# An efficient wavelet and curvelet-based PET image denoising technique

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## Abstract

Positron emission tomography (PET) image denoising is a challenging task due to the presence of noise and low spatial resolution compared with other imaging techniques such as magnetic resonance imaging (MRI) and computed tomography (CT). PET image noise can hamper further processing and analysis, such as segmentation and disease screening. The wavelet transform–based techniques have often been proposed for PET image denoising to handle isotropic (smooth details) features. The curvelet transform–based PET image denoising techniques have the ability to handle multi-scale and multi-directional properties such as edges and curves (anisotropic features) as compared with wavelet transform–based denoising techniques. The wavelet denoising method is not optimal for anisotropic features, whereas the curvelet denoising method sometimes has difficulty in handling isotropic features. In order to handle the weaknesses of individual wavelet and curvelet-based methods, the present research proposes an efficient PET image denoising technique based on the combination of wavelet and curvelet transforms, along with a new adaptive threshold selection to threshold the wavelet coefficients in each subband (except last level low pass (LL) residual). The proposed threshold utilizes the advantages of adaptive threshold taken from BayesShrink along with the neighborhood window concept. The present method was tested on both simulated phantom and clinical PET datasets. Experimental results show that our method has achieved better results than the existing methods such as VisuShrink, BayesShrink, NeighShrink, ModineighShrink, curvelet, and an existing wavelet curvelet-based method with respect to different noise measurement metrics, such as mean squared error (MSE), signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR), and image quality index (IQI). Furthermore, notable performance is achieved in the case of medical applications such as gray matter segmentation and precise tumor region identification.

## Keywords

Image denoising PET Wavelet Curvelet Thresholding Neighborhood coefficients## Notes

### Acknowledgments

Sincere gratitude to Dr. Punit Sharma, MD at Apollo Gleneagles Hospital, Kolkata, India, for providing the clinical PET brain datasets and verified the results throughout this project. 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.

### Funding information

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.

