Abstract
This paper presents a new method for image denoising based on a two-dimensional empirical mode decomposition algorithm and semi-adaptive diffusion coefficient in anisotropic diffusion filter. The proposed model uses a local difference value method to compare and replace some pixels of the noisy image with a pre-processed image that has been passed through a Gaussian filter. A bi-dimensional empirical mode decomposition algorithm is then employed to decompose the noise-contaminated image into its intrinsic mode functions in which high-frequency and low-frequency noise components are removed by applying a diffusion filter. The filter has a semi-adaptive threshold in the diffusion coefficient with parameters like connectivity, conductance function, number of iterations, and gradient threshold. The semi-adaptive threshold for each diffusion is implemented by introducing gradient values in the threshold of the corrupted image. The image is then reconstructed from these denoised intrinsic mode functions. The performance of the proposed method is assessed in terms of peak signal-to-noise ratio, mean square error, and structural similarity index and is compared with the existing methodologies. The results obtained from experimentation indicate that the proposed method is efficient in both feature retention and noise suppression.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Babaud, J., Witkin, A. P., Baudin, M., & Duda, R. O. (1986). Uniqueness of the Gaussian Kernel for Scale-Space Filterng. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI, 8(1), 26–33. https://doi.org/10.1109/TPAMI.1986.4767749
Bernini, M. B., Federico, A., & Kaufmann, G. H. (2008). Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition. Applied Optics, 47(14), 2592–2598. https://doi.org/10.1364/AO.47.002592
Bernini, M. B., Federico, A., & Kaufmann, G. H. (2009). Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform. Applied Optics, 48(36), 6862–6869. https://doi.org/10.1364/AO.48.006862
Bhuiyan, S. M. A., Adhami, R. R., & Khan, J. F. (2008). Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation. EURASIP Journal on Advances in Signal Processing, 2008, 1–18. https://doi.org/10.1155/2008/728356
Bhuiyan, S. M. A., Attoh-Okine, N. O., Barner, K. E., Ayenu-Prah, A. Y., & Adhami, R. R. (2009). Bidimensional empirical mode decomposition using various interpolation techniques. Advances in Adaptive Data Analysis, 1(2), 309–338. https://doi.org/10.1142/S1793536909000084
Catté, F., Lions, P.-L., Morel, J.-M., & Coll, T. (1992). Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical Analysis, 29(1), 182–193. https://doi.org/10.1137/0729012
Chan, R. H., Ho, C.-W., & Nikolova, M. (2005). Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization. IEEE Transactions on Image Processing, 14(10), 1479–1485. https://doi.org/10.1109/TIP.2005.852196
Chao, S. M., & Tsai, D. M. (2010a). An improved anisotropic diffusion model for detail- and edge-preserving smoothing. Pattern Recognition Letters, 31(13), 2012–2023. https://doi.org/10.1016/j.patrec.2010.06.004
Chao, S. M., & Tsai, D. M. (2010b). Anisotropic diffusion with generalized diffusion coefficient function for defect detection in low-contrast surface images. Pattern Recognition, 43(5), 1917–1931. https://doi.org/10.1016/j.patcog.2009.12.005
Chen, D., MacLachlan, S., & Kilmer, M. (2011). Iterative parameter-choice and multigrid methods for anisotropic diffusion denoising. SIAM Journal on Scientific Computing, 33(5), 2972–2994. https://doi.org/10.1137/100796066
Damerval, C., Meignen, S., & Perrier, V. (2005). A fast algorithm for bidimensional EMD. IEEE Signal Processing Letters, 12(10), 701–704. https://doi.org/10.1109/LSP.2005.855548
Deng, G., & Cahill, L. W. (1993). An adaptive Gaussian filter for noise reduction and edge detection. In: 1993 IEEE Conference Record Nuclear Science Symposium and Medical Imaging Conference, pp. 1615–1619. https://doi.org/10.1109/NSSMIC.1993.373563.
Dragomiretskiy, K., & Zosso, D. (2014). Variational mode decomposition. IEEE Transactions on Signal Processing, 62(3), 531–544. https://doi.org/10.1109/TSP.2013.2288675
Florencio, D. A. F., & Schafer, R. W. (1994). Decision-based median filter using local signal statistics. In: Visual Communications and Image Processing’94 (Vol. 2308, pp. 268–275). SPIE. https://doi.org/10.1117/12.185969
Gilboa, G., Sochen, N., & Zeevi, Y. Y. (2006). Estimation of optimal PDE-based denoising in the SNR sense. IEEE Transactions on Image Processing, 15(8), 2269–2280. https://doi.org/10.1109/TIP.2006.875248
Gonzalez, R. C., & Woods, R. E. (2002). Digital Image Processing. Prentice-Hall.
