Abstract
In this paper, we propose a novel model which adaptively estimates the noise probability distribution and noise parameters from the input image and restores the data accordingly choosing appropriate regularization model designed for it. In most imaging applications the noise characteristics are assumed prior to the restoration process. This assumption is generally based on the previous experimental study of the images from a specific modality. The adaptive detection of the noise distribution from the data makes it robust and highly suitable for automated signal and image restoration systems. The non-local framework implemented using fast numerical solvers catalyzes the convergence rate of the model. Here we analyze three different noise distributions such as Gamma, Poisson, and Gaussian. Among this Gaussian is additive and source independent, Gamma is multiplicative and source dependent, and finally Poisson is data dependent (neither multiplicative nor additive). The model can be extended to the other source-dependent distributions such as Rayleigh and Rician by appropriately tuning it. The experimental results conform to the assumption regarding the noise distribution and noise parameters estimation capability of the model.
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Golnabi, H.; Asadpour, A.: Design and application of industrial machine vision systems. Robot. Comput. Integr. Manuf. 23(6), 630–637 (2007)
Bertozzi, M.; Broggi, A.; Fascioli, A.: Vision-based intelligent vehicles: state of the art and perspectives. Robot. Auton. Syst. 32(1), 1–16 (2000)
Subramanian, V.; Burks, T.F.; Arroyo, A.A.: Development of machine vision and laser radar based autonomous vehicle guidance systems for citrus grove navigation. Comput. Electron. Agric. 53(2), 130–143 (2006)
Chang, Y.L.; Chiang, C.Y.; Chen, K.S.: SAR image simulation with application to target recognition. Prog. Electromagn. Res. 119, 35–57 (2011)
Zhang, Q.; Duric, Z.; Michalski, R.S.: Detecting targets in SAR images: a machine learning approach. In: Chin, R., Pong, T.C. (eds.) Lecture Notes in Computer Science, vol. 1351. Springer, Berlin (1997)
Tirandaz, Z.; Akbarizadeh, G.: A two-phase algorithm based on kurtosis curvelet energy and unsupervised spectral regression for segmentation of SAR images. IEEE J. Sel. Topics Appl. Earth Obs. Remote Sens. 9(3), 1244–1264 (2016)
Akbarizadeh, G.: A new statistical-based kurtosis wavelet energy feature for texture recognition of SAR images. IEEE Trans. Geosci. Remote Sens. 50(11), 4358–4368 (2012)
Farbod, M.; Akbarizadeh, G.; Kosarian, A.; Rangzan, K.: Optimized fuzzy cellular automata for synthetic aperture radar image edge detection. J. Electron. Imaging 27(1), 013030 (2018)
Rahmani, M.; Akbarizadeh, G.: Unsupervised feature learning based on sparse coding and spectral clustering for segmentation of synthetic aperture radar images. IET Comput. Vis. 9(5), 629–638 (2015)
Akbarizadeh, G.: Segmentation of SAR satellite images using cellular learning automata and adaptive chains. J. Remote Sens. Technol. 1(2), 44–51 (2013)
Raeisi, N.; Meymand, A.M.; Akbarizadeh, G.: Scour depth prediction in sand beds using artificial neural networks and ANFIS methods. Indian J. Sci. Technol. 8(19), 1–9 (2015)
Akbarizadeh, G.; Rahmani, M.: Efficient combination of texture and color features in a new spectral clustering method for PolSAR image segmentation. Natl. Acad. Sci. Lett. 40(2), 117–120 (2017)
Akbarizadeh, G.; Rahmani, M.: A new ensemble clustering method for PolSAR image segmentation. In: 7th International Conference on Information and Knowledge Technology (IKT2015), IEEE (2015)
