Ultrasound Matrix Imaging—Part I: The Focused Reflection Matrix, the F-Factor and the Role of Multiple Scattering

Abstract

This is the first article in a series of two dealing with a matrix approach for aberration quantification and correction in ultrasound imaging. Advanced synthetic beamforming relies on a double focusing operation at transmission and reception on each point of the medium. Ultrasound matrix imaging (UMI) consists in decoupling the location of these transmitted and received focal spots. The response between those virtual transducers form the so-called focused reflection matrix that actually contains much more information than a confocal ultrasound image. In this paper, a time-frequency analysis of this matrix is performed, which highlights the single and multiple scattering contributions as well as the impact of aberrations in the monochromatic and broadband regimes. Interestingly, this analysis enables the measurement of the incoherent input-output point spread function at any pixel of this image. A fitting process enables the quantification of the single scattering, multiple scattering and noise components in the image. From the single scattering contribution, a focusing criterion is defined, and its evolution used to quantify the amount of aberration throughout the ultrasound image. In contrast to the state-of-the-art coherence factor, this new indicator is robust to multiple scattering and electronic noise, thereby providing a contrasted map of the focusing quality at a much better transverse resolution. After a validation of the proof-of-concept based on time-domain simulations, UMI is applied to the in-vivo study of a human calf. Beyond this specific example, UMI opens a new route for speed-of-sound and scattering quantification in ultrasound imaging.

Windowed Radon Transform and Tensor Rank-1 Decomposition for Adaptive Beamforming in Ultrafast Ultrasound

“…We first suppose that 𝑎 Tx/Rx , ℎ Tx/Rx , and Δ𝜏 Tx/Rx vary slowly in the medium and thus can be assumed constant in V(𝒓 w ) and equal to their value at 𝒓 w . Practically, V(𝒓 w ) is equivalent to the isoplanatic patch used in [20], [23]. Moreover, we introduce a local Rx angle…”

“…Once a single sinogram 𝑓 per window position is obtained using Algorithm 1, we recover the estimations of the corresponding local patches by applying the backprojection operator R * to 𝑓 𝛾 f, p 𝒓 ′ , 𝒓 w = ∫ 𝜃 𝑓 𝜃, 𝒖(𝜃), 𝒓 ′ − 𝒓 w , 𝒓 w d𝜃, (23) in the continuous domain. Backprojection is then repeated for each window position 𝒓 w 𝑝,𝑞 .…”

Imaging the Crustal and Upper Mantle Structure of the North Anatolian Fault: A Transmission Matrix Framework for Local Adaptive Focusing

“…To express this quantity theoretically, we first make a local isoplanatic approximation in the vicinity of each point $$({\boldsymbol{\rho }}_{m},z)$$ (Lambert, Robin, et al., 2022). Isoplanicity means here that waves which focus in this region are assumed to have traveled through approximately the same areas of the medium, thereby undergoing identical phase distortions.…”

Phase Aberration Correction: A Convolutional Neural Network Approach

“…As opposed to methods that model the phase aberration effect by a fixed near-field phase screen in front of the transducer, the locally adaptive phase aberration correction technique [14] assumed a spatially varying near-field phase screen and employed multistatic synthetic aperture data to perform the correction at each point adaptively. Lambert et al suggested compensating for the spatially-distributed aberrations by decoupling aberrations undergone by the outgoing and incoming waves utilizing the distortion matrix built from the focused reflection matrix, which contains the responses between virtual transducers synthesized from the transmitted and received focal spots [15], [16], [17].…”

“…It should be noted that due to the numerical precision of simulations in Field II, the initial sampling frequency was set to 104. 16 MHz, and the simulated data was later downsampled by a factor of 5. All images were simulated using a full synthetic aperture scan, followed by the synthesis of plane-wave images with 384 columns from the acquired data and saved as RF data.…”