Skip to main content
Top
Published in: International Journal of Data Science and Analytics 4/2023

07-09-2022 | Regular Paper

Performance measure for sparse recovery algorithms in compressed sensing perspective

Authors: V. Vivekanand, Deepak Mishra

Published in: International Journal of Data Science and Analytics | Issue 4/2023

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The sparse signal recovery is of great interest in compressed sensed data recovery. Many sparse recovery algorithms were developed in the last decade. However, selection of an appropriate recovery algorithm is an important matter of concern in many applications. The recovery algorithms are generally compared in terms of computational complexity, computational time, recovery probability and recovery precision. Typically, absolute Mean Squared Error (MSE) and relative MSE are used to compare the recovery precision of various sparse recovery algorithms. However, these two metric alone may not qualify to assess all algorithms. This paper presents an algorithm evaluation strategy by ranking the algorithms concerning an observable similarity between the original and reconstructed signal. We aim to propose a recovery similarity measure and an empirically defined factor to compare the performance measure of sparse recovery algorithms.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
2.
go back to reference Zhang, Z., Xu, Y., Yang,J., Li, X., Zhang, D.: A survey of sparse representation: algorithms and applications. IEEE Access (2015) Zhang, Z., Xu, Y., Yang,J., Li, X., Zhang, D.: A survey of sparse representation: algorithms and applications. IEEE Access (2015)
4.
go back to reference Yuan, X., Haimi-Cohen, R.: Image compression based on compressive sensing: end-to-end comparison with JPEG. IEEE Trans. Multimed. 22, 2889–2904 (2020)CrossRef Yuan, X., Haimi-Cohen, R.: Image compression based on compressive sensing: end-to-end comparison with JPEG. IEEE Trans. Multimed. 22, 2889–2904 (2020)CrossRef
5.
go back to reference Crespo Marques, E., Maciel, N., Naviner, L., Cai, H., Yang, J.: A review of sparse recovery algorithms. IEEE Access 7, 1300–1322 (2019)CrossRef Crespo Marques, E., Maciel, N., Naviner, L., Cai, H., Yang, J.: A review of sparse recovery algorithms. IEEE Access 7, 1300–1322 (2019)CrossRef
6.
go back to reference Steffen, P.: Algorithms for Robust and Fast Sparse Recovery, New approaches towards the noise folding problems and the big data challenge, Thesis, Technical University of Munich (2016) Steffen, P.: Algorithms for Robust and Fast Sparse Recovery, New approaches towards the noise folding problems and the big data challenge, Thesis, Technical University of Munich (2016)
7.
go back to reference Candes, E.: The restricted isometry property and its implications for compressed sensing. Compte. Rendus Math. C. R. Acad. Sci. Paris Ser. I 346, 589–592 (2008) Candes, E.: The restricted isometry property and its implications for compressed sensing. Compte. Rendus Math. C. R. Acad. Sci. Paris Ser. I 346, 589–592 (2008)
9.
go back to reference Blanchard, J.D., Cermak, M., Hanle, D., Jing, Y.: Greedy algorithms for joint sparse recovery. IEEE Trans. Signal Process. 62, 1694–1704 (2014)MathSciNetCrossRefMATH Blanchard, J.D., Cermak, M., Hanle, D., Jing, Y.: Greedy algorithms for joint sparse recovery. IEEE Trans. Signal Process. 62, 1694–1704 (2014)MathSciNetCrossRefMATH
10.
go back to reference Tropp, J.A., Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53, 4655–4666 (2007)MathSciNetCrossRefMATH Tropp, J.A., Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53, 4655–4666 (2007)MathSciNetCrossRefMATH
11.
