Image reconstruction from compressed measurements for ultrasound NDT

In ultrasound NDT, Delay-and-Sum schemes are commonly used to reconstruct images from the measurement data. For single channel pulse-echo measurements, this is called Synthetic Aperture Focusing Technique (SAFT). In a multi-channel setup, SAFT is extended to the Total Focusing Method (TFM), where the focused image is reconstructed from measurements of all transmit-receive combinations, called Full Matrix Capture (FMC). In previous work, we showed that both SAFT and TFM can be cast as a sparse recovery problem that enables enhancing the Delay-and-Sum scheme to a physically motivated forward model that leads to improved image quality. The reconstruction is performed using l1 minimization. Further, this also allows to perform the reconstruction from compressed/subsampled measurements following compressed sensing theory. This subsampling was achieved by only measuring a subset of the frequency coefficients of the signal. In both the single channel and the multi-channel setup the amount of measurement data is thereby significantly reduced. Additionally, for the TFM, we added a spatial subsampling by only considering a subset of transmit and receive pairs, further reducing the measurement data and at the same time also reducing the measurement time. In our previous work, the frequency and spatial dimensions were considered separately for simplicity, using the same compression strategy for all spatial measurements. In this work we consider joint frequency/spatial compression schemes. We show that a joint multidimensional compression strategy where different Fourier subsets are considered for each channel pair leads to a superior reconstruction performance when the compression rate is fixed. Analysis based on an analytical model for a single defect and a real-world example with multiple defects shows that the approach works in practice.