Bayesian compressed sensing in ultrasound imaging

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.