An L1-norm phase constraint for half-Fourier compressed sensing in 3D MR imaging

In most half-Fourier imaging methods, explicit phase replacement is used. In combination with parallel imaging, or compressed sensing, half-Fourier reconstruction is usually performed in a separate step. The purpose of this paper is to report that integration of half-Fourier reconstruction into iterative reconstruction minimizes reconstruction errors.

The L1-norm phase constraint for half-Fourier imaging proposed in this work is compared with the L2-norm variant of the same algorithm, with several typical half-Fourier reconstruction methods. Half-Fourier imaging with the proposed phase constraint can be seamlessly combined with parallel imaging and compressed sensing to achieve high acceleration factors.

In simulations and in in-vivo experiments half-Fourier imaging with the proposed L1-norm phase constraint enables superior performance both reconstruction of image details and with regard to robustness against phase estimation errors.

The performance and feasibility of half-Fourier imaging with the proposed L1-norm phase constraint is reported. Its seamless combination with parallel imaging and compressed sensing enables use of greater acceleration in 3D MR imaging.