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Additive White Gaussian Noise Level Estimation for Natural Images Using Linear Scale-Space Features

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Abstract

Noise in images is often modelled with additive white Gaussian noise (AWGN). An accurate estimation of noise level without any prior knowledge of noisy input image leads to effective blind image denoising methods. The performance of certain image denoising methods under AWGN model is dependent on the accuracy of noise level estimation (NLE). Hence, there is a need to develop an effective NLE method in order to achieve better performance in image denoising. Even though the existing NLE methods perform well on natural images, these methods involve complex segmentation tasks such as homogeneous regions extraction and super-pixel decomposition. Hence, a simple, fast, and accurate NLE method for AWGN is proposed in this paper. In the presented NLE method, the statistical features of high-frequency details of noisy input image are obtained at multiple linear (Gaussian) scale-space which are used to construct a feature vector. It is perceived that the features obtained are almost linear and separable. Hence, supervised linear regression (LR) models that are trained globally and locally are suggested for NLE. The proposed method estimates the noise level in two stages. In stage-1, a globally trained LR model is used to estimate the noise level. It is observed that the accuracy of the noise level obtained through stage-1 can be further improved in stage-2 by adopting the proposed locally trained LR model. The proposed NLE method is evaluated with artificially generated noisy natural images using AWGN model. The high-quality natural images from Waterloo and BSD500 datasets are selected using image quality selection module and then used in training and testing phases. The average absolute deviation (AAD) is evaluated from each selected image in the datasets over a wide range of noise levels ([0 100]). The average AAD for selected images in Waterloo (BSD500) dataset is 0.21 (0.18), and execution time required to estimate the noise level is 0.04 s per image. From the obtained results, it is clear that the proposed method is simple, fast, and accurate as compared to several existing NLE methods. The effectiveness of the proposed NLE method is illustrated with fast and flexible denoising convolutional neural network using standard test images at randomly selected noise levels.

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References

  1. P. Arbelaez, M. Maire, C. Fowlkes, J. Malik, Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 33(5), 898–916 (2010)

    Google Scholar 

  2. J. Babaud, A.P. Witkin, M. Baudin, R.O. Duda, Uniqueness of the Gaussian kernel for scale-space filtering. IEEE Trans. Pattern Anal. Mach. Intell. 8(1), 26–33 (1986)

    MATH  Google Scholar 

  3. A. Bosco, A. Bruna, G. Messina, G. Spampinato, Fast method for noise level estimation and integrated noise reduction. IEEE Trans. Consum. Electron. 51(3), 1028–1033 (2005)

    Google Scholar 

  4. D.R. Brownrigg, The weighted median filter. Commun. ACM 27(8), 807–818 (1984)

    Google Scholar 

  5. A. Buades, B. Coll, J.M. Morel, A non-local algorithm for image denoising. IEEE Conf. Comput. Vis. Pattern Recognit. 2, 60–65 (2005a)

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  7. H.C. Burger, C.J. Schuler, S. Harmeling, Image denoising: Can plain neural networks compete with BM3D?, in IEEE Conference on Computer Vision and Pattern Recognition (2012), pp. 2392–2399

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

    MathSciNet  MATH  Google Scholar 

  9. G. Chen, F. Zhu, H.P. Ann, An efficient statistical method for image noise level estimation, in Proceedings of the IEEE International Conference on Computer Vision (2015), pp. 477–485

  10. J.H. Chuah, H.Y. Khaw, F.C. Soon, C.O. Chow, Detection of Gaussian noise and its level using deep convolutional neural network, in IEEE Conferene on TENCON (2017), pp. 2447–2450

  11. B. Corner, R. Narayanan, S. Reichenbach, Noise estimation in remote sensing imagery using data masking. Int. J. Remote Sens. 24(4), 689–702 (2003)

    Google Scholar 

  12. K. Dabov, A. Foi, V. Katkovnik, K. Egiazarian, Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. Image Process. 16(8), 2080–2095 (2007)

    MathSciNet  Google Scholar 

  13. A. De Stefano, P.R. White, W.B. Collis, Training methods for image noise level estimation on wavelet components. EURASIP J. Appl. Signal Process. 2004, 2400–2407 (2004)

    MathSciNet  MATH  Google Scholar 

  14. G. Deng, L. Cahill, An adaptive Gaussian filter for noise reduction and edge detection, in IEEE conference record nuclear science symposium and medical imaging conference (1993), pp. 1615–1619

