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

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 US RF data. The second experiment aimed at showing the experimental feasibility of the method proposed using a data set acquired by imaging a general-purpose phantom (CIRS Model 054GS) using an Ultrasonix MDP scanner. The reconstruction was performed by removing 80% of the initial samples and using wave atoms. The reconstructed image was found to reliably preserve the speckle structure and was associated with an error of 5.5dB.