[Paper Review] Ultrasound Matrix Imaging-Part I: The focused reflection matrix, the F-factor and the role of multiple scattering

William Lambert, Robin, Justine+3 more|arXiv (Cornell University)|Mar 2, 2021

Ultrasound Imaging and Elastography2 references2 citations

TL;DR

This paper introduces ultrasound matrix imaging (UMI) as a novel matrix-based approach to quantify and correct aberrations in ultrasound imaging by analyzing the focused reflection matrix. Using time-frequency analysis, it separates single scattering, multiple scattering, and noise components, enabling a robust F-factor metric that outperforms the traditional coherence factor by being resilient to multiple scattering and noise, thus providing high-resolution focusing quality maps with improved transverse resolution in both simulated and in-vivo calf imaging.

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.

Motivation & Objective

• To address the limitations of conventional ultrasound imaging caused by speed-of-sound variations and aberrations in heterogeneous soft tissues.
• To develop a robust metric for assessing focusing quality that is insensitive to multiple scattering and electronic noise.
• To enable high-resolution, quantitative mapping of aberrations using a matrix-based approach to ultrasound data.
• To validate the method in both time-domain simulations and in-vivo human calf imaging.
• To provide a foundation for future speed-of-sound and scattering quantification in ultrasound imaging.

Proposed method

• Constructs a focused reflection matrix by decoupling transmit and receive focal spots in ultrasound imaging, enabling full spatial sampling of the medium’s response.
• Applies time-frequency analysis to decompose the matrix into contributions from single scattering, multiple scattering, and noise components.
• Defines the F-factor as a focusing quality metric based on the single-scattering component, derived via a fitting process to isolate coherent signal contributions.
• Uses the F-factor to generate a contrasted, high-transverse-resolution map of focusing quality across the image, replacing the coherence factor.
• Validated using time-domain simulations and applied to in-vivo ultrasound data from a human calf to demonstrate clinical feasibility.
• Employs a matrix formalism to model wave propagation and scattering, enabling quantitative analysis of aberration effects in both monochromatic and broadband regimes.

Experimental results

Research questions

• RQ1 Can a matrix-based approach improve the quantification of aberrations in ultrasound imaging beyond conventional beamforming?
• RQ2 How do multiple scattering and electronic noise affect the accuracy of existing focusing quality metrics like the coherence factor?
• RQ3 Can a new metric—derived from the single-scattering component of the focused reflection matrix—provide a more robust and high-resolution assessment of focusing quality?
• RQ4 To what extent does the F-factor outperform the coherence factor in the presence of multiple scattering and noise?
• RQ5 Can this method enable quantitative speed-of-sound and scattering characterization in soft tissues?

Key findings

• The F-factor, derived from the single-scattering component of the focused reflection matrix, provides a robust and accurate measure of focusing quality that is resilient to multiple scattering and noise.
• The F-factor enables high-transverse-resolution mapping of focusing quality, significantly outperforming the coherence factor in spatial resolution and contrast.
• Time-frequency analysis successfully isolates and quantifies single scattering, multiple scattering, and noise contributions within the focused reflection matrix.
• In simulations, the F-factor accurately tracks aberration levels across varying speed-of-sound distributions, demonstrating its sensitivity to wavefront distortions.
• In-vivo application on a human calf showed that the F-factor map revealed spatially varying aberration patterns consistent with tissue heterogeneity, validating its clinical relevance.
• The method enables the measurement of the incoherent input-output point spread function at each pixel, offering new insights into image degradation mechanisms.