Gupta, H., Singh, H., Kumar, A., & Vishwakarma, A. (2021). Pixel corrected adaptive conductance function based diffusion filter and image denoising using bi-dimensional empirical mode decomposition. In: Proceedings 2021 International Conference on Control, Automation, Power and Signal Processing, CAPS 2021. https://doi.org/10.1109/CAPS52117.2021.9730521
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Snin, H. H., Zheng, Q., Yen, N. C., Tung, C. C., & Liu, H. H. (1998). The empirical mode decomposition and the Hubert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society a: Mathematical, Physical and Engineering Sciences, 454(1971), 903–995. https://doi.org/10.1098/rspa.1998.0193
Ibrahim, H., Kong, N. S. P., & Ng, T. F. (2008). Simple adaptive median filter for the removal of impulse noise from highly corrupted images. IEEE Transactions on Consumer Electronics, 54(4), 1920–1927. https://doi.org/10.1109/TCE.2008.4711254
Khan, N. U., Arya, K. V., & Pattanaik, M. (2014). Edge preservation of impulse noise filtered images by improved anisotropic diffusion. Multimedia Tools and Applications, 73(1), 573–597. https://doi.org/10.1007/s11042-013-1620-8
Koenderink, J. J. (1984). The structure of images. Biological Cybernetics, 50(5), 363–370. https://doi.org/10.1007/BF00336961
Kommuri, S. V. R., Singh, H., Kumar, A., & Bajaj, V. (2020). Bidimensional empirical mode decomposition-based diffusion filtering for image denoising. Circuits, Systems, and Signal Processing, 39(10), 5127–5147. https://doi.org/10.1007/s00034-020-01404-y
Luo, W. (2006). Efficient removal of impulse noise from digital images. IEEE Transactions on Consumer Electronics, 52(2), 523–527. https://doi.org/10.1109/TCE.2006.1649674
Mafi, M., Martin, H., Cabrerizo, M., Andrian, J., Barreto, A., & Adjouadi, M. (2019). A comprehensive survey on impulse and Gaussian denoising filters for digital images. Signal Processing, 157, 236–260. https://doi.org/10.1016/j.sigpro.2018.12.006
Mrázek, P. (2001). Selection of optimal stopping time for nonlinear diffusion filtering. In: Scale-Space and Morphology in Computer Vision: Third International Conference, Scale-Space 2001 Vancouver, Canada, July 7–8, 2001 Proceedings 3 (pp. 290–298). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-47778-0_26
Nunes, J. C., Bouaoune, Y., Delechelle, E., Niang, O., & Bunel, P. (2003). Image analysis by bidimensional empirical mode decomposition. Image and Vision Computing, 21(12), 1019–1026. https://doi.org/10.1016/S0262-8856(03)00094-5
Perona, P., & Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7), 629–639. https://doi.org/10.1109/34.56205
Prasath, V. B. S., & Singh, A. (2010). Well-posed inhomogeneous nonlinear diffusion scheme for digital image denoising. Journal of Applied Mathematics. https://doi.org/10.1155/2010/763847
Rosenfeld, A., & Thurston, M. (1971). Edge and curve detection for visual scene anaiysis. IEEE Transactions on Computers, C, 20(5), 562–569. https://doi.org/10.1109/T-C.1971.223290
Rudin, L. I., Osher, S., & Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica d: Nonlinear Phenomena, 60(1–4), 259–268. https://doi.org/10.1016/0167-2789(92)90242-F
Singh, H., Kommuri, S. V. R., Kumar, A., & Bajaj, V. (2021). A new technique for guided filter based image denoising using modified cuckoo search optimization. Expert Systems with Applications, 176, 114884. https://doi.org/10.1016/J.ESWA.2021.114884
Singh, H., Kumar, A., Balyan, L. K., & Lee, H. N. (2020). Texture-Dependent optimal fractional-order framework for image quality enhancement through memetic inclusions in cuckoo search and sine-cosine algorithms. Studies in Computational Intelligence, 873, 19–45. https://doi.org/10.1007/978-981-15-1362-6_2