karimi, D.; Akbarizadeh, G.; Rangzan, K.; Kabolizadeh, M.: Effective supervised multiple-feature learning for fused radar and optical data classification. IET Radar Sonar Navig. 11(5), 768–777 (2016)
Akbarizadeh, G.: A new recognition approach based on genetic algorithm for classifying textures in satellite SAR images. Int. J. Remote Sens. Appl. 2(4), 7–19 (2012)
karimi, D.; Rangzan, K.; Akbarizadeh, G.; Kabolizadeh, M.: Combined algorithm for improvement of fused radar and optical data classification accuracy. J. Electron. Imag. 26(1), 013017 (2017)
Faraji, Z; Akbarizadeh, G.: A new computer vision algorithm for classification of POLSAR images. In: 7th International Conference on Information and Knowledge Technology (IKT2015), IEEE (2015)
Akbarizadeh, G.; Tirandaz, Z.; Kooshesh, M.: A new curvelet-based texture classification approach for land cover recognition of SAR satellite images. Malays. J. Comput. Sci. 27(3), 218–239 (2014)
Modava, M.; Akbarizadeh, G.: Coastline extraction from SAR images using spatial fuzzy clustering and the active contour method. Int. J. Remote Sens. 38(2), 355–370 (2016)
Modava, M.; Akbarizadeh, G.: A level set based method for coastline detection of SAR images. In: 3rd International Conference on Pattern Recognition and Image Analysis (IPRIA 2017), IEEE (2017)
Jidesh, P.: A convex regularization model for image restoration. Comput. Electr. Eng. 40(8), 66–78 (2014)
Liu, X.; Huang, L.: A new nonlocal total variation regularization algorithm for image denoising. Math. Comput. Simul. 97, 224–233 (2014)
Jidesh, P.; Bini, A.A.: Image despeckling and deblurring via regularized complex diffusion. Signal Image Video Process. 11(6), 977–984 (2017)
Dong, F.; Zhang, H.; Kong, D.: Nonlocal total variation models for multiplicative noise removal using split Bregman iteration. Math. Comput. Model. 55(3–4), 939–954 (2012)
Tuthill, T.A.; Sperry, R.H.; Parker, K.J.: Deviation from Rayleigh statistics in ultrasonic speckle. Ultrason. Imaging 10(2), 81–89 (1988)
Aubert, G.; Aujol, J.-F.: A variational approach to removing multiplicative noise. SIAM J. Appl. Math. 68(4), 925–946 (2008)
Jin, Z.; Yang, X.: A variational model to remove the multiplicative noise in ultrasound images. J. Math. Imaging Vis. 39(1), 62–74 (2011)
Burger, M.; Mller, J.; Papoutsellis, E.; Schnlieb, C.B.: Total variation regularization in measurement and image space for PET reconstruction. Inverse Probl. 30(10), 105003 (2014)
Bian, Z.; Huang, J.; Ma, J.; Lu, L.; Niu, S.; Zeng, D.; Feng, Q.; Chen, W.: Dynamic positron emission tomography image restoration via a kinetics-induced bilateral filter. PLoS ONE 9(2), e89282 (2014). https://doi.org/10.1371/journal.pone.0089282
Bertero, M.; Boccacci, P.; Desider, G.; Vicidomini, G.: Image deblurring with Poisson data: from cells to galaxies. Inverse Probl. 25(12), 123006 (2009)
Bertero, M.; Boccacci, P.; Desider, G.; Vicidomini, G.: Wavelets, ridgelets, and curvelets for Poisson noise removal. IEEE Trans. Image Process. 17(7), 1093–1108 (2008)
Wang, W.; He, C.: A fast and effective algorithm for a Poisson denoising model with total variation. IEEE Signal Process. Lett. 24(3), 269–273 (2017)
Lpez-Rubio, Ezequiel: Restoration of images corrupted by Gaussian and uniform impulsive noise. Pattern Recognit. 43(5), 1835–1846 (2010)
Liu, C.; Freeman, W.T.; Szeliski, R.; Kang S.B.: Noise estimation from a single image. In: 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’06), pp. 901–908. IEEE (2006). https://doi.org/10.1109/CVPR.2006.207
