Bayesian compressed sensing in ultrasound imaging

Abstract

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.

Compressed sensing of ultrasound single-orthant analytical signals

“…In addition, on the RF signals that are sampled, the acquisition is again uniform random. With this sampling pattern, there is a gain of time and data while preserving sufficient incoherence in the CS acquisition [2]- [4]. These two sampling schemes are used for both 2-D and 3-D US imaging.…”

“…In preliminary work [2]- [4], we dealt with the feasibility of CS in US imaging. Here, we investigate the search of a sparse representation adapted to US image formation.…”

Enhanced ISAR Imaging by Exploiting the Continuity of the Target Scene

“…Under the framework of Bayesian compressive sensing, a hierarchical prior is used to enforce the sparsity in the signal coefficient vector a, where elements in a are independent and each element a m,n follows a Bernoulli-Gaussian distribution, which is also known as a "spike-and-slab" prior [20][25] [35]:…”

Reconstruction of Partially Sampled Multiband Images—Application to STEM-EELS Imaging

“…The most common key assumptions are to assume that the data is sparse in an appropriate representation space and that the acquisition is random. As a consequence, such algorithms have been implemented in several applied fields such as MRI [6], ultrasonic imaging [7], astronomy [8] or tomography in microscopy [9]. This has been enabled by recent algorithmic advances that efficiently solved high-dimensional optimization problems involving possibly nonsmooth or non-convex penalties.…”