Speckle noise occurs in a wide range of medical images due to sampling and digital degradation. Removing speckle noise from medical images is the key for further automated processing techniques like segmentation, and can help the clinicians with better diagnosis and therapy. We consider partial differential equation (PDE)-based denoising model which is a modified Euler-Lagrange equation derived from the total variation minimization functional with additional speckle noise constraints. The new PDE model is designed and optimized to rectify speckle noise and enhance edges present in medical imagery. We also develop the efficient and stable discretization techniques for the corresponding speckle denoising model. The method is tested for several types of images including ultrasound images, and it is compared favorably to the conventional denoising model. *
In this paper, we develop an efficient numerical scheme for solving one-dimensional hyperbolic interface problems. The immersed finite element (IFE) method is used for spatial discretization, which allows the solution mesh to be independent of the interface. Consequently, a fixed uniform mesh can be used throughout the entire simulation. The method of lines is used for temporal discretization. Numerical experiments are provided to show the features of these new methods.
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