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.
Keywords: dictionary; inverse problems; manifolds; nondestructive testing; rank reduction; ultrasound.