go back to reference Tong, Z., Wang, F., Hu, C., et al.: Preconditioned generalized orthogonal matching pursuit. EURASIP J. Adv. Signal Process. 21, 1 (2020) Tong, Z., Wang, F., Hu, C., et al.: Preconditioned generalized orthogonal matching pursuit. EURASIP J. Adv. Signal Process. 21, 1 (2020)
12.
go back to reference Needell, D., Tropp, J.A.: CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmonic Anal. 26, 301–321 (2008)MathSciNetCrossRefMATH Needell, D., Tropp, J.A.: CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmonic Anal. 26, 301–321 (2008)MathSciNetCrossRefMATH
13.
go back to reference Zhang, Y.: User’s Guide for YALL1: Your ALgorithms for L1 Optimization (2009) Zhang, Y.: User’s Guide for YALL1: Your ALgorithms for L1 Optimization (2009)
14.
go back to reference Hai-Rong, Y., Hong, F., Zhang, C., Sui, W.: Iterative hard thresholding algorithm based on backtracking. Acta Automatica Sinica. 37, 276–282 (2011)MathSciNetCrossRef Hai-Rong, Y., Hong, F., Zhang, C., Sui, W.: Iterative hard thresholding algorithm based on backtracking. Acta Automatica Sinica. 37, 276–282 (2011)MathSciNetCrossRef
15.
go back to reference Beck, A., Teboulle, M.: A fast iterative shrinkage thresholding algorithm for linear inverse problems. SIAM J. Imag. Sci. 2, 183–202 (2009)MathSciNetCrossRefMATH Beck, A., Teboulle, M.: A fast iterative shrinkage thresholding algorithm for linear inverse problems. SIAM J. Imag. Sci. 2, 183–202 (2009)MathSciNetCrossRefMATH
17.
go back to reference Becker, Stephen, Bobin, Jérôme., Candès, Emmanuel J.: NESTA: a fast and accurate first-order method for sparse recovery. SIAM J. Imag. Sci. 4(1), 1–39 (2011)MathSciNetCrossRefMATH Becker, Stephen, Bobin, Jérôme., Candès, Emmanuel J.: NESTA: a fast and accurate first-order method for sparse recovery. SIAM J. Imag. Sci. 4(1), 1–39 (2011)MathSciNetCrossRefMATH
18.
go back to reference Vidya, L., Vivekanand, V., Shyam, Kumar U., Mishra, D.: RBF-network based sparse signal recovery algorithm for compressed sensing reconstruction. Elsevier Neural Netw. 63, 66–78 (2015) Vidya, L., Vivekanand, V., Shyam, Kumar U., Mishra, D.: RBF-network based sparse signal recovery algorithm for compressed sensing reconstruction. Elsevier Neural Netw. 63, 66–78 (2015)
19.
go back to reference Mohimani, G.H., Zadeh, M.B., Jutten, C.: A fast approach for overcomplete sparse decomposition based on smoothed L0 norm. IEEE Trans. Signal Process. 57, 289–301 (2009)MathSciNetCrossRefMATH Mohimani, G.H., Zadeh, M.B., Jutten, C.: A fast approach for overcomplete sparse decomposition based on smoothed L0 norm. IEEE Trans. Signal Process. 57, 289–301 (2009)MathSciNetCrossRefMATH
20.
go back to reference Vivekanand, V., Vidya, L.: Compressed sensing recovery based on polynomial approximated \(l_{0}\) minimization of signal and error: XEL0. In: Proc. IEEE SPCOM Conf. Bangalore, India (2014) Vivekanand, V., Vidya, L.: Compressed sensing recovery based on polynomial approximated \(l_{0}\) minimization of signal and error: XEL0. In: Proc. IEEE SPCOM Conf. Bangalore, India (2014)
21.
go back to reference Daubechies, I., DeVore, R., Fornasier, M., et al.: Iterative re-weighted least squares minimization for sparse recovery. Comm. Pure. Appl. Math. 63, 1–38 (2010)MathSciNetCrossRefMATH Daubechies, I., DeVore, R., Fornasier, M., et al.: Iterative re-weighted least squares minimization for sparse recovery. Comm. Pure. Appl. Math. 63, 1–38 (2010)MathSciNetCrossRefMATH
22.
23.
go back to reference Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. B. 58, 267–288 (1996)MathSciNetMATH Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. B. 58, 267–288 (1996)MathSciNetMATH
24.
