Blind parallel MRI reconstruction with arbitrary k-space trajectories

This paper presents a new blind reconstruction approach for parallel MR imaging with arbitrary k-space sampling patterns. The provided reconstruction model involves an energy compactness regularization on the discrete cosine transform (DCT) coefficients of the coil sensitivities and a total variation regularization on the desired image. The advantage to choose cosine basis is twofold: the smooth sensitivity function can be well approximated by a small number of cosine bases and the (inverse) discrete cosine transform can be efficiently computed. An augmented Lagrangian based alternating minimization method is then implemented to solve the TV regularized optimization problem, where only fast Fourier transforms and component-wise multiplications (or thresholding) are involved. The experimental results show that the proposed reconstruction approach performs well on blind reconstruction of MR imaging.