[Paper Review] Compressed Fourier-Domain Convolutional Beamforming for Wireless Ultrasound imaging

Alon Mamistvalov, Yonina C. Eldar|arXiv (Cornell University)|Oct 25, 2020

Ultrasound Imaging and Elastography41 references4 citations

TL;DR

This paper proposes compressed Fourier-domain convolutional beamforming (CFCOBA), integrating compressed sensing, sparse arrays, and frequency-domain beamforming to enable high-resolution wireless ultrasound imaging. By sampling signals below the Nyquist rate and using convolutional beamforming on sparse arrays, the method achieves up to 142× less data than conventional DAS beamforming while preserving or improving image quality in in vivo scans.

ABSTRACT

Wireless ultrasound (US) systems that produce high-quality images can improve current clinical diagnosis capabilities by making the imaging process much more efficient, affordable, and accessible to users. The most common technique for generating B-mode US images is delay and sum (DAS) beamforming, where an appropriate delay is introduced to signals sampled and processed at each transducer element. However, sampling rates that are much higher than the Nyquist rate of the signal are required for high resolution DAS beamforming, leading to large amounts of data, making transmission of channel data over WIFI impractical. Moreover, the production of US images that exhibit high resolution and good image contrast requires a large set of transducers which further increases the data size. Previous works suggest methods for reduction in sampling rate and in array size. In this work, we introduce compressed Fourier domain convolutional beamforming, combining Fourier domain beamforming, sparse convolutional beamforming, and compressed sensing methods. This allows reducing both the number of array elements and the sampling rate in each element, while achieving high resolution images. Using in vivo data we demonstrate that the proposed method can generate B-mode images using 142 times less data than DAS. Our results pave the way towards wireless US and demonstrate that high resolution US images can be produced using sub-Nyquist sampling and a small number of receiving channels.

Motivation & Objective

• To address the high data rate and power consumption of traditional ultrasound systems, especially for wireless and portable applications.
• To reduce the number of transducer elements and sampling rate without degrading image resolution or contrast.
• To enable practical wireless ultrasound by minimizing data transmission and processing requirements.
• To combine compressed sensing, sparse arrays, and frequency-domain beamforming for efficient, high-quality imaging.
• To validate the method on diverse in vivo data across multiple body parts and imaging systems.

Proposed method

• The method uses Xampling-based sub-Nyquist sampling to reduce the sampling rate below the Nyquist rate, exploiting the finite rate of innovation (FRI) structure of ultrasound signals.
• It performs convolutional beamforming (COBA) in the Fourier domain, enabling efficient beamforming on compressed frequency-domain data.
• Sparse array geometries, such as fractal arrays with generator set {0,1} and order 4, are used to reduce the number of receiving elements while preserving the beampattern of a full uniform linear array via the sum co-array.
• The compressed signal is reconstructed using compressed sensing, specifically the NESTA algorithm, solving an FRI-based model where the signal is represented as replicas of the squared transmitted pulse.
• The approach combines Fourier-domain beamforming with sparse convolutional beamforming to achieve high-resolution images from significantly reduced data.
• The method is validated using both simulated point scatterer data and in vivo data from two ultrasound systems (GE and Verasonics), with consistent performance across different organs.

Experimental results

Research questions

• RQ1 Can sub-Nyquist sampling combined with sparse arrays enable high-quality B-mode ultrasound imaging with drastically reduced data?
• RQ2 Can Fourier-domain convolutional beamforming maintain or improve image resolution and contrast compared to conventional DAS beamforming?
• RQ3 To what extent can the number of transducer elements and sampling rate be reduced without degrading image quality?
• RQ4 Is compressed sensing effective in reconstructing ultrasound signals from partial frequency-domain measurements in a beamforming context?
• RQ5 Can this framework be applied across diverse in vivo anatomical structures and imaging systems?

Key findings

• The proposed CFCOBA method achieved up to 142× reduction in data size compared to standard DAS beamforming using in vivo cardiac data from a GE ultrasound system.
• A 36× data reduction was observed using Verasonics in vivo data, demonstrating robustness across different imaging platforms.
• Image quality using CFCOBA was comparable or superior to DAS, with reduced noise, sharper reflectors, and improved contrast, especially in phantom and in vivo scans.
• The method preserved the beampattern of a full uniform linear array through the use of sum co-arrays from sparse arrays, enabling high-resolution imaging with fewer elements.
• The FRI model of the convolutionally beamformed signal enabled effective compressed sensing recovery, validating the theoretical foundation of the approach.
• The results demonstrate that high-resolution, high-contrast B-mode ultrasound images can be produced using sub-Nyquist sampling and a small number of receiving channels, enabling practical wireless ultrasound systems.