Autofocusing in medical ultrasound: the scaled covariance matrix algorithm

This work develops a class of ultrasound phase aberration correction/autofocusing algorithms that are based upon the properties of the covariance matrix of the channel signals for time-delay focused resolution/speckle cells. The scaled covariance matrix (SCM) algorithms are designed to blindly estimate and correct focusing timing errors due to thin layers of unanticipated fatty tissue located in the near field of the transducer array. An important aspect of the algorithm is that the scaling of the covariance matrix elements fundamentally establishes a channel independent phase reference relative to which the aberrant channel phases are estimated. The model development involved the combination of a rigorous mathematical analysis of the scattering of ultrasound in random scattering media and extensive statistical simulation studies with phase aberrations imposed upon both the transmit and received channel signals. Under the assumption of a near field aberration model, the statistical simulation analyses showed that the SCM algorithms in simulation are capable of accurately estimating relative time delay channel errors with rms timing errors up to approximately 62 ns, with interchannel correlation lengths as short as 1.4 mm.