Fat/water separation in k‐space with real‐valued estimates and its combination with POCS

Purpose To develop reconstruction methods for improved image quality of chemical shift displacement‐corrected fat/water imaging combined with partial Fourier acquisition. Theory Fat/water separation in k‐space enables correction of chemical shift displacement. Modeling fat and water as real‐valued rather than complex improves the conditionality of the inverse problem. This advantage becomes essential for k‐space separation. In this work, it was described how to perform regularized fat/water imaging with real estimates in k‐space, and how fat/water imaging can be combined with partial Fourier reconstruction using Projection Onto Convex Sets (POCS). Methods The reconstruction methods were demonstrated on chemical shift encoded gradient echo and fast spin echo data from volunteers, acquired at 1.5 T and 3 T. Both fully sampled and partial Fourier acquisitions were made. Data was retrospectively rejected from the fully sampled dataset to evaluate POCS and homodyne reconstruction. Results Fat/water separation in k‐space eliminated chemical shift displacement, while real‐valued estimates considerably reduced the noise amplification compared to complex estimates. POCS reconstruction could recover high spatial frequency information in the fat and water images with lower reconstruction error than homodyne. Partial Fourier in the readout direction enabled more flexible choice of gradient echo imaging parameters, in particular image resolution. Conclusion Chemical shift displacement‐corrected fat/water imaging can be performed with regularization and real‐valued estimates to improve image quality by reducing ill‐conditioning of the inverse problem in k‐space. Fat/water imaging can be combined with POCS, which offers improved image quality over homodyne reconstruction.