Skip to main content
Log in

An efficient method for PET image denoising by combining multi-scale transform and non-local means

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

The diagnosis of dementia, particularly in the early stages is very much helpful with Positron emission tomography (PET) image processing. The most important challenges in PET image processing are noise removal and region of interests (ROIs) segmentation. Although denoising and segmentation are performed independently, but the performance of the denoising process significantly affects the performance of the segmentation process. Due to the low signals to noise ratio and low contrast, PET image denoising is a challenging task. Individual wavelet, curvelet and non-local means (NLM) based methods are not well suited to handle both isotropic (smooth details) and anisotropic (edges and curves) features due to its restricted abilities. To address these issues, the present work proposes an efficient denoising framework for reducing the noise level of brain PET images based on the combination of multi-scale transform (wavelet and curvelet) and tree clustering non-local means (TNLM). The main objective of the proposed method is to extract the isotropic features from a noisy smooth PET image using tree clustering based non-local means (TNLM). Then curvelet-based denoising is applied to the residual image to extract the anisotropic features such as edges and curves. Finally, the extracted anisotropic features are inserted back into the isotropic features to obtain an estimated denoised image. Simulated phantom and clinical PET datasets have been used in this proposed work for testing and measuring the performance in the medical applications, such as gray matter segmentation and precise tumor region identification without any interaction with other structural images like MRI or CT. The results in the experimental section show that the proposed denoising method has obtained better performance than existing wavelet, curvelet, wavelet-curvelet, non-local means (NLM) and deep learning methods based on the preservation of the edges. Qualitatively, a notable gain is achieved in the proposed denoised PET images in terms of contrast enhancement than other existing denoising methods.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. Alessio AM, Kinahan PE (2006) Improved quantitation for pet/ct image reconstruction with system modeling and anatomical priors. Med Phys 33 (11):4095–4103

    Article  Google Scholar 

  2. AlZubi S, Islam N, Abbod M (2011) Multiresolution analysis using wavelet, ridgelet, and curvelet transforms for medical image segmentation. J Biomed Imaging 2011:4

    Google Scholar 

  3. Bal A, Banerjee M, Chakrabarti A, Sharma P (2018) MRI brain tumor segmentation and analysis using rough-fuzzy C-Means and shape based properties. Journal of King Saud University-Computer and Information Sciences

  4. Bal A, Banerjee M, Sharma P, Maitra M (2018) Brain tumor segmentation on MR image using k-means and fuzzy-possibilistic clustering. In: 2018 2nd international conference on electronics, materials engineering & Nano-Technology (IEMENTech), pp 1–8

  5. Bal A, Banerjee M, Sharma P, Maitra M (2019) An efficient wavelet and curvelet-based pet image denoising technique. Med Biol Eng Comput 57 (12):2567–2598

    Article  Google Scholar 

  6. Bal A, Banerjee M, Sharma P, Maitra M (2020) Gray matter segmentation and delineation from positron emission tomography (pet) image. In: Emerging technology in modelling and graphics. Springer, pp 359–372

  7. Beghdadi A, Le Negrate A (1989) Contrast enhancement technique based on local detection of edges. Comput Vis Graph Image Process 46(2):162–174

    Article  Google Scholar 

  8. Brox T, Kleinschmidt O, Cremers D (2008) Efficient nonlocal means for denoising of textural patterns. IEEE Trans Image Process 17(7):1083–1092

    Article  MathSciNet  Google Scholar 

  9. Buades A, Coll B, Morel J-M (2005) A non-local algorithm for image denoising. In: 2005. CVPR 2005. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol 2, IEEE, pp 60–65

  10. Buades A, Coll B, Morel J-M (2005) A review of image denoising algorithms, with a new one. Multiscale Model Simul 4(2):490–530

    Article  MathSciNet  MATH  Google Scholar 

  11. Cai TT, Silverman BW (2001) Incorporating information on neighbouring coefficients into wavelet estimation, sankhyā: The Indian Journal of Statistics Series B, pp 127–148

  12. Candès EJ, Donoho DL (2004) New tight frames of curvelets and optimal representations of objects with piecewise c2 singularities. Commun Pure Appl Math 57(2):219–266

    Article  MATH  Google Scholar 

  13. Candes E, Demanet L, Donoho D, Ying L (2006) Fast discrete curvelet transforms. Multiscale Model Simul 5(3):861–899

    Article  MathSciNet  MATH  Google Scholar 

  14. Chang SG, Yu B, Vetterli M (1998) Spatially adaptive wavelet thresholding with context modeling for image denoising. In: 1998. ICIP 98. Proceedings. 1998 International Conference on Image Processing, vol 1, IEEE, pp 535–539

