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De-Noising of Poisson Noise Corrupted CT Images by Using Modified Anisotropic Diffusion-Based PDE Filter

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Advance Concepts of Image Processing and Pattern Recognition

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Abstract

In Poisson noise, the number of collected photons is so small due to the low light environment that degrades the image by reducing image resolution and contrast. Therefore, Poisson noise evaluation is necessary for the restoration of digital images. In this chapter, a filter based on the partial differential equation is introduced to restore noisy images. The proposed PDE-based filter describes Poisson noise-adapted anisotropic diffusion-based method in the L-2 framework. Regularization function and data fidelity are two components of this filter. A regularization parameter lambda is inserted throughout the filtering process to ensure proper stability between the data fidelity and the regularization function. Evaluation of performance parameters for all the described techniques is done with the help of MSE and PSNR.

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References

  • Bardsley JM, Goldes J (2009) Regularization parameter selection methods for ill-posed Poisson maximum likelihood estimation. Inverse Prob 25(9):095005

    Article  MathSciNet  Google Scholar 

  • Bardsley JM, Laobeul ND (2008) Tikhonov regularized Poisson likelihood estimation: theoretical justification and a computational method. Inverse Prob Sci Eng 16(2):199–215

    Article  MathSciNet  Google Scholar 

  • Gilboa G, Sochen N, Zeevi YY (2004) Image enhancement and denoising by complex diffusion processes. IEEE Trans Pattern Anal Mach Intell 26(8):1020–1036

    Article  Google Scholar 

  • https://data.idoimaging.com/dicom/1020_abdomen_ct/1020_abdomen_ct_510_jpg.zip

  • Jain AK (1989) Fundamentals of digital image processing

    Google Scholar 

  • Lane RG (1996) Methods for maximum-likelihood deconvolution. JOSA A 13(10):1992–1998

    Article  MathSciNet  Google Scholar 

  • Llacer J, Núñez J (1991) Iterative maximum likelihood estimator and Bayesian algorithms for image reconstruction in astronomy. In: The restoration of HST images and spectra, p 62

    Google Scholar 

  • Nocedal J, Wright SJ (1999) Numerical optimization. Spring er-Verlag, Berlin, Heidelberg, New York

    Book  Google Scholar 

  • Papoulis A, Pillai SU (2002) Probability, random variables, and stochastic processes. Tata McGraw-Hill Education

    Google Scholar 

  • Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639

    Article  Google Scholar 

  • Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D 60(1–4):259–268

    Article  MathSciNet  Google Scholar 

  • Scherzer O (Ed) (2010) Handbook of mathematical methods in imaging. Springer Science & Business Media

    Google Scholar 

  • Shepp LA, Vardi Y (1982) Maximum likelihood reconstruction for emission tomography. IEEE Trans Med Imaging 1(2):113–122

    Article  Google Scholar 

  • Srivastava R, Srivastava S (2013) Restoration of Poisson noise corrupted digital images with nonlinear PDE based filters along with the choice of regularization parameter estimation. Pattern Recogn Lett 34(10):1175–1185

    Article  Google Scholar 

  • Srivastava R, Gupta JRP, Parthasarthy H (2010b) Comparison of PDE based and other techniques for speckle reduction from digitally reconstructed holographic images. Opt Lasers Eng 48(5):626–635

    Article  Google Scholar 

  • Srivastava R, Gupta JRP, Parthasarathy H (2011) Enhancement and restoration of microscopic images corrupted with poisson’s noise using a nonlinear partial differential equation-based filter. Def Sci J 61(5):452

    Article  Google Scholar 

  • Srivastava S, Srivastava R, Sharma N, Singh SK, Sharma S (2012) A nonlinear complex diffusion based filter adapted to Rayleigh’s speckle noise for de-speckling ultrasound images. Int J Biomed Eng Technol 10(2):101–117

    Article  Google Scholar 

  • Srivastava R (2011) A complex diffusion based nonlinear filter for speckle reduction from optical coherence tomography (OCT) images. In: Proceedings of the 2011 international conference on communication, computing & security, pp 259–264

    Google Scholar 

  • Srivastava R, Gupta JRP, Parthasarthy H (2009) Complex diffusion based speckle reduction from digital images. In: 2009 proceeding of international conference on methods and models in computer science (ICM2CS). IEEE, pp 1–6

    Google Scholar 

  • Srivastava R, Gupta JRP (2010) A PDE-based nonlinear filter adapted to Rayleigh’s speckle noise for de-speckling 2D ultrasound images. In: International conference on contemporary computing. Springer, Berlin, Heidelberg, pp 1–12

    Google Scholar 

  • Takezawa K (2005) Introduction to nonparametric regression, vol 606. John Wiley & Sons

    Google Scholar 

  • Voci F, Eiho S, Sugimoto N, Sekibuchi H (2004) Estimating the gradient in the Perona-Malik equation. IEEE Signal Process Mag 21(3):39–65

    Article  Google Scholar 

  • Wahba G (1990) Spline models for observational data, vol 59. Siam

    Google Scholar 

  • Whittaker ET (1922) On a new method of graduation. Proc Edinb Math Soc 41:63–75

    Article  Google Scholar 

  • You YL, Kaveh M (2000) Fourth-order partial differential equations for noise removal. IEEE Trans Image Process 9(10):1723–1730

    Article  MathSciNet  Google Scholar 

  • Yu Y, Acton ST (2002) Speckle reducing anisotropic diffusion. IEEE Trans Image Process 11(11):1260–1270

    Article  MathSciNet  Google Scholar 

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Singh, N., Yadav, R.B. (2022). De-Noising of Poisson Noise Corrupted CT Images by Using Modified Anisotropic Diffusion-Based PDE Filter. In: Kumar, N., Shahnaz, C., Kumar, K., Abed Mohammed, M., Raw, R.S. (eds) Advance Concepts of Image Processing and Pattern Recognition. Transactions on Computer Systems and Networks. Springer, Singapore. https://doi.org/10.1007/978-981-16-9324-3_7

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  • DOI: https://doi.org/10.1007/978-981-16-9324-3_7

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  • Print ISBN: 978-981-16-9323-6

  • Online ISBN: 978-981-16-9324-3

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