Fig. 1: 3D Ultrasound Matrix Imaging (UMI).
a–c The R-matrix can be acquired in the (a) transducer or (b) plane-wave basis in transmit and (c) recording the back-scattered wave field on each transducer in receive. d Confocal imaging consists in a simultaneous focusing of waves at input and output. e In UMI, the input (rin) and output (rout) focusing points are decoupled. f x−cross-section of the focused R−matrix. g Four-dimensional structure of the focused R-matrix. h UMI enables a quantification of aberrations by extracting a local RPSF (displayed here in amplitude) from each antidiagonal of Rρρ(z). i UMI then consists in a projection of the focused R-matrix in a correction (here transducer) basis at output. The resulting dual R-matrix connects each focusing point to its reflected wave-front. j UMI then consists in realigning those wave-fronts to isolate their distorted component from their geometrical counterpart, thereby forming the D-matrix. k An iterative phase reversal algorithm provides an estimator of the T-matrix between the correction basis and the mid-point of input focusing points considered in panel (i). l The phase conjugate of the T-matrix provides a focusing law that improves the focusing process at output. m RPSF amplitude after the output UMI process. The ultrasound data shown in this figure corresponds to the pork tissue experiment at depth z = 40 mm.
