Pre-beamformed RF signal reconstruction in medical ultrasound using compressive sensing

• Published in: Ultrasonics 2013-02, Vol.53 (2), p.525-533
• Main Authors: Liebgott, Hervé, Prost, Rémy, Friboulet, Denis
• Format: Article
• Language: English
• Subjects: Beamforming; Channels; Compressive sensing; Echocardiography; Engineering Sciences; Errors; Image Processing, Computer-Assisted; Image reconstruction; Imaging; Noise levels; Phantoms, Imaging; Radio frequencies; Reconstruction; Representations; RF signal; Signal and Image processing; Signal Processing, Computer-Assisted; Ultrasonography; Ultrasound echography
• ISSN: 0041-624X; 1874-9968
• DOI: 10.1016/j.ultras.2012.09.008

► We report one of the first attempt of applying compressive sensing to raw RF US data. ► Wave atoms yield better reconstructions as compared to Fourier or wavelets transforms. ► Compressive sensing allows for a reduction of the sampling rate by a factor of 80%. ► The method is tested on simulated and experimental data acquired from a US phantom. Compressive sensing (CS) theory makes it possible – under certain assumptions – to recover a signal or an image sampled below the Nyquist sampling limit. In medical ultrasound imaging, CS could allow lowering the amount of acquired data needed to reconstruct the echographic image. CS thus offers the perspective of speeding up echographic acquisitions and could have many applications, e.g. triplex acquisitions for CFM/B-mode/Doppler imaging, high-frame-rate echocardiography, 3D imaging using matrix probes, etc. The objective of this paper is to study the feasibility of CS for the reconstruction of channel RF data, i.e. the 2D set of raw RF lines gathered at the receive elements. Successful application of CS implies selecting a representation basis where the data to be reconstructed have a sparse expansion. Because they consist mainly in warped oscillatory patterns, channel RF data do not easily lend themselves to a sparse representation and thus represent a specific challenge. Within this perspective, we propose to perform and assess CS reconstruction of channel RF data using the recently introduced wave atoms [1] representation, which exhibit advantageous properties for sparsely representing such oscillatory patterns. Reconstructions obtained using wave atoms are compared with the reconstruction performed with two conventional representation bases, namely Fourier and Daubechies wavelets. The first experiment was conducted on simulated channel RF data acquired from a numerical cyst phantom. The quality of the reconstructions was quantified through the mean absolute error at varying subsampling rates by removing 50–90% of the original samples. The results obtained for channel RF data reconstruction yield error ranges of [0.6–3.0]×10−2, [0.2–2.6]×10−2, [0.1–1.5]×10−2, for wavelets, Fourier and wave atoms respectively. The error ranges observed for the associated beamformed log-envelope images are [2.4–20.6]dB, [1.1–12.2]dB, and [0.5–8.8dB] using wavelets, Fourier, and wave atoms, respectively. These results thus show the superiority of the wave atom representation and the feasibility of CS for the reconstruction of U