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<p>In this study, a new adaptive regularization method is introduced for the combined linear (quadratic) and nonlinear diffusion model to denoise color images. In addition, data normalization is introduced as a complementary ingredient in the design of a variational model. Such complementary data regularization creates a good balance between the diffusion and data parts. The direct application of variational calculus yields a partial differential equation with black boundary conditions. The numerical solution of the equivalent time-dependent problem for the obtained continuous problem was determined at the initial stage. At this stage an adaptive regularization parameter <i>w</i>(<i>x</i>,&#xa0;<i>y</i>) is introduced to control the diffusion process by identifying the image discontinuities like edges and smooth regions in an intelligent manner which is a novel and very interesting aspect of this work. In this way, the method produces a regularized version of the given noisy image. Experimental results show that the proposed method encourages the effective noise removal process in a locally adaptive way and ensures the preservation of significant image features like edges. To validate the results in this work, some confidence measures are considered as quantitative and qualitative metrics like the peak signal-to-noise ratio, structural similarity index, and computational time. The results are compared with those of the well-rated denoising methods.</p>

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Adaptive regularization for combined linear and nonlinear color image diffusion with normalized data

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • Muzaffar Bashir Arain,
  • Khuda Bux Amur,
  • Nek Muhammad Katbar,
  • Fikadu Tesgera Tolasa

摘要

In this study, a new adaptive regularization method is introduced for the combined linear (quadratic) and nonlinear diffusion model to denoise color images. In addition, data normalization is introduced as a complementary ingredient in the design of a variational model. Such complementary data regularization creates a good balance between the diffusion and data parts. The direct application of variational calculus yields a partial differential equation with black boundary conditions. The numerical solution of the equivalent time-dependent problem for the obtained continuous problem was determined at the initial stage. At this stage an adaptive regularization parameter w(x, y) is introduced to control the diffusion process by identifying the image discontinuities like edges and smooth regions in an intelligent manner which is a novel and very interesting aspect of this work. In this way, the method produces a regularized version of the given noisy image. Experimental results show that the proposed method encourages the effective noise removal process in a locally adaptive way and ensures the preservation of significant image features like edges. To validate the results in this work, some confidence measures are considered as quantitative and qualitative metrics like the peak signal-to-noise ratio, structural similarity index, and computational time. The results are compared with those of the well-rated denoising methods.