Compressed sensing or compressive sampling is a recent theory that originated in the applied mathematics field. It suggests a robust way to sample signals or images below the classic Shannon-Nyquist theorem limit. This technique has led to many applications, and has especially been successfully used in diverse medical imaging modalities such as magnetic resonance imaging, computed tomography, or photoacoustics. This paper first revisits the compressive sampling theory and then proposes several strategies to perform compressive sampling in the context of ultrasound imaging. Finally, we show encouraging results in 2D and 3D, on high- and low-frequency ultrasound images.

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This paper proposes a compressed sensing method adapted to 3D ultrasound (US) imaging. Three undersampling patterns suited for 3D US imaging, together with a nonlinear conjugate gradient reconstruction algorithm of the US image kspaces, are investigated in vivo radio-frequency 3D US volumes. Reconstructions from 50% of the samples of the original 3D volume show little information loss in terms of normalized root mean squared errors.

Following our previous study on compressed sensing for ultrasound imaging, this paper proposes to exploit the image sparsity in the frequency domain within a Bayesian approach. A Bernoulli-Gaussian prior is assigned to the Fourier transform of the ultrasound image in order to enforce sparsity and to reconstruct the image via Bayesian compressed sensing. In addition, the Bayesian approach allows the image sparsity level in the spectral domain to be estimated, a significant parameter in the ℓ1 constrained minimization problem related to compressed sensing. Results obtained with a simulated ultrasound image and an in vivo image of a human thyroid gland show a reconstruction performance similar to a classical compressed sensing algorithm from half of spatial samples while estimating the sparsity level during reconstruction.

Compressive sensing in ultrasound imaging has previously been introduced by the authors. This method allows image reconstructions from relatively few samples (below the Nyquist criteria) using the image sparsity in the Fourier domain, leading to a reduced data volume and acquisition time, two limiting factors in 3D US imaging for example. In this paper, we propose to reduce even further the number of samples (and thereby potentially decrease further the acquisition time) using analytical forms of the US signals.

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