Abstract
Image denoising is an essential pre-processing step in medical imaging systems. In this paper, a new adaptive total variation based image regularization algorithm using structure tensor matrices is proposed to eliminate the Rician noise present in the magnetic resonance images. In the proposed algorithm a regularization term based on a variable exponent is used. The variable exponent as well as the regularization parameter in the energy functional both depend on the edge stopping function value. The edge stopping function value is based on the trace of structure tensor matrix. In the noisy inner region the value of the variable exponent becomes two that is in the inner region square of the gradient that is used as a regularization term. So the adaptive model behaves like a Tikhonov model and strong smoothing takes place in the flat inner region. At the object boundaries the variable exponent’s value becomes one that is simply a gradient of an image that is used as a regularizing term. So the model behaves like a Rudin-Osher-Fatemi model and the edges are preserved well. The weight of the fidelity term in the functional is also adaptively selected depending on whether a pixel belongs to an edge or the inner region. The weight of the fidelity term is set to a large value at the edges and the small value is in the inner region. The algorithm is found to be very efficient in removing Rician noise present in the brain’s magnetic resonance images compared to the other variable exponent based adaptive total variation models such as Chen model, Erik model, Chambolle model and Qiang Chen total variation model using difference curvature both qualitatively as well as quantitatively.
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References
Vogel CR, Oman ME (1998) Fast robust total variation based reconstruction of noisy, blurred images. IEEE Trans Image Process 7
Karthik S, Hemanth VK, Soman KP, Balaji V, Sachin Kumar S, Sabarimalai Manikandan M (2012) Directional total variation filtering based image denoising method. Int J Comput Sci Issues 9(2, No 1). ISSN 1694-0814
Beck A, Teboulle M (2009) Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans Image Process 18(11):2419–2434
Fan L, Zhang F, Fan H, Zhang C (2019) Brief review of image denoising techniques. Vis Comput Ind, Biomed Art 2:7. https://doi.org/10.1186/s42492-019-0016-7
Chambolle (2004) An algorithm for total variation minimization and applications. J Math Imaging Vis 20:89–97
Zhao Y, Liu JG, Zhang B, Hongn W, Wu Y-R (2015) Adaptive total variation regularization based SAR image depeckling and despleckling evaluation index. IEEE Trans Geosci Remote Sens 53(5):2765–2774
Liu et al (2016) Hybrid regularizers-based adaptive anisotropic diffusion for image denoising. SpringerPlus. https://doi.org/10.1186/s40064-016-1999-6
Zheng H, Hellwich O Adaptive data-driven regularization for variational image restoration in the BV space. Computer Vision & Remote Sensing, Berlin University of Technology, Berlin
Bresson X, Laurent T, Uminsky D, von Brecht JH (2013) An adaptive total variation algorithm for computing the balanced cut of a graph. Math Commons
Chambolle A, Lions P-L (1997) Image recovery via total variation minimization and related problems. Numer Math 76:167–188
Bollt EM, Chartrand R, Esedoglu S, Schultz P, Vixie KR (2009) Graduated adaptive image denoising: local compromise between total variation and isotropic diffusion. J Adv Comput Math 31(1–3):61–85
Chen, Levine, Rao (2004) Variable exponent, linear growth functionals in image processing. SIAM J Appl Math 66:1383–1406
Sachinkumar S, Mohan N, Prabaharan P, Soman KP (2016) Total variation denoising based approach for R-peak detection in ECG signals. Procedia Comput Sci 93:697–705
Soman KP, Poornachandran P, Athira S, Harikumar K (2015) Recursive variational mode decomposition algorithm for real time power signal decomposition. Procedia Technol 21:540–546
Chen Q, Montesinos P, Sun QS, Heng PA, Xia DS (2010) Adaptive total variation denoising based on difference curvature. Image Vis Comput 28(3):298–306
Kamalaveni V, Veni S, Narayanankutty KA (2017) Improved self-snake based anisotropic diffusion model for edge preserving image denoising using structure tensor. Multimed Tools Appl 76(18):18815–18846
Brox T, Van den Boomgaard R, Lauze FB, Van de Weijer J, Weickert J, Mrazek P, Kornprobst P (2006) Adaptive structure tensors and their applications. In: Weickert J, Hagen H (eds) Visualization and image processing of tensor fields, vol 1. Springer, pp 17–47
Wang H, Chen Y, Fang T, Tyan J, Ahuja N (2006) Gradient adaptive image restoration and enhancement. In: IEEE international conference on image processing (ICIP), Atlanta, GA
Wu J, Feng Z, Ren Z (2014) Improved structure-adaptive anisotropic filter based on a nonlinear structure tensor. Cybern Inf Technol 14(1):112–127
Kamalaveni V, Narayanankutty KA, Veni S (2016) Performance comparison of total variation based image regularization algorithms. Int J Adv Sci Eng Inf Techol 6(4). Scopus and Elsevier indexed
Prasath S, Thanh DNH (2019) Structure tensor adaptive total variation for image restoration. Turk J Electr Eng Comput Sci 27(2):1147–1156. https://doi.org/10.3906/elk-1802-76
Li C, Liu C, Wang Y (2013) Texture image denoising algorithm based on structure tensor and total variation. In: 5th international conference on intelligent networking and collaborative systems (INCoS)
Faouzi B, Amiri H (2011) Image denoising using non linear diffusion tensors. In: 2011 8th international multi-conference on systems, signals & devices
Wu X, Xie M, Wu W, Zhou J (2013) Nonlocal mean image denoising using anisotropic structure tensor. Adv Opt Technol 3013:794728. https://doi.org/10.1155/2013/794728
You YL, Kavesh M (2000) Fourth-order partial differential equations for noise removal. IEEE Trans Image Process 9(10):1723–1730
AksamIftikhar M et al (2014) Robust brain MRI denoising and segmentation using enhanced non-local means algorithm. Int J Imaging Syst Technol 24:54–66
Getreuer P, Tong M, Vese LA (2011) A variational model for the restoration of MR images corrupted by blur and Rician noise. In: Bebis G et al (eds) Advances in visual computing. ISVC 2011. Lecture notes in computer science, vol 6938. Springer, Berlin, Heidelberg
Yang J et al (2015) Brain MR image denoising for Rician noise using pre-smooth non local mean filter. BioMed Eng OnLine
Mohan J, Krishnaveni V, Guo Y (2013) A new neutrosophic approach of Wiener filtering for MRI denoising. Meas Sci Rev 13(4)
Singh, Ghanapriya, and Rawat T (2013) Color image enhancement by linear transformations solving out of gamut problem. Int J Comput Appl 67(14):28–32
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Kamalaveni, V., Veni, S., Narayanankuttty, K.A. (2023). Adaptive Total Variation Based Image Regularization Using Structure Tensor for Rician Noise Removal in Brain Magnetic Resonance Images. In: Singh, P., Singh, D., Tiwari, V., Misra, S. (eds) Machine Learning and Computational Intelligence Techniques for Data Engineering. MISP 2022. Lecture Notes in Electrical Engineering, vol 998. Springer, Singapore. https://doi.org/10.1007/978-981-99-0047-3_50
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