Compressed Sensing Based Synthetic Transmit Aperture Imaging: Validation in a Convex Array Configuration

According to the linear acoustic theory, the channel data of a plane wave emitted by a linear array is a linear combination of the full data set of synthetic transmit aperture (STA). Combining this relationship with compressed sensing (CS), a novel CS based ultrasound beamforming strategy, named compressed sensing based synthetic transmit aperture (CS-STA), was previously proposed to increase the frame rate of ultrasound imaging without sacrificing the image quality for a linear array. In this paper, assuming linear transfer function of a pulse-echo ultrasound system, we derived and applied the theory of CS-STA for a slightly curved array and validated CS-STA in a convex array configuration. Computer simulations demonstrated that, in the convex array configuration, the normalized root-mean-square error between the beamformed radio-frequency data of CS-STA and STA was smaller than 1% while CS-STA achieved four-fold higher frame rate than STA. In addition, CS-STA was capable of achieving good image quality at depths over 100 mm. It was validated in phantom experiments by comparing CS-STA with STA, multielement synthetic transmit aperture (ME-STA), and the conventional focused method (focal depth = 110 mm). The experimental results showed that STA and CS-STA performed better than ME-STA and the focused method at small depths. At the depth of 110 mm, CS-STA, ME-STA, and the focused methods improved the contrast and contrast-to-noise ratio of STA. The improvements in CS-STA are higher than those in ME-STA but lower than those in the focused mode. These results can also be observed qualitatively in the in vivo experiments on the liver of a healthy male volunteer. The CS-STA method is thus proved to increase the frame rate and achieve high image quality at full depth in the convex array configuration.