A Fast MAP Algorithm for 3D Ultrasound

Bayesian methods have been avoided in 3D ultrasound. The multiplicative type of noise which corrupts ultrasound images leads to slow reconstruction procedures if Bayesian principles are used. Heuristic approaches have been used instead in practical applications. This paper tries to overcome this difficulty by proposing an algorithm which is derived from sound theoretical principles and fast. This algorithm is based on the expansion of the noise probability density function as a Taylor series, un the vicinity of the maximum likelihood estimates, leading to a linear set of equations which are easily solved by standard techniques. Reconstruction examples with synthetic and medical data are provided to evaluate the proposed algorithm.