Full Matrix Capture is a multi-channel data acquisition method which enables flexible, high resolution imaging using ultrasound arrays. However, the measurement time and data volume are increased considerably. Both of these costs can be circumvented via compressed sensing, which exploits prior knowledge of the underlying model and its sparsity to reduce the amount of data needed to produce a high resolution image. In order to design compression matrices that are physically realizable without sophisticated hardware constraints, structured subsampling patterns are designed and evaluated in this work. The design is based on the analysis of the Cramér–Rao Bound of a single scatterer in a homogeneous, isotropic medium. A numerical comparison of the point spread functions obtained with different compression matrices and the Fast Iterative Shrinkage/Thresholding Algorithm shows that the best performance is achieved when each transmit event can use a different subset of receiving elements and each receiving element uses a different section of the echo signal spectrum. Such a design has the advantage of outperforming other structured patterns to the extent that suboptimal selection matrices provide a good performance and can be efficiently computed with greedy approaches.

In this paper we propose a method to improve the detection of shadowed flaws in ultrasonic non-destructive testing (NDT). The B-scans are expressed in the context of Sparse Signal Recovery (SSR), where the shadowing effect is incorporated during the reconstruction: Whenever a new defect is found, its shadow on all other dictionary atoms is determined and the dictionary is updated accordingly. We develop models for determining the affected dictionary entries as well as for the intensity of the attenuation due to the shadow. Using Orthogonal Matching Pursuit (OMP), we demonstrate that the proposed method significantly improves the reconstruction amplitudes, i.e., the detection reliability, compared to conventional detection without incorporation of shadowing.

In ultrasonic non-destructive testing, array and matrix transducers are being employed for applications that require in-field steerability or which benefit from a higher number of insonification angles. Having many transmit channels, on the other hand, increases the measurement time and renders the use of array transducers unfeasible for many applications. In the literature, methods for reducing the number of required channels compared to the full matrix capture scheme have been proposed. Conventionally, these are based on choosing the aperture that is as wide as possible. In this publication, we investigate a scenario from the field of pipe inspection, where cracks have to be detected in specific areas near the weld. Consequently, the width of the aperture has to be chosen according to the region of interest at hand. On the basis of ray-tracing simulations which incorporate a model of the transducer directivity and beam spread at the interface, we derive application specific measures of the energy distribution over the array configuration for given regions of interest. These are used to determine feasible subsampling schemes. For the given scenario, the validity/quality of the derived subsampling schemes are compared on the basis of reconstructions using the conventional total focusing method as well as sparsity driven-reconstructions using the Fast Iterative Shrinkage-Thresholding Algorithm. The results can be used to effectively improve the measurement time for the given application without notable loss in defect detectability.

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.