  15. L. Dong, J. Zhou, Y.Y. Tang, Noise level estimation for natural images based on scale-invariant kurtosis and piecewise stationarity. IEEE Trans. Image Process. 26(2), 1017–1030 (2017)

    MathSciNet  MATH  Google Scholar 

  16. D.L. Donoho, J.M. Johnstone, Ideal spatial adaptation by wavelet shrinkage. Biometrika 81(3), 425–455 (1994)

    MathSciNet  MATH  Google Scholar 

  17. R. Ehrich, A symmetric hysteresis smoothing algorithm that preserves principal features. Comput. Graph. Image Process. 8(1), 121–126 (1978)

    Google Scholar 

  18. L. Fan, F. Zhang, H. Fan, C. Zhang, Brief review of image denoising techniques. Vis. Comput. Ind. Biomed. Art 2(1), 7 (2019)

    Google Scholar 

  19. P. Fu, C. Li, Q. Sun, W. Cai, D.D. Feng, Image noise level estimation based on a new adaptive superpixel classification, in IEEE International Conference on Image Processing (2014), pp. 2649–2653

  20. P. Fu, C. Li, W. Cai, Q. Sun, A spatially cohesive superpixel model for image noise level estimation. Neurocomputing 266, 420–432 (2017)

    Google Scholar 

  21. H. Golshan, R.P.R. Hasanzadeh, Fuzzy hysteresis smoothing: a new approach for image denoising. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2961336

  22. R.C. Gonzalez, R.E. Woods, S.L. Eddins, Digital Image Processing Using MATLAB (Pearson Education India, New Delhi, 2004)

    Google Scholar 

  23. B. Goyal, A. Dogra, S. Agrawal, B. Sohi, A. Sharma, Image denoising review: from classical to state-of-the-art approaches. Inf. Fusion 55, 220–244 (2020)

    Google Scholar 

  24. S. Greenland, S.J. Senn, K.J. Rothman, J.B. Carlin, C. Poole, S.N. Goodman, D.G. Altman, Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. Eur. J. Epidemiol. 31(4), 337–350 (2016)

    Google Scholar 

  25. R.P. Hasanzadeh, M.B. Daneshvar, A novel image noise reduction technique based on hysteresis processing. Optik 126(21), 3039–3046 (2015)

    Google Scholar 

  26. J. Immerkaer, Fast noise variance estimation. Comput. Vis. Image Underst. 64(2), 300–302 (1996)

    Google Scholar 

  27. V. Jain, S. Seung, Natural image denoising with convolutional networks, in Advances in Neural Information Processing Systems (2009), pp. 769–776

  28. G. Jeon, S. Kang, Y.S. Lee, Noise level estimation for image processing, in International Conference on Hybrid Information Technology (Springer, 2012), pp. 350–356

  29. P. Jiang, J. Zhang, No-reference image quality assessment based on local maximum gradient. J. Electron. Inf. Technol. 37(11), 2587–2593 (2015)

    Google Scholar 

  30. B.J. Kang, K.R. Park, Real-time image restoration for iris recognition systems. IEEE Trans. Syst. Man Cybern. 37(6), 1555–1566 (2007)

    Google Scholar 

  31. H. Kaufman, J. Woods, S. Dravida, A. Tekalp, Estimation and identification of two-dimensional images. IEEE Trans. Autom. Control 28(7), 745–756 (1983)

    MATH  Google Scholar 

  32. A. Khireddine, K. Benmahammed, W. Puech, Digital image restoration by Wiener filter in 2d case. Adv. Eng. Softw. 38(7), 513–516 (2007)

    Google Scholar 

  33. A. Khmag, S.A.R. Al Haddad, R.A. Ramlee, N. Kamarudin, F.L. Malallah, Natural image noise removal using nonlocal means and hidden Markov models in transform domain. Vis. Comput. 34(12), 1661–1675 (2018a)

    Google Scholar 

  34. A. Khmag, A.R. Ramli, S. Al-Haddad, N. Kamarudin, Natural image noise level estimation based on local statistics for blind noise reduction. Vis. Comput. 34(4), 575–587 (2018b)

    Google Scholar 

  35. O. Laligant, F. Truchetet, E. Fauvet, Noise estimation from digital step-model signal. IEEE Trans. Image Process. 22(12), 5158–5167 (2013)

