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

Abstract

Model-based image reconstruction has brought improvements in terms of contrast and spatial resolution to imaging applications such as magnetic resonance imaging and emission computed tomography. However, their use for pulse-echo techniques like ultrasound imaging is limited by the fact that model-based algorithms assume a finite grid of possible locations of scatterers in a medium -- which 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 based on a truncated singular value decomposition. We develop a greedy algorithm, based on the Orthogonal Matching Pursuit (OMP), 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 2-dimensional ultrasound image reconstructions 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.

A Compressed Sensing Approach for Multiple Obstacle Localisation Using Sonar Sensors in Air

“…For systems with more than one transducer, the PSF is formed by concatenation of the reflection signals received from each transducer. This process is based on medical ultrasound imaging research and is detailed in [ 24 , 25 , 26 , 27 ].…”

“…Compressed sensing provides several approaches to solve the reconstruction problem [ 37 , 38 ], such as convex optimisations, greedy algorithms and Bayesian methods. Greedy algorithms have shown success in medical imaging [ 26 ] and studies with radar and sonar imaging systems [ 14 , 15 , 17 ].…”