Abstract
Block-matching and 3D filtering algorithm (BM3D) is the current state-of-the-art for image denoising. This algorithm has a high capacity to achieve better noise removal results as compared with other existing algorithms. Nevertheless, there is still much room for improvement in this algorithm to achieve more attractive results. To address the shortcomings of BM3D filtering, our paper algorithm makes the following contributions: Firstly, the traditional hard-thresholding of the BM3D method is substituted by an adaptive filtering technique. This technique has a high capacity to acclimate and change according to the noise intensity. More accurately, in the proposed algorithm, soft-thresholding is applied to the high-noise areas, whereas the total variation filter is applied to the light-noise areas. The self-adaptation and stability of the proposed adaptive filtering technique have enabled this technique to achieve optimal noise reduction performance and preserve the high spatial frequency detail (e.g. sharp edges). Secondly, since too small threshold leaves the most amount of the noise without removing, in contrast, a too large threshold fails to maintain the significant information of the image such as edges. Accordingly, in our proposed algorithm, applying the adaptive filtering function in the first stage is based on an adaptive threshold. This threshold is adaptable and changeable according to the amount of the noise. Thirdly, an Adaptive Weight Function (AWF) that depends on the spatial distance between the reference patch and its candidate patches, is adopted in the proposed dissimilarity measurement. When the distance between the reference patch and the candidate patch is small enough (nearby patches), AWF adopts the proposed dissimilarity measurement in computing this distance. On the other hand, when the distance between the reference patch and the candidate patch is large enough (where the candidate patches are located out of the region of the reference patch), AWF adopts the k-means clustering and the Formula (21) in computing this distance. The k-means clustering is adopted at the last estimate. Utilizing the k-means clustering to partition the image into several regions and identify the boundaries between these regions obliges the block matching to search within the region of the reference patch, which leads to reducing the risk of finding poor matching. Our proposed filter is tested on various digital images for different filtering quality measures. This filter shows significant improvements over BM3D filtering in terms of visual quality, Peak Signal-to-Noise Ratio (PSNR) index, and Structural Similarity (SSIM) index.
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References
Babu YMM, Subramanyam MV, Prasad MNG (2015) A modified BM3D algorithm for SAR image despeckling. In: Proceedings of 4th International conference on eco-friendly computing and communication systems, vol 70, pp 69–75
Buades A, Coll B, Morel JM (2005) A non-local algorithm for image denoising. In: Proceedings of IEEE computer society conference on computer vision and pattern recognition, vol 2, pp 60–65
Chatterjee P, Milanfar P (2012) Patch-based near-optimal image denoising. IEEE Trans Image Process 21(4):1635–1649
Chen LL, Gou SP, Yao Y, Ba J, Jiao L, Sheng K (2016) Denoising of low dose CT image with context-based BM3D. In: Proceedings of 10the IEEE Region Conference, Singapore, pp 682–685
Chen Q, Wu D (2010) Image denoising by bounded block matching and 3D filtering. Signal Process 90(9):2778–2783
Dabov K, Foi A, Katkovnik V, Egiazarian K (2007) Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans Image Process 16 (8):2080–2095
Dabov K, Foi A, Katkovnik V, Egiazarian K (2009) BM3D image denoising with shape-adaptive principal component analysis. Proc Workshop on Signal Processing with Adaptive Sparse Structured Representations, pp 1–6
Danielyan A, Katkovnik V, Egiazarian K (2012) BM3D frames and variational image deblurring. IEEE Trans Image Process 21(4):1715–1728
Djurović I (2016) BM3D filter in salt-and-pepper noise removal. EURASIP Journal on Image and Video Processing 13:1–11
Dogra A, Agrawal S, Goyal B, Khandelwal N, Ahuja CK (2016) Color and grey scale fusion of osseous and vascular information. J Comput Sci 17:103–114
Dogra A, Goyal B, Agrawal S (2017) From multi-scale decomposition to non-multi-scale decomposition methods: a comprehensive survey of image fusion techniques and its applications. IEEE Access 5:16040–16067
Dong W, Zhang L, Shi G, Li X (2013) Nonlocally centralized sparse representation for image restoration. IEEE Trans Image Process 22(4):1620–1630
Eksioglu EM (2016) Decoupled algorithm for MRI reconstruction using nonlocal block matching model: BM3D-MRI. Journal of Mathematical Imaging and Vision 56 (3):430–440
Fredj AH, Malek J (2017) GPU-based anisotropic diffusion algorithm for video image denoising. Microprocess Microsyst 53:190–201
Gao J, Wang Q (2016) BM3D image denoising algorithm based on k-means clustering. Advanced Graphic Communications and Media Technologies (Lecture Notes in Electrical Engineering ) 417:265–272
Goyal B, Dogra A, Agrawal S, Sohi BS (2018) Two-dimensional gray scale image denoising via morphological operations in NSST domain & bitonic filtering. Futur Gener Comput Syst 82:158–175
