has received funding from the European Union’s H2020 Framework Programme (H2020-MSCA-ITN-2014) under grant agreement no 642685 MacSeNet.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
The MATLAB code and some examples are available at http://www.cvssp.org/Personal/LucasRencker/software.html.
References
Janssen, A., Veldhuis, R.N., Vries, L.B.: Adaptive interpolation of discrete-time signals that can be modeled as autoregressive processes. IEEE Trans. Acoust. Speech Signal Process. 34(2), 317–330 (1986)
Abel, J.S., Smith, J.O.: Restoring a clipped signal. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Toronto, Canada, pp. 1745–1748 (1991)
Godsill, S.J., Wolfe, P.J., Fong, W.N.: Statistical model-based approaches to audio restoration and analysis. J. New Music Res. 30(4), 323–338 (2001)
Adler, A., Emiya, V., Jafari, M., Elad, M., Gribonval, R., Plumbley, M.D.: Audio inpainting. IEEE Trans. Audio Speech Lang. Process. 20(3), 922–932 (2012)
Adler, A., Emiya, V., Jafari, M.G., Elad, M., Gribonval, R., Plumbley, M.D.: A constrained matching pursuit approach to audio declipping. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 329–332 (2011)
Kitić, S., Bertin, N., Gribonval, R.: Sparsity and cosparsity for audio declipping: a flexible non-convex approach. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds.) LVA/ICA 2015. LNCS, vol. 9237, pp. 243–250. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-22482-4_28
Mansour, H., Saab, R., Nasiopoulos, P., Ward, R.: Color image desaturation using sparse reconstruction. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 778–781 (2010)
Defraene, B., Mansour, N., Hertogh, S.D., van Waterschoot, T., Diehl, M., Moonen, M.: Declipping of audio signals using perceptual compressed sensing. IEEE Trans. Audio Speech Lang. Process. 21(12), 2627–2637 (2013)
Foucart, S., Needham, T.: Sparse recovery from saturated measurements. Inf. Inference J. IMA 6(2), 196–212 (2016)
Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)
Grant, M., Boyd, S., Ye, Y.: CVX: Matlab software for disciplined convex programming (2008)
Kitić, S., Jacques, L., Madhu, N., Hopwood, M.P., Spriet, A., Vleeschouwer, C.D.: Consistent iterative hard thresholding for signal declipping. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 5939–5943, May 2013
Siedenburg, K., Kowalski, M., Dörfler, M.: Audio declipping with social sparsity. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Florence, Italy, pp. 1577–1578, May 2014
Ozerov, A., Bilen, Ç., Pérez, P.: Multichannel audio declipping. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 659–663 (2016)
Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15(12), 3736–3745 (2006)
Mairal, J., Elad, M., Sapiro, G.: Sparse representation for color image restoration. IEEE Trans. Image Process. 17(1), 53–69 (2008)
Engan, K., Aase, S.O., Husoy, J.H.: Method of optimal directions for frame design. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 5, pp. 2443–2446 (1999)
Blumensath, T., Davies, M.E.: Iterative hard thresholding for compressed sensing. Appl. Comput. Harmon. Anal. 27(3), 265–274 (2009)
Mairal, J., Bach, F., Ponce, J.: Sparse modeling for image and vision processing. Found. Trends Comput. Graph. Vis. 8(2–3), 85–283 (2014)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)
Bonnans, J.F., Shapiro, A.: Optimization problems with perturbations: a guided tour. SIAM Rev. 40(2), 228–264 (1998)
Danskin, J.M.: The Theory of Max-Min and its Application to Weapons Allocation Problems. Ökonometrie und Unternehmensforschung. Springer, Heidelberg (1967). https://doi.org/10.1007/978-3-642-46092-0
Holmes, R.B.: Smoothness of certain metric projections on Hilbert space. Trans. Am. Math. Soc. 184, 87–100 (1973)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Rencker, L., Bach, F., Wang, W., Plumbley, M.D. (2018). Consistent Dictionary Learning for Signal Declipping. In: Deville, Y., Gannot, S., Mason, R., Plumbley, M., Ward, D. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2018. Lecture Notes in Computer Science(), vol 10891. Springer, Cham. https://doi.org/10.1007/978-3-319-93764-9_41
Download citation
DOI: https://doi.org/10.1007/978-3-319-93764-9_41
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93763-2
Online ISBN: 978-3-319-93764-9
eBook Packages: Computer ScienceComputer Science (R0)