Combining Total Variation Regularization with Window-Based Time Delay Estimation in Ultrasound Elastography.

A major challenge of free-hand palpation ultrasound elastography (USE) is estimating the displacement of RF samples between pre- and post-compressed RF data. The problem of displacement estimation is ill-posed since the displacement of one sample by itself cannot be uniquely calculated. To resolve this problem, two categories of methods have emerged. The first category assumes that the displacement of samples within a small window surrounding the reference sample is constant. The second class imposes smoothness regularization and optimizes an energy function. Herein, we propose a novel method that combines both approaches, and as such, is more robust to noise. The second contribution of this work is the introduction of the L1 norm as the regularization term in our cost function, which is often referred to as the total variation (TV) regularization. Compared to previous work that used the L2 norm regularization, optimization of the new cost function is more challenging. However, the advantages of using the L1 norm are twofold. First, it leads to substantial improvement in the sharpness of displacement estimates. Second, to optimize the cost function with the L1 norm regularization, we use an iterative method that further increases the robustness. We name our proposed method tOtal Variation Regularization and WINDow-based time delay estimation (OVERWIND) and show that it is robust to signal decorrelation and generates sharp displacement and strain maps for simulated, experimental phantom and in-vivo data. In particular, OVERWIND improves strain contrast-to-noise ratio (CNR) by 27.26%, 144.05%, and 49.90% on average in simulation, phantom, and in-vivo data, respectively, compared to our recent Global Ultrasound Elastography (GLUE) method.