An improved method for reduction of truncation artifact in magnetic resonance imaging

In Fourier magnetic resonance imaging (MR;I), signals from different positions in space are phase-encoded by the application of a gradient before the total signal from the imaged subject is acquired. In practice, a limited number of the phase-encoded signals are often acquired in order to minimize the duration of the studies and maintain adequate signal-to-noise ratio. However, this results in incomplete sampling in spatial frequency or truncation of the Ic-space data. The truncated data, when Fourier transformed to reconstruct, give rise to images degraded by limited resolution and ringing near sharp edges, which is known as the truncation artifact. A variety of methods have been proposed to reconstruct images with reduced truncation artifact. In this work, we use a regularization method in the context of a Bayesian framework. Unlike the approaches that operate on the raw data, the regularization approach is applied directly to the reconstructed image. In this framework, the two dimensional image is modeled as a random held whose posterior probability conditioned on the observed image is represented by the product of the likelihood of the observed data with the prior based on the local spatial structure of the underlying image. Since the truncation artifact appears in only one of the two spatial directions, the use of conventional piecewise-constant constraints may degrade soft edge regions in the other direction that are less affected by the truncation artifact. Here, we consider more elaborate forms of constraints than the conventional piecewise-smoothness constraints, which can capture actual spatial information about the MR images. In order to reduce the computational cost for optimizing non-convex objective functions, we use a deterministic annealing method. Our experimental results indicate that the proposed method not only reduces the truncation artifact, but also improves tissue regularity and boundary definition without degrading soft edge regions.