A method is proposed that provides estimates of the spatial variation of elastic moduli using local displacements of the elastic body. A central issue of elastography imaging has been the limited area of measurement. With the proposed method, stiffness parameter estimations are considered as minimization problems using finite-element models. The sparseness of the gradient of tissue elasticity is also exploited to improve estimation accuracy. Simulation experiments show that based on a 5% area of observation of a simple plate model with non-uniform elasticity the spatial variation of Young's modulus is reconstructed to within 5% accuracy. This result suggests that the proposed framework significantly extends the area of estimation overcoming the limitations of conventional elastography techniques.
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