Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
De-noising by soft-thresholding
IEEE Transactions on Information Theory
Image enhancement and denoising by complex diffusion processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
Speckle reducing anisotropic diffusion
IEEE Transactions on Image Processing
Image quality assessment: from error visibility to structural similarity
IEEE Transactions on Image Processing
The contourlet transform: an efficient directional multiresolution image representation
IEEE Transactions on Image Processing
The Nonsubsampled Contourlet Transform: Theory, Design, and Applications
IEEE Transactions on Image Processing
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A novel multiscale anisotropic diffusion method is proposed for ultrasonic speckle reduction. This method, which extends the nonlinear complex diffusion to a nonsubsampled contourlet domain, is called a contourlet transform based complex diffusion (CTCD). The nonsubsampled contourlet transform provides a flexible, multiscale, multidirection, and shift-invariant image decomposition with a good contour capturing and representation. Then, the nonlinear complex diffusion removes noise from the contourlet coefficients with the imaginary values serving as a robust edge-detector. The directionality and multiresolution features of the nonsubsampled contourlet transform and the robust anisotropic smoothing feature of the complex diffusion make the hybrid filter produce satisfactory despeckling results. Both synthetic and real ultrasound images are used to evaluate the performance of the filter, and denoising results are also compared with other three competitive speckle reduction algorithms. It is shown that the proposed method is superior to other methods in both noise reduction and structure preservation.