Random Incident Waves for Fast Compressed Pulse-Echo Ultrasound Imaging

TL;DR

This paper introduces a novel random incident wave approach for fast compressed pulse-echo ultrasound imaging, improving image quality and convergence speed by leveraging randomness and sparsity in soft tissue structures.

Contribution

It proposes a new method using random incident waves and $ ext{l}_q$-minimization to enhance compressed ultrasound imaging beyond traditional plane wave models.

Findings

Random incident waves outperform quasi-plane waves in simulations.

Significant reduction in point spread function extents by up to 73.7%.

Method effectively recovers images with fewer measurements.

Abstract

Established image recovery methods in fast ultrasound imaging, e.g. delay-and-sum, trade the image quality for the high frame rate. Cutting-edge inverse scattering methods based on compressed sensing (CS) disrupt this tradeoff via a priori information. They iteratively recover a high-quality image from only a few sequential pulse-echo measurements or less echo signals, if (i) a known dictionary of structural building blocks represents the image almost sparsely, and (ii) their individual pulse echoes, which are predicted by a linear model, are sufficiently uncorrelated. The exclusive modeling of the incident waves as steered plane waves or cylindrical waves, however, has so far limited the convergence speed, the image quality, and the potential to meet condition (ii). Motivated by the benefits of randomness in CS, a novel method for the fast compressed acquisition and the subsequent recovery of images is proposed to overcome these limitations. It recovers the spatial compressibility fluctuations in weakly-scattering soft tissue structures, where an orthonormal basis meets condition (i), by a sparsity-promoting $\ell_{q}$-minimization method, $q \in [0; 1]$. A realistic $d$-dimensional model, $d \in \{2, 3\}$, accounting for diffraction, single monopole scattering, the combination of power-law absorption and dispersion, and the specifications of a planar transducer array, predicts the pulse echoes of the individual basis functions. Three innovative types of incident waves, whose syntheses leverage random apodization weights, time delays, or combinations thereof, aid in meeting condition (ii). In two-dimensional numerical simulations, single realizations of these waves outperform the prevalent quasi-plane wave for both the canonical and the Fourier bases. They significantly reduce the full extents at half maximum of the point spread functions by up to 73.7 %.