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Open AccessArticle

Sparse Ultrasound Imaging via Manifold Low-Rank Approximation and Non-Convex Greedy Pursuit

Graduate Program in Electrical and Computer Engineering (CPGEI), Federal University of Technology, Paraná (UTFPR), Curitiba PR 80230-901, Brazil
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Sensors 2018, 18(12), 4097; https://doi.org/10.3390/s18124097
Received: 19 October 2018 / Revised: 16 November 2018 / Accepted: 20 November 2018 / Published: 23 November 2018
(This article belongs to the Special Issue Ultrasonic Sensors 2018)
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. View Full-Text
Keywords: ultrasound; nondestructive testing; manifolds; inverse problems; dictionary; rank reduction ultrasound; nondestructive testing; manifolds; inverse problems; dictionary; rank reduction
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Rigo Passarin, T.A.; Wüst Zibetti, M.V.; Rodrigues Pipa, D. Sparse Ultrasound Imaging via Manifold Low-Rank Approximation and Non-Convex Greedy Pursuit. Sensors 2018, 18, 4097.

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