Spatially variant regularization for tissue strain measurement and shear modulus reconstruction

Purpose Regarding the regularization of the displacement vector measurement and shear modulus reconstruction, we propose to properly set the regularization parameters, i.e., to use spatially variant regularization parameters at each point in the region of interest, because the measurement accuracies of the displacements and strains vary spatially. Method As the measurement accuracies of the strains can be evaluated using the correlation coefficient when using the cross-spectrum phase gradient method, preliminarily the regularization parameters were set proportional to the reciprocal of a power of the correlation coefficient. Results and conclusion Such a regularization scheme realizes the spatially uniform stabilities of the strain measurement and shear modulus reconstruction. The effectiveness of this method was verified by showing the regularized results of the axial strain measurement and of one-dimensional (1-D) shear modulus reconstruction obtained in vivo from a human liver carcinoma (that was treated by interstitial microwave coagulation therapy) as well as by a 1-D shear modulus reconstruction obtained using an agar phantom.