Abstract
Model-based image reconstruction has improved contrast and spatial resolution in imaging applications such as magnetic resonance imaging and emission computed tomography. However, these methods have not succeeded in pulse-echo applications like ultrasound imaging due to the typical assumption of a finite grid of possible scatterer locations in a medium–an assumption that does not reflect the continuous nature of real world objects and creates a problem known as off-grid deviation. To cope with this problem, we present a method of dictionary expansion and constrained reconstruction that approximates the continuous manifold of all possible scatterer locations within a region of interest. The expanded dictionary is created using a highly coherent sampling of the region of interest, followed by a rank reduction procedure. We develop a greedy algorithm, based on the Orthogonal Matching Pursuit, that uses a correlation-based non-convex constraint set that allows for the division of the region of interest into cells of any size. To evaluate the performance of the method, we present results of two-dimensional ultrasound imaging with simulated data in a nondestructive testing application. Our method succeeds in the reconstructions of sparse images from noisy measurements, providing higher accuracy than previous approaches based on regular discrete models.
Highlights
Model-based image reconstruction methods provided important advances to imaging techniques such as magnetic resonance imaging (MRI) [1] and emission computed tomography (ECT) [2] in the last few decades
The stop criterion is based on the residual yielded by the least squares (LS) solution with a given cardinality, yet, instead of comparing the residual to a fixed parameter e, we compare it to an estimate of the current residual that takes into account the expected acquisition noise and the estimated residuals resulting from the reduced-rank approximation
To cope with the problem of off-grid deviation in image reconstruction from pulse-echo ultrasound data, we developed a technique of dictionary expansion based on a highly coherent sampling of the point spread functions (PSF) manifold followed by a rank reduction procedure, as well as a generalization of the OMP algorithm with non-convex constraints
Summary
Model-based image reconstruction methods provided important advances to imaging techniques such as magnetic resonance imaging (MRI) [1] and emission computed tomography (ECT) [2] in the last few decades. These methods rely on a known model that results in the captured signal being represented by a sum of N coefficient-weighted responses. Many previous studies with model-based algorithms for ultrasound imaging [4,5,6,7,8,9,10,11] have reported that resolution and contrast are substantially improved in comparison to delay-and-sum (DAS) algorithms when data comes from simulations with scatterers located strictly on a modelled grid. Sensors 2018, 18, 4097 state-of-the-art for ultrasound imaging, despite having well understood physical limitations regarding spatial resolution [12,13]
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