Iterative image reconstruction in MRI with separate magnitude and phase regularization

Iterative methods for image reconstruction in MRI are useful in several applications, including reconstruction from non-Cartesian k-space samples, compensation for magnetic field inhomogeneities, and imaging with multiple receive coils. Existing iterative MR image reconstruction methods are either unregularized, and therefore sensitive to noise, or have used regularization methods that smooth the complex valued image. These existing methods regularize the real and imaginary components of the image equally. In many MRI applications, including T₂*-weighted imaging as used in fMRI BOLD imaging, one expects most of the signal information of interest to be contained in the magnitude of the voxel value, whereas the phase values are expected to vary smoothly spatially. This paper proposes separate regularization of the magnitude and phase components, preserving the spatial resolution of the magnitude component while strongly regularizing the phase component. This leads to a non-convex regularized least-squares cost function. We describe a new iterative algorithm that monotonically decreases this cost function. The resulting images have reduced noise relative to conventional regularization methods.