Fundamentals of digital image processing
Fundamentals of digital image processing
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
De-noising by soft-thresholding
IEEE Transactions on Information Theory
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A new approach to filter out multiplicative noise from ultrasound images is presented in this paper. The noisy image is segmented into small segments, and the global covariance matrix is found. A projection matrix is formed by selecting the maximum eigenvectors of the global covariance matrix. This projection matrix is then used to filter noise by projecting the segment into the signal subspace. This approach is based on the fact that signal and noise are independent (orthogonal) and the signal subspace is spanned by a subset of the eigenvectors corresponding to the set of largest eigenvalues. When applied on simulated and real ultrasound images, our approach has outperformed popular nonlinear denoising techniques, such as Wavelets, Total Variation Filtering and Anisotropic Diffusion Filtering. It also showed less sensitivity to outliers resulted from the log transformation of the multiplicative noise.