Comparison of virtual source synthetic aperture beamforming with an element-based model

Abstract

Ultrasound beamforming relies on models of propagation to convert samples of the backscattered field through time into spatial image samples. The most common model is straight-line propagation of a focused wave, assuming a narrow steered and focused beam that propagates along a selected direction. The reconstructed image suffers from defocusing, reduced signal-to-noise ratio (SNR), and contrast loss away from the focus. "Virtual source" methods coherently combine the recorded data from multiple transmissions to form a synthetic transmit focus by making geometric assumptions about the transmissions. These also include diverging waves (virtual source behind the array) and plane waves (virtual source at infinity). Retrospective encoding for conventional ultrasound sequences (REFoCUS) beamforming has been proposed to instead model transmission as the superposition of the responses of individual transmit elements on the transducer array and to efficiently estimate the "complete data set"-individual element transmit and receive responses. In addition to isolating individual element contributions, the result of this unifying framework is a high-SNR, two-way focused image from focused plane wave or diverging transmissions. No significant differences were observed for either SNR or image quality measured by contrast-to-noise ratio between the appropriate virtual source method and REFoCUS beamforming in simulation and experimental imaging.

Fourier-based Synthetic-aperture Imaging for Arbitrary Transmissions by Cross-correlation of Transmitted and Received Wave-fields

“…Previous work has also demonstrated the similarity of REFoCUS and virtual source reconstructions when imaging with phased arrays. 30…”

Mixed Imaging Sequences for Improved Spatiotemporal Resolution in Cardiac Imaging

“…With n transmissions and T elements, a given time delay τ nT is calculated according to Equation 1.1 for focused waves, Equation 1.2 for plane waves, and Equation 1.3 for diverging waves. (x f ,z f ) gives the position of the virtual source, x n gives the element position, c is the speed of sound, and θ is the steering angle used to direct plane waves [6].…”

“…Assuming planar wave propagation near the focal point allows for the reconstruction of pixels between the focal points of neighboring beams [25]. The shapes of focused, plane, and diverging wave geometric masks are shown in Figure 1.2 [6]. Note that the planar region near the focal point of the focused transmission is not shown in this configuration.…”

The Spectrum-Beamformer for Conventional B-Mode Ultrasound Imaging System: Principle, Validation, and Robustness

“…18 For FUI modality, the recent retrospective encoding for conventional ultrasound sequences (REFoCUS) beamforming was introduced, which uses the time shift decoder to remove the transmit delays for each transmitting element to recover the complete data set. 19 Similarly, applying spatially coding in transmission (e.g., Hadamard matrix, S-sequence) and decoding in reception has extended the virtual sources-based beamforming theory for FUI system. 20,21 In addition, shot-profile migration was considered applicable for focused transmit beams, and shows contrast improvement over BiPBF and REFoCUS.…”