Optimal two-stage filtering of elastograms

In ultrasound elastography, tissue axial strains are obtained through the differentiation of measured axial displacements. However, during the measurement process, the displacement signals are often contaminated with de-correlation noise caused by changes in the speckle pattern in the tissue. Thus, the application of the gradient operator on the displacement signals results in the presence of amplified noise in the axial strains, which severely obscures the useful information. The use of an effective denoising scheme is therefore imperative. In this paper, a method based on a two-stage consecutive filtering approach is proposed for the accurate estimation of axial strains. The presented method considers a cascaded system of a frequency filter and a time window, which are both designed such that the overall system operates optimally as a minimum variance estimator. Experimentation on simulated signals shows that the two-stage scheme employed in this study has good potential as a denoising method for ultrasound elastograms

Solving a variational image restoration model which involves L∞ constraints

In this paper, we seek a solution to linear inverse problems arising in image restoration in terms of a recently posed optimization problem which combines total variation minimization and wavelet-thresholding ideas. The resulting nonlinear programming task is solved via a dual Uzawa method in its general form, leading to an efficient and general algorithm which allows for very good structure-preserving reconstructions. Along with a theoretical study of the algorithm, the paper details some aspects of the implementation, discusses the numerical convergence and eventually displays a few images obtained for some difficult restoration tasks