Compensating the combined effects of absorption and dispersion in plane wave pulse-echo ultrasound imaging using sparse recovery

Abstract

We extended our concept for fast image acquisition in pulse-echo ultrasound imaging based on sparse recovery (SR) to compensate for the combined effects of absorption and dispersion. Using measurement data obtained from a multi-tissue phantom (A) and a human thyroid (B, in vivo), we demonstrated that image quality can be significantly improved by this extension. Emitting only two steered plane waves, our extended SR-based concept outperformed synthetic aperture (SA) imaging (128 wave emissions), delay-and-sum beamforming (11 wave emissions), and minimum variance beamforming (11 wave emissions) in terms of contrast for object A. Lateral −6 dB-widths were similar to SA. For object B, SR improved the visibility of anatomical contours in contrast to the algorithms used for comparison.

The separate recovery of spatial fluctuations in compressibility and mass density in plane wave pulse-echo ultrasound imaging

“…For a polyfrequent perturbation exhibiting N f components with equispaced discrete frequencies f l ∈ R + , 0 ≤ l < N f , the acoustic pressure p l associated with each component is governed by [1] Δ +k 2 l p l (r) = k l 2 γ κ (r)p l (r) + ∇ · γ ρ (r)∇p l (r) , (1) where Δ denotes the Laplacian,k l is a complex-valued wavenumber depending on the absorption mechanism (cf. [3], [1], [2]), k l = 2πf l c 0 −1 is the wavenumber in the lossless case and c 0 = (κ 0 ρ 0 ) −1/2 is the small-signal equilibrium sound speed in the homogeneous medium. The acoustic pressurep l in the time domain is related to each component p l via the identityp l (r, t) = Re p l (r)e j2πf l t .…”

“…We utilized the sparse recovery formalism [3] to solve the ill-posed system (8). For this purpose, we assumed that there exist orthonormal linear transforms Ψ (κ) and Ψ (ρ) such that γ κ,ρ,BP = Ψ (κ,ρ) θ (κ,ρ) with nearly sparse coefficient vectors θ (κ,ρ) .…”

“…In this study, we investigated the separate recovery of spatial fluctuations in compressibility and mass density by extending our concept for plane wave pulse-echo UI based on sparse recovery (SR) [3]. Our goals were to obtain spaceresolved maps of the two material parameters and to reduce image artifacts.…”

“…005-0908-0117. frequency compressibility and mass density. Similar to [3], we approximated both the relative spatial fluctuations in compressibility and mass density by point scatterers located on a regular lattice. The resulting scattering was described by the Born approximation.…”

“…The resulting scattering was described by the Born approximation. As in the companion paper [3], we accounted for absorption and dispersion according to the time causal model [2]. To distinguish both material parameters by their radiation patterns, we incorporated the radio frequency (RF) data obtained from multiple steered plane wave emissions in the image reconstruction process.…”