Spatiotemporal matrix image formation for programmable ultrasound scanners

Abstract

As programmable ultrasound scanners become more common in research laboratories, it is increasingly important to develop robust software-based image formation algorithms that can be obtained in a straightforward fashion for different types of probes and sequences with a small risk of error during implementation. In this work, we argue that as the computational power keeps increasing, it is becoming practical to directly implement an approximation to the matrix operator linking reflector point targets to the corresponding radiofrequency signals via thoroughly validated and widely available simulations software. Once such a spatiotemporal forward-problem matrix is constructed, standard and thus highly optimized inversion procedures can be leveraged to achieve very high quality images in real time. Specifically, we show that spatiotemporal matrix image formation produces images of similar or enhanced quality when compared against standard delay-and-sum approaches in phantoms and in vivo, and show that this approach can be used to form images even when using non-conventional probe designs for which adapted image formation algorithms are not readily available.

Notice of Removal: Random incident sound waves for fast compressed pulse-echo ultrasound imaging

“…whose dependences on the incident acoustic pressure fields (26) are omitted for the sake of notational lucidity. The right multiplication of the sensing matrix (33) by the diagonal inverse weighting matrix (38b) yields the complex-valued normalized N obs × N lat sensing matrix…”

“…The identical spacings between the adjacent grid points on each vibrating face and in the FOV, i.e. ∆r lat,1 = ∆r lat,2 = ∆r mat,1 , simplified the computations of the incident acoustic pressure fields (26) and the implementation of the FMM.…”

“…The acoustic pressure fields (26) were computed for all types of incident waves. For the wire phantom, their spatial and spectral dependencies were analyzed for the discrete frequency closest to the center frequency and three closely spaced positions next to the r 2 -axis, respectively.…”

“…17(f) to 17(h)) indicate the robustness of the compressibility fluctuations (43) recovered by the random waves against the additive errors. In contrast to the wires, the spatially extended complex exponential functions scattered the incident acoustic pressure fields (26) at all grid points in the FOV and, thus, completely reradiated their spatial variations. The significantly enlarged passbands of the sensing matrices (33) induced by the random waves (cf.…”

Sparse sampling and reconstruction for an optoacoustic ultrasound volumetric hand-held probe

“…We investigate feature fidelity to the object that is associated with the merit of the reconstruction algorithm. In practical terms, the use of inverse problems in array imaging forms the deconvolution problem, which faces the ill-posedness [29,30] and large-scale [31][32][33] challenges. Given the partial view angle of the hand-held probe, the forward model is rankdeficient [28], and thus effective regularization must be incorporated.…”