Reconstrução de imagens esparsas de ultrassom através de aproximação linear do manifold de aquisição e busca iterativa não convexa

Abstract

Model-based image and signal reconstruction has brought important improvements in terms of contrast and spatial resolution to 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 -- 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 (ROI). The creation of the expanded dictionary is based on a highly coherent sampling of the ROI, followed by a rank reduction of the corresponding data that encompasses two possible approximation criteria: one based on singular-value decomposition (SVD) and one minimize-maximum (Minimax). Although we develop here a formulation for two-dimensional sparse imaging problems, it can be readily extended to any D dimensions. 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 ROI into cells of any size. To evaluate the performance of the proposed method, we present results of two-dimensional ultrasound image reconstructions with simulated data in a nondestructive testing application. The proposed method succeeds at reconstructing sparse images from noisy measurements and provides higher accuracy than previous approaches based on regular discrete models. Results also confirm a theoretical expectation that the Minimax dictionary outperforms the SVD dictionary on the estimation of the cardinality of the solution.