[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

An Automatic Threshold OMP Algorithm Based on QR Decomposition for Magnetic Resonance Image Reconstruction

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In magnetic resonance (MR) image reconstruction, the orthogonal matching pursuit (OMP) is widely recognized for its simplicity and competitive performance. However, OMP designs a termination condition based on some prior information such as sparsity and noise intensity. In practice, the unknown prior information of MR images cannot guarantee accurate reconstruction. To make OMP suitable for magnetic resonance imaging (MRI), we propose an automatic threshold OMP algorithm based on QR decomposition (ATOMP-QR). The termination condition of ATOMP-QR, which utilizes the mutual incoherence property of the sensing matrix, is related to whether the residual vector includes the orthogonal projection component of measurements. Then, to avoid the computation of pseudo-inverse and accelerate reconstruction speed, we perform QR decomposition on the measurement matrix. We conduct the MRI experiments to evaluate the superiority and effectiveness of ATOMP-QR in peak signal-to-noise ratio (PSNR), structure similarity index measure (SSIM), and running time. Specifically, for the T1-w image with a sparsity of 10, the PSNR was improved from 24 to 32 dB; the SSIM was increased from 0.87 to 0.99. The maximum time consumed decreased from 0.2276 to 0.0107 s.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Algorithm 1
Fig. 3
Algorithm 2
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data Availability

Data sharing was not applicable to this article as no datasets were generated. This article describes entirely theoretical research during the current study.

References

  1. S. Babu, S.G. Lingala, N. Vaswani, Fast low rank column-wise compressive sensing for accelerated dynamic MRI. IEEE Trans. Comput. Imaging 9, 409–424 (2023)

    Article  Google Scholar 

  2. T.T. Cai, L. Wang, Orthogonal matching pursuit for sparse signal recovery with noise. IEEE Trans. Inf. Theory 57(7), 4680–4688 (2011)

    Article  MathSciNet  Google Scholar 

  3. A. Carmi, P. Gurfil, D. Kanevsky, Methods for sparse signal recovery using Kalman filtering with embedded pseudo-measurement norms and quasi-Norms. IEEE Trans. Signal Process. 58(4), 2405–2409 (2010)

    Article  MathSciNet  Google Scholar 

  4. S. Chen, Z. Cheng, C. Liu, F. Xi, A blind stopping condition for orthogonal matching pursuit with applications to compressive sensing radar. Signal Process. 165, 331–342 (2019)

    Article  Google Scholar 

  5. E. Crespo Marques, N. Maciel, L. Naviner, H. Cai, J. Yang, A review of sparse recovery algorithms. IEEE Access 7, 1300–1322 (2019)

  6. J. Duan, Y. Liu, J. Wang, Accelerated SPIRiT parallel MR image reconstruction based on joint sparsity and sparsifying transform learning. IEEE Trans. Comput. Imaging 9, 276–288 (2023)

    Article  MathSciNet  Google Scholar 

  7. C. Ebersole, R. Ahmad, A.V. Rich, L.C. Potter, H. Dong, A. Kolipaka, A Bayesian method for accelerated magnetic resonance elastography of the liver. Magn. Reson. Med. 80(3), 1178–1188 (2018)

    Article  Google Scholar 

  8. A. Fischer et al., SElf-gated Non-Contrast-Enhanced FUnctional Lung imaging (SENCEFUL) using a quasi-random fast low-angle shot (FLASH) sequence and proton MRI. NMR Biomed. 27(8), 907–917 (2014)

    Article  Google Scholar 

  9. J. Hennig, A. Nauerth, H. Friedburg, RARE imaging: A fast imaging method for clinical MR. Magn. Reson. Med. 3(6), 823–833 (1986)

    Article  Google Scholar 

  10. O.N. Jaspan, R. Fleysher, M.L. Lipton, Compressed sensing MRI: a review of the clinical literature. Brit. J. Radiol. 88(1056), 20150487 (2015)

    Article  Google Scholar 

  11. Y.-C. Kim, J.-F. Nielsen, K.S. Nayak, Automatic correction of echo-planar imaging (EPI) ghosting artifacts in real-time interactive cardiac MRI using sensitivity encoding. J. Magn. Reson. Imaging 27(1), 239–245 (2008)

    Article  Google Scholar 

  12. H. Kiragu, G. Kamucha, E. Mwangi, A fast procedure for acquisition and reconstruction of magnetic resonance images using compressive sampling, AFRICON 2015, Addis Ababa, Ethiopia, pp. 1–5 (2015)

