Image Reconstruction from Sparse Data in Echo-Planar Imaging

Abstract

While echo-planar imaging (EPI) has emerged as one of the fastest of the common magnetic resonance imaging (MRI) methods, there remains a need to further reduce EPI scan times. We present a method for obtaining accurate image reconstruction from EPI data along highly sparse horizontal lines in Fourier space. This method iteratively minimizes the total variation (TV) of the estimated image using gradient descent, 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 Fourier space samples obtained along as few as 20% of the horizontal lines used in a typical full EPI scan. This corresponds to at least a factor of five decrease in the required scan time. The algorithm should also increase EPI scan efficiency by allowing for greatly improved image resolution and signal to noise ratio in a scan of a given time. By adding Gaussian noise to the Fourier samples, we demonstrate that the algorithm has the added benefit of regularizing the reconstructed image, making it very effective for noisy data. Although our results are discussed in the context of two-dimensional MRI, they are directly applicable to higher dimensional imaging and to other non-uniform grids in Fourier space.