A Total Variation Based Reconstruction Algorithm for 3D Ultrasound

This paper presents an algorithm for reconstructing a three dimensional image from a set of noisy two dimensional images, corrupted with Rayleigh distributed multiplicative noise, which is the observational model for Ultrasound imaging. The proposed method performs a variable splitting to introduce an auxiliary variable to serve as the argument of the 3D total variation term. Applying the Augmented Lagrangian framework and using an iterative alternating minimization method leads to simpler problems involving TV minimization with a least squares term. The resulting Gauss Seidel scheme is an instance of the Alternating Direction Method of Multipliers (ADMM) method, for which convergence is guaranteed. Experimental results show that the proposed method is faster and achieves a lower mean square error than existing methods.