Resolution and Noise Properties of Linear Phase-Constrained Partial Fourier Reconstruction

Justin P. Haldar¹, Kenneth Sakaie², Zhi-Pei Liang¹

Phase-constrained partial Fourier (PF) reconstruction is a classical technique that leverages prior knowledge of the image phase to reduce k-space sampling requirements. While the technique has seen wide use, the characteristics of PF reconstructions are usually only evaluated empirically. In this work, we show that resolution and noise properties of the class of linear PF reconstruction methods (including homodyne, projection onto convex sets with linear projections, and matrix inversion methods) can be characterized theoretically in terms of spatial response functions and interference response functions. We demonstrate an application of these theoretical characterizations in the context of regularized PF reconstruction.