On Homotopy Continuation for Speech Restoration

详细信息    查看全文

• 关键词：Homotopy continuation ; Speech restoration ; Basis pursuit ; \(\ell ^1\) ; regularization ; Gabor frames ; Numerical algorithm
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9667
• 期：1
• 页码：152-156
• 全文大小：445 KB
• 参考文献：1.Abel, J.S., Smith III., J.O.: Restoring a clipped signal. In: Proceedings of the International Conference on Acoustics, Speech, and Signal Processing. IEEE, pp. 1745–1748 (1991)
  2.Godsill, S.J., Rayner, P.J.: A Bayesian approach to the restoration of degraded audio signals. IEEE Trans. Speech Audio Process. 3(4), 267–278 (1995)CrossRef
  3.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)CrossRef
  4.Emmanuel Candes. http://​statweb.​stanford.​edu/​~candes/​l1magic/​
  5.Numerical Tours of Signal Processing. http://​www.​numerical-tours.​com/​matlab/​optim8homotopy/​
  6.Malioutov, D.M., Cetin, M., Willsky, A.S.: Homotopy continuation for sparse signal representation. In: IEEE International Conference on Acoustics, Speech and Signal Processing, Philadelphia, PA, vol. 5, pp. 733–736, March 2005
  7.Candes, E.J., Tao, T.: Decoding by linear programming. IEEE Trans. Inf. Theor. 51(12), 4203–4215 (2005)MathSciNet CrossRef MATH
  8.Herman, M.A., Strohmer, T.: High-resolution radar via compressed sensing. IEEE Trans. Signal Process. 57(6), 2275–2284 (2009)MathSciNet CrossRef
  9.Strohmer, T., Heath, R.: Grassmanian frames with applications to coding and communication. Appl. Comput. Harmon. Anal. 14(3), 257–275 (2003)MathSciNet CrossRef MATH
  10.Gill, P.R., Wang, A., Molnar, A.: The in-crowd algorithm for fast basis pursuit denoising. IEEE Trans. Signal Process. 59(10), 4595–4605 (2011)MathSciNet CrossRef
  11.Ricaud, B., Stempfel, G., Torresani, B., Wiesmeyr, C., Lachambre, H., Onchis, D.: An optimally concentrated Gabor transform for localized time-frequency components. Adv. Comput. Math. 40(3), 683–702 (2014)MathSciNet CrossRef MATH
  
• 作者单位：Darian M. Onchis (15)
  Pedro Real (16)
  
  15. Faculty of Mathematics, University of Vienna, Vienna, Austria
  16. Department of Applied Mathematics I, University of Seville, Seville, Spain
  
• 丛书名：Computational Topology in Image Context
• ISBN：978-3-319-39441-1
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：9667

文摘

In this paper, a homotopy-based method is employed for the recovery of speech recordings from missing or corrupted samples taken in a noisy environment. The model for the acquisition device is a compressed sensing scenario using Gabor frames. To recover an approximation of the speech file, we used the basis pursuit denoising method with the homotopy continuation algorithm. We tested the proposed method with various speech recordings.