Compressed Sensing for Fast Image Acquisition in Pulse-Echo Ultrasound

Abstract

We propose a concept for fast image acquisition in diagnostic ultrasound imaging using compressed sensing (CS). Our concept is based on the formulation of an inverse scattering problem (ISP) to recover deviations in compressibility in a specified region from measurements of the scattered sound. For its derivation, we utilize the Born approximation and assume the emission of a single broadband plane sound wave. We employ CS to regularize this ill-posed ISP, assuming the existence of a sparse representation of the deviations in compressibility in a suitable basis or tight frame. We validate our concept experimentally and compare the recovered images to those generated by synthetic aperture (SA; 128 wave emissions), filtered backpropagation (FBP; single plane wave emission), and delay-and-sum (DAS; single plane wave emission) algorithms. For a sparse wire phantom, our concept outperformed SA, FBP and DAS in terms of sidelobe reduction and lateral -6 dB-widths. Axial -6 dB-widths were comparable. Using wave atoms or curvelets for sparse representation, our concept recovered a commercial multi-tissue phantom with fewer image artifacts and smaller lateral -6 dB-widths than FBP and DAS. Moreover, the achieved contrast was comparable to SA.

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

“…We introduced a mechanism into our concept for fast image acquisition in pulse-echo UI [5], [6] to compensate for the combined effects of absorption and dispersion. The mechanism is based on the time causal model [4] for power law absorption commonly encountered in biological tissues.…”

“…As in our earlier work [5], [6], we approximated the relative spatial fluctuations in compressibility by point scatterers located on a regular lattice. The resulting scattering was described by the first Born approximation.…”

“…To enable the usage of the SR / CS formalism [5], [6] for the solution of the ill-posed system (10), we assume that there exists an orthonormal linear transform Ψ such that γ κ,BP = Ψθ with a nearly sparse coefficient vector θ. The relative spatial fluctuations γ κ,BP can then be recovered by solving the 1 -minimization problem…”

“…However, TGC can only approximately compensate for absorption and neglects the consequences of dispersion. In this contribution, we extended our concept for fast image acquisition in pulse-echo ultrasound imaging (UI) based on sparse recovery (SR) / compressed sensing (CS) [5], [6] to compensate for the combined effects of absorption and dispersion. We augmented our inverse scattering concept with the time causal model [4] to account for absorption and dispersion and with the capability to incorporate the RF data obtained from multiple steered plane wave emissions in the image reconstruction process.…”

Reconstruction of Ultrasound RF Echoes Modeled as Stable Random Variables

“…Nevertheless, a few groups have started to show the feasibility of this type of systems in real-world scanners. These include applications to compressed beamforming in cardiac imaging [13], plane-wave imaging [14], and duplex Doppler [15].…”