Ultrafast Ultrasound Imaging as an Inverse Problem: Matrix-Free Sparse Image Reconstruction

Abstract

Abstract-Conventional ultrasound (US) image reconstruction methods rely on delay-and-sum (DAS) beamforming, which is a relatively poor solution of the image reconstruction problem. An alternative to DAS consists in using iterative techniques which require both an accurate measurement model and a strong prior on the image under scrutiny. Towards this goal, much effort has been deployed in formulating models for US imaging which usually require a large amount of memory to store the matrix coefficients. We present two different techniques which take advantage of fast and matrix-free formulations derived for the measurement model and its adjoint, and rely on sparsity of US images in well-chosen models. Sparse regularization is used for enhanced image reconstruction. Compressed beamforming exploits the compressed sensing framework to restore high quality images from fewer raw-data than state-of-the-art approaches. Using simulated data and in vivo experimental acquisitions, we show that the proposed approach is three orders of magnitude faster than non-DAS state-of-the-art methods, with comparable or better image quality.

USSR: An ultrasound sparse regularization framework

“…The linear measurement operator H d {γ} described in Section II-A defines an ill-posed linear inverse problem which can be equivalently written as [12]:…”

“…Compute the value to sum tom p i , t l according to Equation (6) (12). Regarding the optimization algorithm, Problem (14) is solved using the fast iterative shrinkage algorithm (FISTA) [13] in which each step involves the evaluation of the measurement model and the adjoint, in order to compute the derivative of the data-discrepancy term.…”

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

“…For instance, they theoretically support incident waves and array geometries of any complexity, the separate recovery of multiple acoustic material parameters, efficient spatiotemporal sampling concepts for data rate reduction, denoising, and the inclusion of a priori information about the image. Cutting-edge variants [24], [25], [27]- [30], [32]- [34] have recently adopted "compressed sensing" 2 (CS), a data acquisition and recovery method providing essential benefits in other modalities [39]- [41], to disrupt the tradeoff between the image quality and the frame rate. They iteratively recover a high-quality image from only a single pulse-echo measurement or less echo signals, if (i) a known dictionary of structural building blocks represents the image almost sparsely, and (ii) their individual pulse echoes, which are predicted by the linear model, are sufficiently uncorrelated.…”

“…The linear models, which are formulated in the time domain [24], [25], [28], [29] or the temporal [30]- [34] and spatiotemporal [27] Fourier domains, however, currently limit the convergence speed, the image quality, and the potential to meet condition (ii). Like the established methods, they partly neglect diffraction, the combination of frequency-dependent absorption and dispersion, and the specifications of the instrumentation, including the array geometry, the acoustic lens, and the electromechanical transfer behavior.…”

“…Moreover, they partly limit the number of spatial dimensions to only two, intermix results for the two-and three-dimensional Euclidean spaces, and replace the acoustic material parameters by an abstract reflectivity function. The exclusive usage of steered PWs [24], [25], [27]- [34] or outgoing cylindrical waves [25] ignores basic abilities of programmable UI systems. The latter typically specifies pulse shapes, apodization weights, and time delays for the waves emitted by the individual array elements and provides hundreds of degrees of freedom to synthesize alternative types of incident waves.…”