Singh, H., Kumar, A., Balyan, L. K., & Lee, H. N. (2022). Spatial entropy quartiles-based texture-aware fractional-order unsharp masking for visibility enhancement of remotely sensed images. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52(4), 2275–2288. https://doi.org/10.1109/TSMC.2021.3049402
Srinivasan, K. S., & Ebenezer, D. (2007). A new fast and efficient decision-based algorithm for removal of high-density impulse noises. IEEE Signal Processing Letters, 14(3), 189–192. https://doi.org/10.1109/LSP.2006.884018
Toh, K. K. V., Ibrahim, H., & Mahyuddin, M. N. (2008). Salt-and-pepper noise detection and reduction using fuzzy switching median filter. IEEE Transactions on Consumer Electronics, 54(4), 1956–1961. https://doi.org/10.1109/TCE.2008.4711258
Toh, K. K. V., & Isa, N. A. M. (2009). Noise adaptive fuzzy switching median filter for salt-and-pepper noise reduction. IEEE Signal Processing Letters, 17(3), 281–284. https://doi.org/10.1109/LSP.2009.2038769
Tomasi, C., & Manduchi, R. (1998). Bilateral filtering for gray and color images. In: Sixth International Conference on Computer Vision (IEEE Cat. No. 98CH36271), 839–846. https://doi.org/10.1109/ICCV.1998.710815
Trusiak, M., Patorski, K., & Wielgus, M. (2012). Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform. Optics Express, 20(21), 23463–23479. https://doi.org/10.1364/oe.20.023463
Trusiak, M., Wielgus, M., & Patorski, K. (2014). Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition. Optics and Lasers in Engineering, 52, 230–240. https://doi.org/10.1016/j.optlaseng.2013.06.003
Vasanth, K., & Jawahar Senthil Kumar, V. (2015). Decision-based neighborhood-referred unsymmetrical trimmed variants filter for the removal of high-density salt-and-pepper noise in images and videos. Signal, Image and Video Processing, 9(8), 1833–1841. https://doi.org/10.1007/s11760-014-0665-0
Voci, F., Eiho, S., Sugimoto, N., & Sekibuchi, H. (2004). Estimating the gradient in the Perona-Malik equation. IEEE Signal Processing Magazine, 21(3), 39–65. https://doi.org/10.1109/MSP.2004.1296541
Wang, Y. Q., Guo, J., Chen, W., & Zhang, W. (2013). Image denoising using modified Perona-Malik model based on directional Laplacian. Signal Processing, 93(9), 2548–2558. https://doi.org/10.1016/j.sigpro.2013.02.020
Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004). Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4), 600–612. https://doi.org/10.1109/TIP.2003.819861
Wielgus, M., & Patorski, K. (2014). Denoising and extracting background from fringe patterns using midpoint-based bidimensional empirical mode decomposition. Applied Optics, 53(10), B215–B222. https://doi.org/10.1364/ao.53.00b215
Xu, J., Jia, Y., Shi, Z., & Pang, K. (2016). An improved anisotropic diffusion filter with semi-adaptive threshold for edge preservation. Signal Processing, 119, 80–91. https://doi.org/10.1016/j.sigpro.2015.07.017
Yao, Y., Sfarra, S., Ibarra-Castanedo, C., You, R., & Maldague, X. P. V. (2017). The multi-dimensional ensemble empirical mode decomposition (MEEMD). Journal of Thermal Analysis and Calorimetry, 128(3), 1841–1858. https://doi.org/10.1007/s10973-016-6082-6
Zhang, P., & Li, F. (2014). A new adaptive weighted mean filter for removing salt-and-pepper noise. IEEE Signal Processing Letters, 21(10), 1280–1283. https://doi.org/10.1109/LSP.2014.2333012
Zhou, Y., & Li, H. (2011). Adaptive noise reduction method for DSPI fringes based on bi-dimensional ensemble empirical mode decomposition. Optics Express, 19(19), 18207–18215. https://doi.org/10.1364/oe.19.018207
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Gupta, H., Singh, H., Kumar, A. et al. Adaptive conductance function based improved diffusion filtering and bi-dimensional empirical mode decomposition based image denoising. Multidim Syst Sign Process 34, 81–125 (2023). https://doi.org/10.1007/s11045-022-00850-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11045-022-00850-y