go back to reference Asif, M.S., Romberg, J.: Fast and accurate algorithm for reweighted \(\ell _{1}\) norm minimization. IEEE Trans. Signal Process. 61, 5905–5916 (2012)CrossRefMATH Asif, M.S., Romberg, J.: Fast and accurate algorithm for reweighted \(\ell _{1}\) norm minimization. IEEE Trans. Signal Process. 61, 5905–5916 (2012)CrossRefMATH
25.
go back to reference Vila, Jeremy, Schniter, Philip: Expectation-Maximization Gaussian-Mixture Approximate Message Passing. IEEE Trans. Signal Processing 61, 4658–4672 (2013)MathSciNetCrossRefMATH Vila, Jeremy, Schniter, Philip: Expectation-Maximization Gaussian-Mixture Approximate Message Passing. IEEE Trans. Signal Processing 61, 4658–4672 (2013)MathSciNetCrossRefMATH
26.
go back to reference Joseph, Geethu, Murthy, Chandra: A non-iterative online Bayesian algorithm for the recovery of temporally correlated sparse vectors. IEEE Trans. Signal Process. 65, 5510–5525 (2017)MathSciNetCrossRefMATH Joseph, Geethu, Murthy, Chandra: A non-iterative online Bayesian algorithm for the recovery of temporally correlated sparse vectors. IEEE Trans. Signal Process. 65, 5510–5525 (2017)MathSciNetCrossRefMATH
27.
go back to reference Fan, J., Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Stat. Assoc. 96, 1348–1360 (2001) Fan, J., Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Stat. Assoc. 96, 1348–1360 (2001)
28.
go back to reference Mehranian, A., Saligheh Rad, H., Ay, M.R., Rahmim, A., Zaidi, H.: Smoothly clipped absolute deviation (SCAD) regularization for compressed sensing MRI using an augmented Lagrangian scheme. IEEE NSS/MIC CA, USA, pp. 3646-3653 (2012) Mehranian, A., Saligheh Rad, H., Ay, M.R., Rahmim, A., Zaidi, H.: Smoothly clipped absolute deviation (SCAD) regularization for compressed sensing MRI using an augmented Lagrangian scheme. IEEE NSS/MIC CA, USA, pp. 3646-3653 (2012)
29.
go back to reference Mohammadi, M.M., Koochakzadeh, A., Zadeh, M.B., Jansson, M., Rojas, C.R.: Successive concave sparsity approximation for compressed sensing. IEEE Trans. Signal Process. 64, 5657–5671 (2016)MathSciNetCrossRefMATH Mohammadi, M.M., Koochakzadeh, A., Zadeh, M.B., Jansson, M., Rojas, C.R.: Successive concave sparsity approximation for compressed sensing. IEEE Trans. Signal Process. 64, 5657–5671 (2016)MathSciNetCrossRefMATH
30.
go back to reference Ghayem, F., Sadeghi, M., Babaie-Zadeh, M., Chatterjee, S., Skoglund, M., Jutten, C.: Sparse signal recovery using iterative proximal projection. IEEE Trans. Signal Process. 66, 879–894 (2018)MathSciNetCrossRefMATH Ghayem, F., Sadeghi, M., Babaie-Zadeh, M., Chatterjee, S., Skoglund, M., Jutten, C.: Sparse signal recovery using iterative proximal projection. IEEE Trans. Signal Process. 66, 879–894 (2018)MathSciNetCrossRefMATH
31.
go back to reference Castro, E.A., Eldar, Y.C.: Noise Folding in Compressed Sensing. IEEE Sig. Process. Lett. 18, 478–481 (2011) Castro, E.A., Eldar, Y.C.: Noise Folding in Compressed Sensing. IEEE Sig. Process. Lett. 18, 478–481 (2011)
32.
go back to reference Herman, M.A., Strohmer, T.: General deviants: an analysis of perturbations in compressed sensing. IEEE J. Sel. Top. Signal Process. (2010) Herman, M.A., Strohmer, T.: General deviants: an analysis of perturbations in compressed sensing. IEEE J. Sel. Top. Signal Process. (2010)
Metadata
Title
Performance measure for sparse recovery algorithms in compressed sensing perspective
Authors
V. Vivekanand
Deepak Mishra
Publication date
07-09-2022
Publisher
Springer International Publishing
Published in
International Journal of Data Science and Analytics / Issue 4/2023
Print ISSN: 2364-415X
Electronic ISSN: 2364-4168
DOI
https://doi.org/10.1007/s41060-022-00357-6

Other articles of this Issue 4/2023

International Journal of Data Science and Analytics 4/2023 Go to the issue

Premium Partner