Ultrasound image de-noising through Karhunen-Loeve (K-L) transformwith overlapping segments

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.