A hybrid one-step inversion method for shear modulus imaging using time-harmonic vibrations

We propose a hybrid inversion method for imaging the shear modulus μ in tissue-like subjects using internal measurement of the displacement u induced by an external low-frequency mechanical vibrations made on the boundary of the subject. The proposed method is designed to provide high-resolution imaging in a heterogeneous subject, with no need for an iterative procedure, and deal with the intrinsically noisy displacement data. We recover the shear modulus μ by decomposing it into two components: one is for capturing the main feature of μ using a relatively noise-insensitive inversion method, and the other is to correct the residual caused by the quantity Δμ × Δμ. Numerical simulations show that the proposed method significantly improves reconstructions without requiring boundary conditions.