  15. Chang SG, Yu B, Vetterli M (2000) Adaptive wavelet thresholding for image denoising and compression. IEEE Trans Image Process 9(9):1532–1546

    Article  MathSciNet  MATH  Google Scholar 

  16. Chen G, Bui TD, Krzyzak A (2005) Image denoising using neighbouring wavelet coefficients. Integr Comput-Aided Eng 12(1):99–107

    Article  Google Scholar 

  17. Christian BT, Vandehey NT, Floberg JM, Mistretta CA (2010) Dynamic pet denoising with hypr processing, Journal of nuclear medicine: official publication. Soc Nuclear Med 51(7):1147

    Article  Google Scholar 

  18. Cui J, Gong K, Guo N, Wu C, Meng X, Kim K, Zheng K, Wu Z, Fu L, Xu B et al (2019) Pet image denoising using unsupervised deep learning. Eur J Nuclear Med Mol Imaging 46(13):2780–2789

    Article  Google Scholar 

  19. Donoho DL, Johnstone IM (1994) Ideal spatial adaptation by wavelet shrinkage, biometrika, pp 425–455

  20. Donoho DL (1995) De-noising by soft-thresholding. IEEE Trans Inf Theory 41(3):613–627

    Article  MathSciNet  MATH  Google Scholar 

  21. Dutta J, Leahy RM, Li Q (2013) Non-local means denoising of dynamic pet images. PloS one 8(12):e81390

    Article  Google Scholar 

  22. Ellis S, Mallia A, McGinnity CJ, Cook GJ, Reader AJ (2018) Multitracer guided pet image reconstruction. IEEE Trans Rad Plasma Med Sci 2 (5):499–509

    Article  Google Scholar 

  23. Gong K, Guan J, Liu C-C, Qi J (2018) Pet image denoising using a deep neural network through fine tuning. IEEE Trans Radiat Plasma Med Sci 3(2):153–161

    Article  Google Scholar 

  24. Green GC (2005) Wavelet-based denoising of cardiac PET data. Carleton University

  25. Huerga C, Castro P, Corredoira E, Coronado M, Delgado V, Guibelalde E (2017) Denoising of pet images by context modelling using local neighbourhood correlation. Phys Med Biol 62(2):633

    Article  Google Scholar 

  26. Hyder SA, Sukanesh R (2011) An efficient algorithm for denoising mr and ct images using digital curvelet transform. In: Software Tools and Algorithms for Biological Systems. Springer, pp 471–480

  27. Kekre H, Gharge S (2010) Texture based segmentation using statistical properties for mammographic images. Entropy 1:2

    Google Scholar 

  28. Kervrann C, Boulanger J, Coupé P (2007) Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal. In: International conference on scale space and variational methods in computer vision. Springer, pp 520–532

  29. Le Pogam A, Hanzouli H, Hatt M, Le Rest CC, Visvikis D (2013) Denoising of pet images by combining wavelets and curvelets for improved preservation of resolution and quantitation. Med Image Anal 17(8):877–891

    Article  Google Scholar 

  30. Luisier F, Blu T, Unser M (2007) A new sure approach to image denoising: Interscale orthonormal wavelet thresholding. IEEE Trans Image Process 16(3):593–606

    Article  MathSciNet  Google Scholar 

  31. Mahmoudi M, Sapiro G (2005) Fast image and video denoising via nonlocal means of similar neighborhoods. IEEE Signal Process Lett 12(12):839–842

    Article  Google Scholar 

  32. Maji P, Pal SK (2011) Rough-fuzzy pattern recognition: applications in bioinformatics and medical imaging, vol. 3. Wiley, New York

  33. Mejia JM, Domínguez HdJO, Villegas OOV, Máynez LO, Mederos B (2014) Noise reduction in small-animal pet images using a multiresolution transform. IEEE Trans med Imaging 33(10):2010–2019

    Article  Google Scholar 

  34. Mohideen SK, Perumal SA, Sathik MM (2008) Image de-noising using discrete wavelet transform. Int J Comput Sci Netw Secur 8(1):213–216

    Google Scholar 

  35. Mohl B, Wahlberg M, Madsen P (2003) Ideal spatial adaptation via wavelet shrinkage. J Acoust Soc Amer 114:1143–1154

    Article  Google Scholar 

  36. Nguyen V-G, Lee S-J (2010) Nonlocal-means approaches to anatomy-based pet image reconstruction. In: 2010 IEEE Nuclear science symposium conference record (NSS/MIC). IEEE, pp 3273–3277