    MathSciNet  MATH  Google Scholar 

  36. Z. Li, L. Yu, J.D. Trzasko, D.S. Lake, D.J. Blezek, J.G. Fletcher, C.H. McCollough, A. Manduca, Adaptive nonlocal means filtering based on local noise level for CT denoising. Med. Phys. 41(1), 011908 (2014)

    Google Scholar 

  37. T. Lindeberg, Scale-Space, Wiley Encyclopedia of Computer Science and Engineering (Wiley, Hoboken, 2007), pp. 2495–2504

    Google Scholar 

  38. C. Liu, R. Szeliski, S.B. Kang, C.L. Zitnick, W.T. Freeman, Automatic estimation and removal of noise from a single image. IEEE Trans. Pattern Anal. Mach. Intell. 30(2), 299–314 (2008)

    Google Scholar 

  39. W. Liu, W. Lin, Additive white Gaussian noise level estimation in SVD domain for images. IEEE Trans. Image Process. 22(3), 872–883 (2013)

    MathSciNet  MATH  Google Scholar 

  40. X. Liu, M. Tanaka, M. Okutomi, Noise level estimation using weak textured patches of a single noisy image, in IEEE International Conference on Image Processing (2012), pp. 665–668

  41. X. Liu, M. Tanaka, M. Okutomi, Single-image noise level estimation for blind denoising. IEEE Trans. Image Process. 22(12), 5226–5237 (2013)

    Google Scholar 

  42. X. Liu, M. Tanaka, M. Okutomi, Practical signal-dependent noise parameter estimation from a single noisy image. IEEE Trans. Image Process. 23(10), 4361–4371 (2014)

    MathSciNet  MATH  Google Scholar 

  43. D.G. Lowe, Object recognition from local scale-invariant features, in IEEE Proceedings of the International Conference on Computer Vision, vol. 2 (1999), pp. 1150–1157

  44. K. Ma, Z. Duanmu, Q. Wu, Z. Wang, H. Yong, H. Li, L. Zhang, Waterloo exploration database: new challenges for image quality assessment models. IEEE Trans. Image Process. 26(2), 1004–1016 (2017)

    MathSciNet  MATH  Google Scholar 

  45. M. Mazhari, R.P. Hasanzadeh, Suppression of noise in SEM images using weighted local hysteresis smoothing filter. Scanning 38(6), 634–643 (2016)

    Google Scholar 

  46. A. Mittal, R. Soundararajan, A.C. Bovik, Making a completely blind image quality analyzer. IEEE Signal Process. Lett. 20(3), 209–212 (2013)

    Google Scholar 

  47. J. Neter, M.H. Kutner, C.J. Nachtsheim, W. Wasserman, Applied Linear Statistical Models, vol. 4 (Irwin, Chicago, 1996)

    Google Scholar 

  48. T.A. Nguyen, M.C. Hong, Filtering-based noise estimation for denoising the image degraded by Gaussian noise, in Pacific-Rim Symposium on Image and Video Technology (Springer, 2011), pp. 157–167

  49. E. Oho, N. Ichise, W.H. Martin, K.R. Peters, Practical method for noise removal in scanning electron microscopy. Scanning 18(1), 50–54 (1996)

    Google Scholar 

  50. S.I. Olsen, Estimation of noise in images: an evaluation. Graph. Models Image Process. 55(4), 319–323 (1993)

    Google Scholar 

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

    Google Scholar 

  52. T. Pratap, P. Kokil, Computer-aided diagnosis of cataract using deep transfer learning. Biomed. Signal Process. Control 53, 101533 (2019)

    Google Scholar 

  53. S. Pyatykh, J. Hesser, L. Zheng, Image noise level estimation by principal component analysis. IEEE Trans. Image Process. 22(2), 687–699 (2013)

    MathSciNet  MATH  Google Scholar 

  54. M. Rakhshanfar, M.A. Amer, Estimation of Gaussian, Poissonian–Gaussian, and processed visual noise and its level function. IEEE Trans. Image Process. 25(9), 4172–4185 (2016)

    MathSciNet  MATH  Google Scholar 

  55. K. Rank, M. Lendl, R. Unbehauen, Estimation of image noise variance. IEE Proc. Vis. Image Signal Process. 146(2), 80–84 (1999)

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  57. J. Shen, Y. Du, W. Wang, X. Li, Lazy random walks for superpixel segmentation. IEEE Trans. Image Process. 23(4), 1451–1462 (2014)

