SAMIR: Sparsity Amplified Iteratively-reweighted Beamforming for High-rsolution Ultrasound Imaging

Abstract

In ultrasound imaging, one typically employs delay-and-sum (DAS) beamformers for image reconstruction. An apodization window is used to suppress the side-lobes of an array beam pattern. The application of an apodization window to suppress the side-lobes widens the main-lobe width. We consider a statistical beamformer and present two variants. The signal of interest is modeled as a Laplacian-distributed random variable and additive interference components as Gaussian distributed. The resultant LASSO formulation is known to suffer from underestimation of large signal amplitudes due to the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm regularization. In the first variant, we reformulate the LASSO problem with a minimax-concave penalty (called Sparsity AMplified (SAM)) to contain the bias, thereby enhancing the beamformed image. A closed-form pointwise estimator is obtained for the optimization problem. In the second variant, we propose Sparsity AMplified Iteratively-Reweighted (SAMIR) beamforming algorithm, which leverages the properties of an apodization function. In SAMIR beamforming, we jointly optimize the cost over the signal of interest and the extrinsic apodization weights. This beamformer results in high-resolution ultrasound images, especially in the lateral direction. The proposed methods are compared with the standard DAS and a recently proposed statistically-modeled beamformer, iMAP, for a different number of plane-wave insonifications.