Progressive online 3-D SAFT processing by matrix structure exploitation

In this paper, we formulate an efficient progressive version of 3-D SAFT by exploiting the block Toeplitz structure of the matrix unfolding of the underlying tensor. This reduces the calculation to a simple striding operation followed by a matrix vector product of the corresponding submatrix per measured A-scan. Our approach enables to feedback 3-D SAFT images to the engineer during the measurement, e.g., by using augmented reality techniques. The usefulness of the progressive updates is illustrated by presenting snapshots of the iterative SAFT reconstruction of ultrasound measurement data of a steel specimen.