Axial super-resolution in ultrasound imaging with application to non-destructive evaluation.

A fundamental challenge in non-destructive evaluation using ultrasound is to accurately estimate the thicknesses of different layers or cracks present in the object under examination, which implicitly corresponds to accurately localizing the point-sources of the reflections from the measured signal. Conventional signal processing techniques cannot overcome the axial-resolution limit of the ultrasound imaging system determined by the wavelength of the transmitted pulse. In this paper, starting from the solution to the 1-D wave equation, we show that the ultrasound reflections could be effectively modeled as finite-rate-of-innovation (FRI) signals. The FRI modeling approach is a new paradigm in signal processing. Apart from allowing for the signals to be sampled below the Nyquist rate, the FRI framework also transforms the reconstruction problem into one of parametric estimation. We employ high-resolution parametric estimation techniques to solve the problem. We demonstrate axial super-resolution capability (resolution below the theoretical limit) of the proposed technique both on simulated as well as experimental data. A comparison of the FRI technique with time-domain and Fourier-domain sparse recovery techniques shows that the FRI technique is more robust. We also assess the resolvability of the proposed technique under different noise conditions on data simulated using the Field-II software and show that the reconstruction technique is robust to noise. For experimental validation, we consider Teflon sheets and Agarose phantoms of varying thicknesses. The experimental results show that the FRI technique is capable of super-resolving by a factor of three below the theoretical limit.

Compressed Sensing with Gaussian Sampling Kernel for Ultrasound Imaging.

Recently, compressed sensing (CS) has been applied to ultrasound imaging for either data reduction or frame rate improvement. However, there are no detailed reports yet on strategies for lateral undersampling of channel data in conventional focused beamforming (CFB) and its recovery exploiting the CS approach. We propose a strategic lateral undersampling approach for channel data using the Gaussian sampling scheme and compare it with a direct extension of the often-used uniform undersampling reported for axial undersampling to the lateral direction and 2-D random sampling reported in the literature. As opposed to the reported 2-D random undersampling, we explore undersampling of channel data in the lateral direction by acquiring radiofrequency data from only a reduced number of chosen receive elements and subjecting these data to further undersampling in the axial direction. The effect of the sampling schemes on CS recovery was studied using data from simulations and experiments for various lateral and axial undersampling rates. The results suggest that CS-recovered data from the Gaussian distribution-based channel data subsampling yielded better recovery and contrast in comparison to those obtained from the often-used uniform distribution-based undersampling. Although 90% of the samples from the original data using the proposed sampling scheme were discarded, the contrast of the CS-recovered image was comparable to that of the reference image. Thus, CS with the proposed Gaussian sampling scheme for channel data subsampling not only reduces the data size significantly, but also strategically uses only a few active receive elements in the process; thus, it can provide an attractive option for the affordable point-of-care ultrasound system.