Simultaneous image reconstruction and sensitivity estimation in parallel MRI using blind compressed sensing

Parallel magnetic resonance imaging (MRI) reconstruction problem can be formulated as a multichannel sampling problem where solutions can be sought analytically. However, the channel functions given by the coil sensitivities in parallel imaging are not known exactly and the estimation error usually leads to artifacts or degraded SNR. In the context of parallel MRI, this work investigates the blind multichannel under-sampling problem where both the channel functions and signal are reconstructed simultaneously under sparseness constraints. We propose a novel algorithm to reconstruct both the coil sensitivities and image simultaneously from randomly undersampled, multichannel k-space data. The algorithm effectively applies the concept of compressed sensing (CS) to solve an underdetermined nonlinear problem, but is different from the conventional CS in that the sensing matrix is not known exactly. The proposed algorithm is shown to improve the reconstruction accuracy of SparseSENSE and L₁-SPIRiT when the same number of measurements is used.