Joint Deconvolution of Fundamental and Harmonic Ultrasound Images

This paper studies the interest of using harmonic ultrasound (US) images in the process of tissue reflectivity function restoration from RF data. To this end, two direct models (one for fundamental and another for harmonique images) derived from the equation of US wave propagation are proposed. In particular, an axially varying attenuation matrix is used within the harmonic image model in order to account for the attenuation of harmonic echoes. Based on these two image formation models, a joint deconvolution problem is investigated. The solution of this problem is obtained by minimizing a cost function composed of two data fidelity terms representing the linear and non-linear model components,regularized by an ℓ1-norm regularization. The tissue reflectivity function minimizing this function is finally determined using an alternating direction method of multipliers. The performance of the proposed algorithm is quantitatively and qualitatively evaluated on synthetic data, and compared with a classical restoration method used for US images.

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