Non-linear spatial encoding magnetic (SEM) fields can accelerate data acquisitions and improve the image quality. O-Space imaging generates a radially varying SEM field for spatial encoding in order to achieve more efficient encoding. In this work, we introduce and evaluate a novel primal dual algorithm which can handle the inverse problems of non-smooth convex optimization with non-linear forward operators to reconstruct O-Space images from undersampled data. The experimental results on simulated data show that the proposed method can achieve better image quality compared with the existing methods.
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