  37. Om H, Biswas M (2012) An improved image denoising method based on wavelet thresholding. J Signal Inf Proces 3(01):109

    Google Scholar 

  38. Peter DJ, Govindan V, Mathew AT (2010) Nonlocal-means image denoising technique using robust m-estimator. J Comput Sci Technol 25(3):623–631

    Article  Google Scholar 

  39. Qi J, Leahy RM (1999) A theoretical study of the contrast recovery and variance of map reconstructions from pet data. IEEE Trans Med Imaging 18(4):293–305

    Article  Google Scholar 

  40. Qi J, Leahy RM (2000) Resolution and noise properties of map reconstruction for fully 3-d pet. IEEE Trans Med Imaging 19(5):493–506

    Article  Google Scholar 

  41. RIDGELETS E (1998) Ridgelets: theory and applications, Ph.D. thesis, Ph. D. thesis, Stanford University, USA

  42. Said AB, Hadjidj R, Melkemi KE, Foufou S (2016) Multispectral image denoising with optimized vector non-local mean filter. Digital Signal Process 58:115–126

    Article  Google Scholar 

  43. Shalchian B, Rajabi H, Soltanian-Zadeh H (2009) Assessment of the wavelet transform in reduction of noise from simulated pet images. J Nuclear Med Technol 37(4):223–228

    Article  Google Scholar 

  44. Shidahara M, Ikoma Y, Kershaw J, Kimura Y, Naganawa M, Watabe H (2007) Pet kinetic analysis: wavelet denoising of dynamic pet data with application to parametric imaging. Ann Nuclear Med 21(7):379–386

    Article  Google Scholar 

  45. Shih Y-Y, Chen J-C, Liu R-S (2005) Development of wavelet de-noising technique for pet images. Comput Med Imaging Graph 29(4):297–304

    Article  Google Scholar 

  46. Starck J-L, Candès EJ, Donoho DL (2002) The curvelet transform for image denoising. IEEE Trans Image Process 11(6):670–684

    Article  MathSciNet  MATH  Google Scholar 

  47. Starck J-L, Murtagh F, Fadili JM (2010) Sparse image and signal processing: wavelets, curvelets, morphological diversity. Cambridge University Press

  48. Taswell C (2000) The what, how, and why of wavelet shrinkage denoising. Comput Sci Eng 2(3):12–19

    Article  Google Scholar 

  49. Turkheimer FE, Banati RB, Visvikis D, Aston JA, Gunn RN, Cunningham VJ (2000) Modeling dynamic pet-spect studies in the wavelet domain. J Cereb Blood Flow Metabol 20(5):879–893

    Article  Google Scholar 

  50. Wang G, Qi J (2014) Pet image reconstruction using kernel method. IEEE Trans Med Imaging 34(1):61–71

    Article  Google Scholar 

  51. Wink AM, Roerdink JB (2004) Denoising functional mr images: a comparison of wavelet denoising and gaussian smoothing. IEEE Trans Med Imaging 23 (3):374–387

    Article  Google Scholar 

  52. Xu Z, Bagci U, Seidel J, Thomasson D, Solomon J, Mollura DJ (2014) Segmentation based denoising of pet images: An iterative approach via regional means and affinity propagation, in: International Conference on Medical Image Computing and Computer-Assisted Intervention. Springer, pp 698–705

  53. Yang H-Y, Wang X-Y, Wang Q-Y, Zhang X-J (2012) Ls-svm based image segmentation using color and texture information. J Vis Commun Image Represent 23(7):1095–1112

    Article  Google Scholar 

Download references

Acknowledgment

This research work was supported by the Board of Research in Nuclear Sciences (BRNS), DAE, Government of India, under the Reference No. 34/14/13/2016-BRNS/34044. Sincere gratitude to Dr. Punit Sharma, MD at Apollo Gleneagles Hospital, Kolkata, India for providing the clinical PET brain datasets and valuable comments throughout this work. The authors would like to thank Dr. Haseeb Hassan, MD, DM at Rabindranath Tagore International Institute of Cardiac Sciences, Kolkata, India, and Dr. Arindam Chatterjee, MD, at Variable Energy Cyclotron Centre (VECC), Kolkata, India for their helpful comments. The authors would like to thank the referees for providing their very valuable comments on the original version of the manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Abhishek Bal.

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

Bal, A., Banerjee, M., Chaki, R. et al. An efficient method for PET image denoising by combining multi-scale transform and non-local means. Multimed Tools Appl 79, 29087–29120 (2020). https://doi.org/10.1007/s11042-020-08936-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-020-08936-0

Keywords

Navigation