A study of pulseecho image formation using nonquadratic regularization with specklebased images

Abstract: Objective: B-mode imaging is a standard way of presenting results when pulse-echo data acquisition is used. Inverse approaches have been explored to a limited extent. The goals of this study are to explore the feasibility and effectiveness of regularization by: (a) evaluating the quality of the reconstruction of speckle-based images as a function of imaging parameters (i.e., bandwidth of the transducer, f/number, and distance between region of interest (ROI) and focal region), and (b) comparing the reconstructed images with those obtained by conventional imaging techniques (e.g., B-mode and synthetic aperture focusing techniques (SAFT)). Methodology: Two-dimensional pulse-echo data from a single-element focused transducer with center frequency of 6 MHz and focal distance of 19 mm were simulated using fractional bandwidths of 33%, 50 % and 100%, f/numbers of 1, 2 and 3, and distances between ROI and focus of 0, 2.5 and 5 mm. A minimum scatterer density of 4 scatterers per resolution cell was used. The images were reconstructed using non-quadratic regularization. Because the desired image was known, the normalized mean squared error (MSE) was used as a quantitative indicator of reconstruction performance. The reconstructed images were also evaluated by visual inspection. Results: The best reconstructions were achieved when the ROI was at the focus, the bandwidth was 100 % and the f/number was 1, for which the MSE was 25 % for a 20-dB signal-to-noise ratio (SNR). The MSE increased as the bandwidth decreased, the f/number increased, and the distance between ROI and focus increased. The bandwidth was the most sensitive parameter, increasing the MSE up to 86 % for a SNR of 20 dB. For all cases, parameter selection techniques such as the L-curve and generalized cross-validation (GCV) gave a clos