  13. Z. Li, X. Zheng, G. Chen, et al. A matching pursuit algorithm for sparse signal reconstruction based on Jaccard coefficient and backtracking. Circuits Syst. Signal Process. 1–18 (2023)

  14. S. Liu, F.-Y. Wu, Self-training dictionary based approximated \({\ell _0}\) norm constraint reconstruction for compressed ECG. Biomed. Signal Process. Control 68, 102768–102768 (2021)

    Article  Google Scholar 

  15. L. Lu, W. Xu, Y. Wang, Z. Tian, Blind orthogonal least squares based compressive spectrum sensing. IEEE Trans. Veh. Technol. (2023)

  16. M. Lustig, D. Donoho, J.M. Pauly, Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58(6), 1182–1195 (2007)

    Article  Google Scholar 

  17. M. Lustig, D.L. Donoho, J.M. Santos, J.M. Pauly, Compressed sensing MRI. IEEE Signal Process. Mag. 25(2), 72–82 (2008)

    Article  Google Scholar 

  18. M. V. R. Manimala, C. D. Naidu, M. N. Giriprasad, Sparse recovery algorithms based on dictionary learning for MR image reconstruction, in 2016 International Conference on Wireless Communications, Signal Processing and Networking (WiSPNET), Chennai, India, pp. 1354–1360 (2016)

  19. Q. Mu, J. Xie, Z. Wen, Y. Weng, S. Zhang, A quantitative MR study of the hippocampal formation, the amygdala, and the temporal horn of the lateral ventricle in healthy subjects 40 to 90 years of age. AJNR Am. J. Neuroradiol. 20(2), 207–211 (1999)

    Google Scholar 

  20. Y.-Y. Ni, F.-Y. Wu, H.-Z. Yang, K. Yang, The A* orthogonal least square algorithm with the self-training dictionary for propeller signals reconstruction. Appl. Acoust. 215, 109709 (2023)

    Article  Google Scholar 

  21. S. B. Öztürk, A. B. Öztürk, G. Soker G, M. Parlak, Evaluation of brain volume changes by magnetic resonance imaging in obstructive sleep apnea syndrome. Niger. J. Clin. Pract. 21(2), 236–241 (2018)

  22. D.B. Plewes, W. Kucharczyk, Physics of MRI: a primer. J. Magn. Reson. Imaging 35(5), 1038–1054 (2012)

    Article  Google Scholar 

  23. M.A. Richards, Fundamentals of Radar Signal Processing (Mcgraw-Hill Education, Cop, New York, 2014)

    Google Scholar 

  24. S. Saladi, N. Amutha Prabha, Analysis of denoising filters on MRI brain images. Int. J. Imaging Syst. Technol. 27(3), 201–208 (2017)

  25. A. Shah, S. Jhawar, A. Goel, A. Goel, Corpus callosum and its connections: a fiber dissection study. World Neurosurg. 151, e1024–e1035 (2021)

    Article  Google Scholar 

  26. Y.-C. Song, F.-Y. Wu, Y.-Y. Ni, K. Yang, A fast threshold OMP based on self-learning dictionary for propeller signal reconstruction. Ocean Eng. 287, 115792 (2023)

    Article  Google Scholar 

  27. Y.-C. Song, F.-Y. Wu, R. Peng, A neighborhood-based multiple orthogonal least square method for sparse signal recovery. Signal Process. 209, 109044 (2023)

    Article  Google Scholar 

  28. S.R. Sreeja, S. Rajmohan, M.S. Sodhi, et al., Dictionary learning and greedy algorithms for removing eye blink artifacts from EEG signals. Circuits Syst. Signal Process. 1–21 (2023)

  29. Q. Sun, F.-Y. Wu, K. Yang, Estimation of multipath delay-Doppler parameters from moving LFM signals in shallow water. Ocean Eng. 232, 109125 (2021)

    Article  Google Scholar 

  30. Q. Sun, F.-Y. Wu, K. Yang, C. Huang, Sparse signal recovery from noisy measurements via searching forward OMP. Electron. Lett. 58(3), 124–126 (2021)

    Article  Google Scholar 

  31. M. Usman, C. Prieto, F. Odille, D. Atkinson, T. Schaeffter, P.G. Batchelor, A computationally efficient OMP-based compressed sensing reconstruction for dynamic MRI. Phys. Med. Biol. 56(7), N99–N114 (2011)

    Article  Google Scholar 

  32. P.P. Vaidyanathan, Generalizations of the sampling theorem: seven decades after Nyquist. IEEE Trans. Circuit Syst. I 48(9), 1094–1109 (2001)