## References

- 1.Pieterman RM, van Putten JWG, Meuzelaar JJ, Mooyaart EL, Vaalburg W, Koëter GH, Fidler V, Pruim J, Groen HJM (2000) Preoperative staging of non–small-cell lung cancer with positron-emission tomography. England J Med 343(4):254–261CrossRefGoogle Scholar
- 2.Iwata R, Ido T (1990) Differential diagnosis of lung tumor with positron emission tomography: a prospectiveGoogle Scholar
- 3.Weber W, Carter Y, Abdel-Dayem HM, Sfakianakis G, et al. (1999) Assessment of pulmonary lesions with (18) f-fluorodeoxyglucose positron imaging using coincidence mode gamma cameras. J Nucl Med 40(4):574PubMedGoogle Scholar
- 4.Coxson PG, Huesman RH, Borland L (1997) Consequences of using a simplified kinetic model for dynamic pet data. J Nucl Med 38(4):660PubMedGoogle Scholar
- 5.Rodrigues I, Sanches J, Bioucas-Dias J (2008) Denoising of medical images corrupted by poisson noise. In: 15th IEEE International conference on image processing, 2008. ICIP 2008. IEEE, pp 1756–1759Google Scholar
- 6.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):297–304PubMedCrossRefGoogle Scholar
- 7.Le Pogam A, Hanzouli H, Hatt M, Cheze Le Rest C, Visvikis D (2013) Denoising of pet images by combining wavelets and curvelets for improved preservation of resolution and quantitation. Med Image Anal 17 (8):877–891PubMedCrossRefGoogle Scholar
- 8.Turkheimer FE, Banati RB, Visvikis D, Aston JAD, Gunn RN, Cunningham VJ (2000) Modeling dynamic pet-spect studies in the wavelet domain. J Cerebral Blood Flow Metabol 20(5):879–893CrossRefGoogle Scholar
- 9.Hannequin P, Mas J (2002) Statistical and heuristic image noise extraction (shine): a new method for processing poisson noise in scintigraphic images. Phys Med Biol 47(24):4329PubMedCrossRefGoogle Scholar
- 10.Seret A, Vanhove C, Defrise M (2009) Resolution improvement and noise reduction in human pinhole spect using a multi-ray approach and the shine method. Nuklearmedizin Nucl Med 48(4):159–165CrossRefGoogle Scholar
- 11.Ollinger JM, Fessler JA (1997) Positron-emission tomography. IEEE Signal Process Mag 14(1):43–55CrossRefGoogle Scholar
- 12.Ito K, Xiong K (2000) Gaussian filters for nonlinear filtering problems. IEEE Trans Autom control 45 (5):910–927CrossRefGoogle Scholar
- 13.Alpert NM, Reilhac A, Chio TC, Selesnick I (2006) Optimization of dynamic measurement of receptor kinetics by wavelet denoising. Neuroimage 30(2):444–451PubMedCrossRefGoogle Scholar
- 14.Candes E, Demanet L, Donoho D, Ying L (2006) Fast discrete curvelet transforms. Multiscale Model Simul 5(3):861–899CrossRefGoogle Scholar
- 15.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):219–266CrossRefGoogle Scholar
- 16.Ridgelets EJC (1998) Ridgelets: theory and applications. PhD thesis, Ph. D. Thesis, Stanford University USAGoogle Scholar
- 17.Starck J-L, Candès EJ, Donoho DL (2002) The curvelet transform for image denoising. IEEE Trans Image Process 11(6):670–684PubMedCrossRefGoogle Scholar
- 18.Binh NT, Khare A (2010) Multilevel threshold based image denoising in curvelet domain. J Comput Sci Technol 25(3):632–640CrossRefGoogle Scholar
- 19.Donoho DL, Johnstone IM (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika, 425–455Google Scholar
- 20.Chang SG, Yu B, Vetterli M (2000) Adaptive wavelet thresholding for image denoising and compression. IEEE Trans Image Process 9(9):1532–1546PubMedCrossRefGoogle Scholar
- 21.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 Nucl Med 21(7):379PubMedCrossRefGoogle Scholar
- 22.Cai TT, Silverman BW (2001) Incorporating information on neighbouring coefficients into wavelet estimation. Sankhyā Indian J Statist, Series B, 127–148Google Scholar
- 23.Chen GY, Tien D, Bui, Krzyżak A (2005) Image denoising with neighbour dependency and customized wavelet and threshold. Pattern Recogn 38(1):115–124CrossRefGoogle Scholar
- 24.Mohideen KS, Perumal AS, Sathik MM (2008) Image de-noising using discrete wavelet transform. Int J Comput Sci Netw Secur 8(1):213–216Google Scholar
- 25.Om H, Biswas M (2012) An improved image denoising method based on wavelet thresholdingCrossRefGoogle Scholar
- 26.Green GC (2005) Wavelet-based denoising of cardiac PET data. Carleton UniversityGoogle Scholar
- 27.Taswell C (2000) The what, how, and why of wavelet shrinkage denoising. Comput Sci Eng 2(3):12–19CrossRefGoogle Scholar
- 28.Mohl B, Wahlberg M, Madsen PT (2003) Ideal spatial adaptation via wavelet shrinkage. J Acoust Soc Am 114:1143–1154PubMedCrossRefGoogle Scholar
- 29.Donoho DL (1995) De-noising by soft-thresholding. IEEE Trans Inf Theory 41(3):613–627CrossRefGoogle Scholar
- 30.Donoho DL, Johnstone IM (1995) Adapting to unknown smoothness via wavelet shrinkage. J Am Stat Assoc 90(432):1200–1224CrossRefGoogle Scholar
- 31.Chang GS, Yu B, Vetterli M (1998) Spatially adaptive wavelet thresholding with context modeling for image denoising. In: 1998 International conference on image processing, 1998. ICIP 98. Proceedings, vol 1. IEEE, pp 535–539Google Scholar
- 32.AlZubi S, Islam N, Abbod M (2011) Multiresolution analysis using wavelet, ridgelet, and curvelet transforms for medical image segmentation. J Biomed Imag 2011:4Google Scholar
- 33.Kumar YK (2009) Comparison of fusion techniques applied to preclinical images: fast discrete curvelet transform using wrapping technique & wavelet transform. J Theor Appl Inf Technol, 5(6)Google Scholar
- 34.Ali Hyder S, 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 471–480Google Scholar
- 35.Starck J-L, Murtagh F, Fadili JM (2010) Sparse image and signal processing: wavelets, curvelets, morphological diversity. Cambridge University PressGoogle Scholar
- 36.Mallat S (2008) A wavelet tour of signal processing: the sparse way. Academic PressGoogle Scholar
- 37.Wang Z, Bovik AC (2002) A universal image quality index. IEEE Signal Process Lett 9(3):81–84CrossRefGoogle Scholar
- 38.Slifstein M, Mawlawi O, Laruelle M (2001) Partial volume effect correction: methodological considerations. In: Gjedde A, Hansen SB, GMK, Paulson OB (eds) Physiological imaging of the brain with PET, pp 65–71Google Scholar
- 39.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 SciencesGoogle Scholar
- 40.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). IEEE, pp 1–8Google Scholar
- 41.Maji P, Pal SK (2011) Rough-fuzzy pattern recognition: applications in bioinformatics and medical imaging, vol 3. WileyGoogle Scholar
- 42.Kekre HB, Gharge S (2010) Texture based segmentation using statistical properties for mammographic images. Entropy 1:2Google Scholar
- 43.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):1095–1112CrossRefGoogle Scholar
- 44.Yu S, Muhammed HH (2016) Noise type evaluation in positron emission tomography images. In: International conference on biomedical engineering (IBIOMED). IEEE, pp 1–6Google Scholar
- 45.Hasinoff SW (2014) Photon, poisson noise. In: Computer vision. Springer, pp 608–610Google Scholar
- 46.Consul PC, Jain GC (1973) A generalization of the poisson distribution. Technometrics 15(4):791–799CrossRefGoogle Scholar
- 47.Stollnitz EJ, DeRose TD, Salesin DH (1995) Wavelets for computer graphics: a primer part 1 y. Way 6 (2):1Google Scholar
- 48.Mulcahy C (1997) Image compression using the haar wavelet transform. Spelman Sci Math J 1(1):22–31Google Scholar
- 49.Kara B, Watsuji N (2003) Using wavelets for texture classification. In: IJCI proceedings of international conference on signal processing, vol 1Google Scholar
- 50.Candes EJ, Donoho DL (2000) Curvelets, multiresolution representation, and scaling laws. In: International symposium on optical science and technology. International Society for Optics and Photonics, pp 1–12Google Scholar
- 51.Donoho DL (2000) Orthonormal ridgelets and linear singularities. SIAM J Math Anal 31(5):1062–1099CrossRefGoogle Scholar
- 52.Do MN, Vetterli M (2003) The finite ridgelet transform for image representation. IEEE Trans Image Process 12(1):16–28PubMedCrossRefGoogle Scholar
- 53.Candès EJ, Donoho DL (1999) Ridgelets: a key to higher-dimensional intermittency? Philos Trans R Soc London A: Math Phys Eng Sci 357(1760):2495–2509CrossRefGoogle Scholar