Skip to main content
Springer Nature Link
Log in

Multiresolution vessel detection in magnetic particle imaging using wavelets and a Gaussian mixture model

  • Original Article
  • Published:
International Journal of Computer Assisted Radiology and Surgery Aims and scope Submit manuscript

Abstract

Purpose

Magnetic particle imaging is a tomographic imaging technique that allows one to measure the spatial distribution of superparamagnetic nanoparticles, which are used as tracer. The magnetic particle imaging scanner measures the voltage induced due to the nonlinear magnetization behavior of the nanoparticles. The tracer distribution can be reconstructed from the voltage signal by solving an inverse problem. A possible application is the imaging of vessel structures. In this and many other cases, the tracer is only located inside the structures and a large part of the image is related to background. A detection of the tracer support in early stages of the reconstruction process could improve reconstruction results.

Methods

In this work, a multiresolution wavelet-based reconstruction combined with a segmentation of the foreground structures is performed. For this, different wavelets are compared with respect to their reconstruction quality. For the detection of the foreground, a segmentation with a Gaussian mixture model is performed, which leads to a threshold-based binary segmentation. This segmentation is done on a coarse level of the reconstruction and then transferred to the next finer level, where it is used as prior knowledge for the reconstruction. This is repeated until the finest resolution is reached.

Results

The approach is evaluated on simulated vessel phantoms and on two real measurements. The results show that this method improves the structural similarity index of the reconstructed images significantly. Among the compared wavelets, the 9/7 wavelets led to the best reconstruction results.

Conclusions

The early detection of the vessel structures at low resolution helps to improve the image quality. For the wavelet decomposition, the use of 9/7 wavelets is recommended.

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
$34.99 /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 excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Bathke C, Kluth T, Brandt C, Maass P (2017) Improved image reconstruction in magnetic particle imaging using structural a priori information. Int J Magn Part Imaging. https://doi.org/10.18416/ijmpi.2017.1703015

  2. Beck A, Teboulle M (2009) A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imaging Sci 2(1):183–202. https://doi.org/10.1137/080716542

    Article  Google Scholar 

  3. Caballero J, Bai W, Price AN, Rueckert D, Hajnal JV (2014) Application-driven MRI: joint reconstruction and segmentation from undersampled MRI data. In: International conference on medical image computing and computer-assisted intervention. Springer, pp 106–113

  4. Droigk C, Maass M, Englisch C, Mertins A (2019) Joint multiresolution and background detection reconstruction for magnetic particle imaging. In: Handels H, Deserno TM, Meinzer HP, Tolxdorff T (eds) Bildverarbeitung für die Medizin 2019, Informatik aktuell. Springer, Berlin, pp 165–170

    Chapter  Google Scholar 

  5. Droigk C, Maass M, Koch P, Möller A, Mertins A (2019) Multiresolution magnetic particle imaging of vessel structures with support detection. In: Proceedings of international workshop on magnetic particle imaging, pp 113–114

  6. Gleich B, Weizenecker J (2005) Tomographic imaging using the nonlinear response of magnetic particles. Nature 435(7046):1214–1217. https://doi.org/10.1038/nature03808

    Article  CAS  PubMed  Google Scholar 

  7. Knopp T, Buzug TM (2012) Magnetic particle imaging: an introduction to imaging principles and scanner instrumentation. Springer, Berlin. https://doi.org/10.1007/978-3-642-04199-0

    Book  Google Scholar 

  8. Knopp T, Viereck T, Bringout G, Ahlborg M, von Gladiss A, Kaethner C, Neumann A, Vogel P, Rahmer J, Möddel M (2016) MDF: magnetic particle imaging data format. arXiv preprint arXiv:1602.06072

  9. Knopp T, Weber A (2015) Local system matrix compression for efficient reconstruction in magnetic particle imaging. Adv Math Phys 2015:1–7 (Article ID 472818). https://doi.org/10.1155/2015/472818