Forouzanfar, M.; Moghaddam, H.A.: Ultrasound speckle reduction in the complex wavelet domain. In: Principles of waveform diversity and design. SciTech Publishing an imprint of the IET, pp. 558–577 (2010)
Liu, X.; Tanaka, M.; Okutomi, M.: Single-image noise level estimation for blind denoising. IEEE Trans. Image Process. 22(12), 1260–1270 (2013)
Liu, X.; Tanaka, M.; Okutomi, M.: Practical signal-dependent noise parameter estimation from a single noisy image. IEEE Trans. Image Process. 23(10), 4361–4371 (2014)
Vozel,B.; Chehdi, K.; Klaine, L.; Lukin, V.V.; Abramov, S.K.: Noise identification and estimation of its statistical parameters by using unsupervised variational classification. In: Proceedings of 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 2, pp. 841–844. IEEE (2006)
Chen, Y.; Das, M.: An automated technique for image noise identification using a simple pattern classification approach. In: Proceedings of 50th Midwest Symposium on Circuits and Systems (MWSCAS), pp. 819–822 (2007)
Chehdi, K.; Sabri, M.: A new approach to identify the nature of the noise affecting an image. In: Proceedings of IEEE ICASSP 92, vol. 3, pp. 285–288 (1992)
Koay, C.; Zarslan, E.; Pierpaoli, C.: Simultaneous identification of noise and estimation of noise standard deviation in MRI. In: Proceedings of the International Society of Magnetic Resonance in Medicine, vol. 17, pp. 4691–4691 (2009)
Chan, T.; Vese, L.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001)
Bali, A.; Singh, S.N.: A review on the strategies and techniques of image segmentation. In: Proc. Fifth International Conference on Advanced Computing and Communication Technologies (ACCT), pp. 113–120 (2015)
Nock, R.; Nielsen, F.: Statistical region merging. IEEE Trans. Pattern Anal. Mach. Intell. 26(11), 1452–1458 (2004)
Gomez, L.; Ospina, R.; Frery, A.C.: Unassisted quantitative evaluation of despeckling filters. Remote Sens. 9(4), 389 (2017)
Rudin, L.I.; Osher, S.; Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D. 60(1), 259–268 (1992)
Rudin, L.; Lions, P.-L.; Osher, S.: Multiplicative denoising and deblurring: theory and algorithms. In: Osher, S., Paragios, N. (eds.) Geometric Level Set Methods in Imaging, Vision, and Graphics, pp. 103–119. Springer, New York (2003)
Huang, L.L.; Xiao, L.; Wei, Z.H.: Multiplicative noise removal via a novel variational model. J. Image Video Process. (2010). https://doi.org/10.1155/2010/250768
Xiao, L.; Huang, L.L.; Wei, Z.H.: A weberized total variation regularization-based image multiplicative noise removal algorithm. EURASIP J. Adv. Signal Process. (2010). https://doi.org/10.1155/2010/490384
Le, T.; Chartrand, R.; Asaki, T.J.: A variational approach to reconstructing images corrupted by Poisson noise. J. Math. Imaging Vis. 27(3), 257–263 (2007)
Buades, A.; Coll, B.; Morel, J.M.: A non-local algorithm for image denoising. In: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), vol. 2, pp. 60–65. IEEE (2005)
Gilboa, G.; Osher, S.: Nonlocal operators with applications to image processing. Multiscale Model. Simul. 7(3), 1005–1028 (2008)
Wang, Z.; Bovik, A.C.; Sheikh, H.R.; Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
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Jidesh, P., Febin, I.P. Estimation of Noise Using Non-local Regularization Frameworks for Image Denoising and Analysis. Arab J Sci Eng 44, 3425–3437 (2019). https://doi.org/10.1007/s13369-018-3542-2
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DOI: https://doi.org/10.1007/s13369-018-3542-2