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Image reconstruction from sparse data samples along spiral trajectories in MRI

We present a method for obtaining accurate image reconstruction from sparsely sampled magnetic resonance imaging (MRI) data obtained along spiral trajectories in Fourier space. This method minimizes the total variation (TV) of the estimated image, subject to the constraint that the Fourier transform of the image matches the known samples in Fourier space. Using this method, we demonstrate accurate image reconstruction from sparse Fourier samples. We also show that the algorithm is reasonably robust to the effects of measurement noise. Reconstruction from such sparse sampling should reduce scan times, improving scan quality through reduction of motion-related artifacts and allowing more rapid evaluation of time-critical conditions such as stroke. Although our results are discussed in the context of two-dimensional MRI, they are directly applicable to higher dimensional imaging and to other sampling patterns in Fourier space.