    MathSciNet  MATH  Google Scholar 

  58. D.H. Shin, R.H. Park, S. Yang, J.H. Jung, Block-based noise estimation using adaptive Gaussian filtering. IEEE Trans. Consum. Electron. 51(1), 218–226 (2005)

    Google Scholar 

  59. C. Tomasi, R. Manduchi, Bilateral filtering for gray and color images, in IEEE International Conference on Computer Vision (1998), pp. 839–846

  60. N. Venkatanath, D. Praneeth, M.C. Bh, S.S. Channappayya, S.S. Medasani, Blind image quality evaluation using perception based features, in IEEE National Conference on Communications (2015), pp. 1–6

  61. J.S. Walker, Combined image compressor and denoiser based on tree-adapted wavelet shrinkage. Opt. Eng. 41(7), 1520–1528 (2002)

    Google Scholar 

  62. J.H. Wang, L.D. Lin, Improved median filter using minmax algorithm for image processing. Electron. Lett. 33(16), 1362–1363 (1997)

    Google Scholar 

  63. Z. Wang, G. Yuan, Image noise level estimation by neural networks, in International Conference on Information Technology Applications (2015), pp. 692–697

  64. C.H. Wu, H.H. Chang, Superpixel-based image noise variance estimation with local statistical assessment. J. Image Video Process. 2015(1), 38 (2015)

    Google Scholar 

  65. S. Xu, L. Hu, X. Yang, Quality-aware features-based noise level estimator for block matching and three-dimensional filtering algorithm. J. Electron. Imaging 25(1), 1–14 (2016)

    Google Scholar 

  66. S. Xu, X. Zeng, Y. Jiang, Y. Tang, A multiple image-based noise level estimation algorithm. IEEE Signal Process. Lett. 24(11), 1701–1705 (2017)

    Google Scholar 

  67. S. Xu, T. Liu, G. Zhang, Y. Tang, A two-stage noise level estimation using automatic feature extraction and mapping model. IEEE Signal Process. Lett. 26(1), 179–183 (2019)

    Google Scholar 

  68. S.M. Yang, S.C. Tai, Fast and reliable image-noise estimation using a hybrid approach. J. Electron. Imaging 19(3), 033,007 (2010)

    Google Scholar 

  69. K. Zhang, W. Zuo, Y. Chen, D. Meng, L. Zhang, Beyond a Gaussian denoiser: residual learning of deep CNN for image denoising. IEEE Trans. Image Process. 26(7), 3142–3155 (2017a)

    MathSciNet  MATH  Google Scholar 

  70. K. Zhang, W. Zuo, L. Zhang, FFDNet: toward a fast and flexible solution for CNN-based image denoising. IEEE Trans. Image Process. 27(9), 4608–4622 (2018)

    MathSciNet  Google Scholar 

  71. X. Zhang, Y. Xiong, Impulse noise removal using directional difference based noise detector and adaptive weighted mean filter. IEEE Signal Process. Lett. 16(4), 295–298 (2009)

    Google Scholar 

  72. Y. Zhang, N. He, X. Zhen, X. Sun, Image denoising based on the wavelet semi-soft threshold and total variation, in International Conference on Vision, Image and Signal Processing (2017b), pp. 55–62

  73. W. Zhiming, Y. Guobin, et al., Image noise level estimation by neural networks, in International Conference on Materials Engineering and Information Technology Applications (2015), pp. 1–6

  74. X. Zhu, P. Milanfar, A no-reference sharpness metric sensitive to blur and noise, in IEEE International Workshop on Quality of Multimedia Experience (2009), pp. 64–69

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Acknowledgements

The authors are thankful to the Editor and to anonymous Reviewers for their constructive comments and suggestions. This work was supported by Science and Engineering Research Board (SERB), Department of Science and Technology (DST), India [Grant Nos. ECR/2017/000135 and EEQ/2016/000803].

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  1. Department of Electronics and Communication Engineering, Indian Institute of Information Technology Design and Manufacturing, Kancheepuram, Chennai, 600127, India

    Priyanka Kokil & Turimerla Pratap

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  1. Priyanka Kokil
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Kokil, P., Pratap, T. Additive White Gaussian Noise Level Estimation for Natural Images Using Linear Scale-Space Features. Circuits Syst Signal Process 40, 353–374 (2021). https://doi.org/10.1007/s00034-020-01475-x

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