Hasan M, El-Sakka MR (2018) Improved BM3D image denoising using SSIM-optimized Wiener filter. EURASIP Journal on Image and Video Processing 25:1–12
Hou Y, Shen D (2018) Image denoising with morphology- and size-adaptive block-matching transform domain filtering. EURASIP Journal on Image and Video Processing 59:1–16
Huang X-L, Tang X, Huan X, Wang P, Wu J (2018) Improved KMV-Cast with BM3D denoising. Mobile Netw Appl 23(1):100–107
Jia DX, Ge YR (2012) Underwater image denoising algorithm based on nonsubsampled Contourlet transform and total variation. In: Proceedings of the IEEE international conference on computer science and information processing, pp 76–80
Katkovnik V, Ponomarenko M, Egiazarian K (2017) Sparse approximations in complex domain based on BM3D modeling. Signal Process 141:96–108
Knausand C, Zwicker M (2014) Progressive image denoising. IEEE Trans Image Process 23(7):3114–3125
Kuans C, Zwicker B (2013) Dual-domain image denoising. In: Proceedings of 20th IEEE International Conference on Image Processing (ICIP), pp 440–444
Lee TH, Song BC (2011) De-noising algorithm using sparse 3D transform-domain collaborative filtering and adaptive soft thresholding. In: Proceedings of IEEE 15th International Symposium on of Consumer Electronics (ISCE), pp 128–131
Li Y, Chen R-M, Liang S (2011) A new image denoising method based on shearlet shrinkage and improved total variation. In: Proceedings of international conference on intelligent science and intelligent data engineering, pp 382–388
Maggioni M, Monge E, Foi A (2014) Joint removal of random and fixed-pattern noise through spatiotemporal video filtering. IEEE Trans Image Process 23(10):4282–4296
Mairal J, Bach F, Ponce J, Sapiro G, Zisserman A (2009) Non-local sparse models for image restoration. In: Proceedings of 12th IEEE international conference on computer vision, pp 2272–2279
Mamaev N, Yurin D, Krylov A (2018) Choice of the parameter for BM3D denoising algorithm using no- reference metric. In: Proceedings of 7th European Workshop on Visual Information Processing (EUVIP), Finland, pp 1–6
Mevenkamp N, Binev P, Dahmen W, Voyles PM, Yankovich AB, Berkels B (2015) Poisson noise removal from high-resolution STEM images based on periodic block matching. Advanced Structural and Chemical Imaging 1(3):1–19
Naveen S, Aiswarya VA (2015) Image denoising by Fourier block processing and Wiener filtering. Procedia Computer Science 58:683–690
Perona P, Malik J (1990) Scale space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639
Ping X, Bingqiang C, Lingyun X, Jingcheng Z, Lei Z, Hangbo D (2019) A new MNF-BM4D denoising algorithm based on guided filtering for hyperspectral images. ISA Trans 92:315–324
Rafsanjani HK, Sedaaghi MH, Saryazdi S (2016) Efficient diffusion coefficient for image denoising. Computers and Mathematics with Applications 72(4):893–903
Tikhonov AN, Arsenin VY (1977) Solutions of Ill-Posed problem, Winston and Sons, Washington, D.C.
Wang HZ, Qian LY, Zhao JT (2010) An image denoising method based on fast discrete curvelet transform and total variation. In:Proceedings of the IEEE international conference on software processing, pp 1040–1043
Wang X, Zhang D, Zhu M, Ji Y, Wang J (2015) Improved image denoising based on 3D collaborative filtering. International Journal of Signal Processing Image Processing and Pattern Recognition 8(4):227–236
Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13 (4):600–612
Yahya AA, Tan J, Hu M (2014) A blending method based on partial differential equations for image denoising. Multimed Tools Appl 73(3):1843–1862
Yahya AA, Tan J, Su B, Liu K, Hadi ANr (2019) Image noise reduction based on adaptive thresholding and clustering. Multimed Tools Appl 78(11):15545–15573
Yahya AA, Tan J, Su B, Liu K, Hadi AN (2017) Image noise reduction based on applying adaptive thresholding onto PDEs methods. The Journal of Engineering 2017(6):1–8
Yang D, Sun J (2018) BM3D-Net: A convolutional neural network for transform-domain collaborative filtering. IEEE Signal Processing Letters 25(1):55–59
Yang J, Zhang X, Yue H, Cai C, Hou C (2019) IBM3D: Integer BM3D for efficient image denoising. Circuits, Systems, and Signal Processing 38(2):750–763
Zhang C, Chen Y, Duanmu C, Yang Y (2016) Image denoising by using PDE and GCV in tetrolet transform domain. Engineering ApplicationsofArtificial Intelligence 48:204–229
Zhang X, Ye W (2017) An adaptive fourth-order partial differential equation for image denoising. Computers and Mathematics with Applications 74(10):2529–2545
Zhong H, Ma K, Zhou Y (2015) Modified BM3D algorithm for image denoising using nonlocal centralization prior. Signal Process 106:342–347
Zhou S, Lou Z, Hu YH, Jiang H (2018) Multiple view image denoising using 3D focus image stacks. Comput Vis Image Underst 171:34–47
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This work is supported by ANHUI Province Key Laboratory of Affective Computing & Advanced Intelligent Machine, Grant (No.ACAIM180201).
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Yahya, A.A., Tan, J., Su, B. et al. BM3D image denoising algorithm based on an adaptive filtering. Multimed Tools Appl 79, 20391–20427 (2020). https://doi.org/10.1007/s11042-020-08815-8
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DOI: https://doi.org/10.1007/s11042-020-08815-8