Circuits, Systems, and Signal Processing

, Volume 38, Issue 4, pp 1654–1683 | Cite as

A Nonlinear Coupled Diffusion System for Image Despeckling and Application to Ultrasound Images

  • Subit K. Jain
  • Rajendra K. RayEmail author
  • Arnav Bhavsar


Despite extensive availability of filters for denoising, speckle noise suppression remains a challenging task. Speckle noise also hinders tasks such as efficient extraction of features, recognition, analysis, detection of edges, etc. Therefore, in this paper, motivated by the impressive performance of time delay regularization in additive noise removal, we develop a class of nonlinear diffusion-based coupled partial differential equation models for multiplicative noise removal. This denoising framework considers separate partial differential equations to handle diffusion function as well as fidelity term. By using a maximum a posteriori regularization approach, we can derive an energy functional and study the associated evolution problem which corresponds to the denoised image we want to recover. We then evaluate the effectiveness of our model with several standard test images and real ultrasound images. Qualitative and quantitative studies confirm that the proposed model is robust in comparison with state-of-the-art approaches. The denoised images have appealing visual characteristics with different levels of noise and textures while preserving the important details of the original image.


Despeckling Speckle noise Nonlinear diffusion Coupled system Numerical scheme Filtering Ultrasound imaging 

Mathematics Subject Classification

35K55 65M06 68U10 


Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Subit K. Jain
    • 1
    • 2
  • Rajendra K. Ray
    • 1
    Email author
  • Arnav Bhavsar
    • 3
  1. 1.School of Basic SciencesIndian Institute of Technology MandiMandiIndia
  2. 2.Department of MathematicsNational Institute of Technology HamirpurHamirpurIndia
  3. 3.School of Computing and Electrical EngineeringIndian Institute of Technology MandiMandiIndia

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