Nullspace compressed sensing for accelerated imaging

Introduction Compressed sensing techniques have recently become very popular for image reconstruction given sparsely sampled data. However, previous methods only approximately enforce the constraint that the reconstructed image has k-space data at specified locations, which requires manual parameter tuning and slower speeds for convergence [1,2,3,4]. In this work we show that it is possible to quickly reconstruct a sparsely sampled image that does not alter the initial k-space data.