    Article  Google Scholar 

  10. Lampe J, Bassoy C, Rahmer J, Weizenecker J, Voss H, Gleich B, Borgert J (2012) Fast reconstruction in magnetic particle imaging. Phys Med Biol 57(4):1113–1134. https://doi.org/10.1088/0031-9155/57/4/1113

    Article  CAS  PubMed  Google Scholar 

  11. Layer T, Blaickner M, Knäusl B, Georg D, Neuwirth J, Baum RP, Schuchardt C, Wiessalla S, Matz G (2015) PET image segmentation using a Gaussian mixture model and Markov random fields. EJNMMI Phys. https://doi.org/10.1186/s40658-015-0110-7

    Article  PubMed  PubMed Central  Google Scholar 

  12. Maass M, Bente K, Ahlborg M, Medimagh H, Phan H, Buzug TM, Mertins A (2016) Optimized compression of MPI system matrices using a symmetry-preserving secondary orthogonal transform. Int J Magn Part Imaging. https://doi.org/10.18416/ijmpi.2016.1607002

  13. Maass M, Mink C, Mertins A (2018) Joint multiresolution magnetic particle imaging and system matrix compression. Int J Magn Part Imaging. https://doi.org/10.18416/ijmpi.2018.1811002

  14. Rahmer J, Weizenecker J, Gleich B, Borgert J (2009) Signal encoding in magnetic particle imaging: properties of the system function. BMC Med Imaging 9(4):4. https://doi.org/10.1186/1471-2342-9-4

    Article  PubMed  PubMed Central  Google Scholar 

  15. Siebert H, Maass M, Ahlborg M, Buzug TM, Mertins A (2016) MMSE MPI reconstruction using background identification. In: Proceedings of the international workshop on magnetic particle imaging, p 58

  16. Storath M, Brandt C, Hofmann M, Knopp T, Salamon J, Weber A, Weinmann A (2016) Edge preserving and noise reducing reconstruction for magnetic particle imaging. IEEE Trans Med Imaging 36(1):74–85

    Article  Google Scholar 

  17. Storath M, Weinmann A, Frikel J, Unser M (2015) Joint image reconstruction and segmentation using the Potts model. Inverse Probl 31(2):025003

    Article  Google Scholar 

  18. Unser M, Blu T (2003) Mathematical properties of the jpeg2000 wavelet filters. IEEE Trans Image Process 12(9):1080–1090. https://doi.org/10.1109/TIP.2003.812329

    Article  PubMed  Google Scholar 

  19. Villasenor JD, Belzer B, Liao J (1995) Wavelet filter evaluation for image compression. IEEE Trans Image Process 4(8):1053–1060. https://doi.org/10.1109/83.403412

    Article  CAS  PubMed  Google Scholar 

  20. Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612. https://doi.org/10.1109/TIP.2003.819861

    Article  PubMed  Google Scholar 

  21. Weber A, Knopp T (2015) Symmetries of the 2d magnetic particle imaging system matrix. Phys Med Biol 60(10):4033–4044

    Article  CAS  Google Scholar 

  22. Weizenecker J, Borgert J, Gleich B (2007) A simulation study on the resolution and sensitivity of magnetic particle imaging. Phys Med Biol 52(21):6363

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This work was supported by the German Research Foundation under Grant Number ME 1170/7-1.

Author information

Authors and Affiliations

  1. Institute for Signal Processing, Universität zu Lübeck, Lübeck, Germany

    Christine Droigk, Marco Maass & Alfred Mertins

Authors
  1. Christine Droigk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marco Maass
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alfred Mertins
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christine Droigk.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

This article does not contain patient data.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Droigk, C., Maass, M. & Mertins, A. Multiresolution vessel detection in magnetic particle imaging using wavelets and a Gaussian mixture model. Int J CARS 14, 1913–1921 (2019). https://doi.org/10.1007/s11548-019-02079-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11548-019-02079-w

Keywords