    Article  MathSciNet  Google Scholar 

  33. A. Wahid, J.A. Shah, A.U. Khan, M. Ahmed, H. Razali, Multi-Layer basis pursuit for compressed sensing MR image reconstruction. IEEE Access 8, 186222–186232 (2020)

    Article  Google Scholar 

  34. J. Wang, Support recovery with orthogonal matching pursuit in the presence of noise. IEEE Trans. Signal Process. 63(21), 5868–5877 (2015)

    Article  MathSciNet  Google Scholar 

  35. J. Wang, P. Li, Recovery of sparse signals using multiple orthogonal least squares. IEEE Trans. Signal Process. 65(8), 2049–2062 (2017)

    Article  MathSciNet  Google Scholar 

  36. J. Wen, Z. Zhou, J. Wang, X. Tang, Q. Mo, A sharp condition for exact support recovery with orthogonal matching pursuit. IEEE Trans. Signal Process. 65(6), 1370–1382 (2017)

    Article  MathSciNet  Google Scholar 

  37. R. Wu, W. Huang, D.-R. Chen, The exact support recovery of sparse signals with noise via orthogonal matching pursuit. IEEE Signal Process. Lett. 20(4), 403–406 (2013)

    Article  Google Scholar 

  38. F.-Y. Wu, F. Tong, Mean-square analysis of the gradient projection sparse recovery algorithm based on non-uniform norm. Neurocomputing 223(5), 103–106 (2017)

    Article  Google Scholar 

  39. F.-Y. Wu, F. Tong, Z. Yang, EMGdi signal enhancement based on ICA decomposition and wavelet transform. Appl. Soft Comput. 43, 561–571 (2016)

    Article  Google Scholar 

  40. F.-Y. Wu, K. Yang, X. Sheng, Optimized compression and recovery of electrocardiographic signal for IoT platform. Appl. Soft Comput. 96, 106659–106659 (2020)

    Article  Google Scholar 

  41. F.-Y. Wu, K. Yang, X. Sheng, F.-Y. Huang, A blocked MCC estimator for group sparse system identification. AEU-Int. J. Electron. Commun. 115, 153033–153033 (2020)

    Article  Google Scholar 

  42. F.-Y. Wu, K. Yang, Z. Yang, Compressed acquisition and denoising recovery of EMGdi signal in WSNs and IoT. IEEE Trans. Ind. Inf. 14(5), 2210–2219 (2018)

    Article  Google Scholar 

  43. Y. Xie, Q. Yang, G. Xie, J. Pang, Z. Fan, D. Li, Improved black-blood imaging using DANTE-SPACE for simultaneous carotid and intracranial vessel wall evaluation. Magn. Reson. Med. 75(6), 2286–2294 (2016)

    Article  Google Scholar 

  44. M. Yang, F. de Hoog, Orthogonal matching pursuit with thresholding and its application in compressive sensing. IEEE Trans. Signal Process. 63(20), 5479–5486 (2015)

    Article  MathSciNet  Google Scholar 

  45. T. Zhang, Sparse recovery with orthogonal matching pursuit under RIP. IEEE Trans. Inf. Theory 57(9), 6215–6221 (2011)

    Article  MathSciNet  Google Scholar 

  46. H. Zhang, X. Ren, Y. Liu, Q. Zhou, The application of compressed sensing reconstruction algorithms for MRI of glioblastoma, in 2017 10th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI), Shanghai, China, pp. 1–6 (2017)

  47. H. Zhu, W. Chen, Y. Wu, Efficient implementations for orthogonal matching pursuit. Electronics 9(9), 1507 (2020)

    Article  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China (Project No. 62171369).

Author information

Authors and Affiliations

  1. School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, Shaanxi, China

    Yi-Yang Ni & Hui-Zhong Yang

  2. Navigation Institute, Jimei University, Xiamen, Fujian, China

    Fei-Yun Wu

Authors
  1. Yi-Yang Ni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fei-Yun Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hui-Zhong Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fei-Yun Wu.

Ethics declarations

Conflict of interest

The authors declare no competing financial interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ni, YY., Wu, FY. & Yang, HZ. An Automatic Threshold OMP Algorithm Based on QR Decomposition for Magnetic Resonance Image Reconstruction. Circuits Syst Signal Process 43, 3697–3717 (2024). https://doi.org/10.1007/s00034-024-02624-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-024-02624-2

Keywords

Search

Navigation