Aberration estimation using FDORT: insights and improved method for speckle signals

Clinical ultrasound imaging is degraded by tissue velocity inhomogeneities that reduce resolution and contrast. The Focused DORT (French acronym for decomposition of the time reversal operator) method, here denoted FDORT, can be used as an aberration estimation method. FDORT uses per-channel received RF data obtained from several focused transmissions. An aberration profile is estimated using a singular value decomposition method. The advantage of FDORT over a cross-correlation based method is its ability to identify individual wavefronts in complex RF regions. It also allows frequency-dependent estimation. FDORT exhibits good results with point scatterers but significant residual rms errors (between applied and estimated aberrator) in speckle regions (typically 15ns for a 45ns aberration). This study aims to explain the behavior of FDORT in speckle by interpreting the FDORT matrix as a cross-spectrum matrix of the backscattered signal, similar to the one studied by Masoy et al. [JASA 117 (1) 2005]. This explanation is then used to improve the method; reducing both the bias and variance of the estimation. Originally, the first singular vector was used for the estimation: it contained the amplitude and delay law that maximized the speckle brightness. A bias results from the fact that the transmit itself is aberrated. We propose a method to reduce the bias to a linear shift by using a combination of all eigenvectors. A new scheme is introduced to reduce the variance, typically by a factor of 2. Finally, we introduce a non-biased estimator by forming a tensor from a full synthetic aperture data set. Its first singular vector maximizes the speckle brightness by correcting both transmit and receive - this is equivalent to an FDORT estimation when the aberration is completely corrected in transmit and provides the lowest error. We performed Field-II (Jensen) simulations using a 45ns, 4mm FWHM near-field phase screen on a speckle phantom with point scatterers and cysts. Cyst contrast improvements and rms residual errors are computed for the different methods. In-vivo aberration estimation results are also presented. The theoretical understanding of the speckle behavior in FDORT has led to improved performance and further insights into using statistical-based approaches for aberration measurement.