A Variational Model for Mixed Noise Removal Using Weberized Total Variation Regularization

Main Article Content

Sopida Sukyankij
Siriwan Chankan

Abstract

The problem of removing noise from digital images has attracted considerable attention as it can improve image quality and the visual interpretability of information. In the case of medical imaging, effective denoising can lead to more accurate diagnoses and reduce the likelihood of errors. In this research, the researchers developed the ASN-WTV model to eliminate mixed additive and speckle noise by using the data fitting term of the ROF model to eliminate additive noise, the data fitting term of the KKWV model to eliminate speckle noise, and the Weberized total variation regularization. Two numerical methods, namely the fixed point method and the split Bregman method, were presented to find the solution of the ASN-WTV model and compare the performance of the resulting images with that of the KKWV-TVL model. The numerical experimental results showed that the ASN-WTV model provided better quality output images than the KKWV-TVL model and that the split Bregman method performed better than the fixed point method.

Article Details

How to Cite
Sukyankij, S., & Chankan, S. (2025). A Variational Model for Mixed Noise Removal Using Weberized Total Variation Regularization. KKU Science Journal, 53(2), 170–184. https://doi.org/10.14456/kkuscij.2025.14
Section
Research Articles

References

ศิริวรรณ จันทร์แก่น และ โสภิดา สุขญาณกิจ. (2567a). ตัวแบบเชิงการแปรผันที่ปรับปรุงสำหรับกำจัดสัญญาณรบกวนออก จากภาพที่เกิดจากสัญญาณรบกวนแบบผสม. วารสารวิทยาศาสตร์และเทคโนโลยี 32(5): 1 – 16.

ศิริวรรณ จันทร์แก่น และ โสภิดา สุขญาณกิจ. (2567b). การกำจัดสัญญาณรบกวนแบบการบวกและแบบการคูณออกจากภาพโดยใช้วิธีการปริทเบรกแมน. วารสารวิทยาศาสตร์และเทคโนโลยีมหาวิทยาลัยราชภัฏบุรีรัมย์ 8(1): 15 – 28.

Chankan, S., Chumchob, N. and Sroisangwan, P. (2023). A novel image denoising approach based on a curvature-based regularization. Signal Image and Video Processing 17: 2129 - 2136.

Chumchob, N., Chen, K. and Brito-Loeza, C. (2013). A new variational model for removal of combined additive and multiplicative noise and a fast algorithm for its numerical approximation. International

Journal of Computer Mathematics 90(1): 140 – 161.

Chumchob, N. and Prakit, I. (2019). An improved variational model and its numerical solutions for speckle noise removal from real ultrasound image. Journal of Computational Mathematics 37(2): 1 - 39.

De los Reyes, J.C., and Schnlieb, C.B. (2013). Image denoising learning the noise model via nonsmooth PDE- constrained optimization. Inverse Problems and Imaging 7(4): 1183 - 1214.

Goldstein, T. and Osher, S. (2009). The split Bregman method for l1-regularized problems. SIAM Journal on Sciences 2(2): 323 - 343.

Jin, Z. and Yang, X. (2010). Analysis of a new variational model for multiplicative noise removal. Journal of Mathematical Analysis and Applications 362: 415 – 426.

Kang, M., Jung, M. and Kang, M. (2018). Higher-order regularization based image restoration with automatic regularization parameter selection. Computers and Mathematics with Applications 76: 58 - 80.

Krissian, K., Kikinis, R., Westin, C.F. and Vosburgh, K. (2005). Speckle constrained filtering of ultrasound images. IEEE Computer Society Conference on Computer Vision and Pattern Recognition 2: 547 – 552.

Kumar, B.B.S. and Satyanarayana, P.S. (2022). A mixture of Noise Image Denoising using Sevenlets Wavelet Techniques. Trends in Sciences 19(10): 4186 - 4186. doi: 10.48048/tis.2022.4186.

Lysaker, M., Lundervold, A. and Tai, X.C. (2003). Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Transactions on Image Processing 12(12): 1579 – 1590.

Rudin, L., Lions, P.L. and Osher, S. (2003). Multiplicative denoising and deblurring: theory and algorithms. In: Geometric Level Sets in Imaging, Vision, and Graphics. New York: Springer. 103 - 119

Rudin, L., Osher, S. and Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60(1-4): 259 - 268.

Shama, M.G., Huang, T.Z., Liu, J. and Wang, S. (2016). A convex total generalized variation regularized model for multiplicative noise and blur removal. Applied Mathematics and Computation 276: 109 - 121.

Tavakkol. E., Hosseini, S.M. and Hosseini, A.R. (2019). A new regularization term based on second order total generalized variational for image denoising problems. Iranian Journal of Numerical Analysis and Optimization 9(2): 141 - 163.

Thao, T.T.T., Pham, C.T., Kopylov, A.V. and Nguyen, V.N. (2019). An adaptive variational model for medical images restoration. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences 12(2): 219 - 224.

You, Y.L. and Kaveh, M. (2000). Fourth-order partial differential equations for noise removal. IEEE Transactions on Image Processing 9(10): 1723 - 1730.