We consider a planar circular array of ultrasound emitter-receiver elements. Due to manufacturing reasons, the actual positions of the elements slightly differ from the ideal equidistant positions exactly on the circle; also, there exist delays in emitting and receiving the signals. This leads to corrupted resulting ultrasound images, and these misplacements and delays are to be evaluated in order to obtain better images. It is assumed that the only available information that we possess is the noisy measurements of the times between the instant of activation of every sensor and the instant of registration of the signal at the receiver.
Some of the existing approaches to this \emph{calibration problem} have various drawbacks such as very high dimensions of the associated convex optimization problem or convergence to local minima in nonconvex formulations, etc.
To solve this problem, we developed a very simple iterative procedure that requires solving moderately-sized systems of linear equations.
At every iteration, we first optimize by a part of variables and then use their updated values to optimize over the rest of the variables. With simple tricks, both problems are converted into linear ones, thus making solution very fast. Preliminary experiments over synthetic data testify to a rather promising performance of the method.