4094 Analogy of phase-constrained parallel MRI formulations

Purpose: One major drawback of parallel MRI (pMRI) is the noise amplification due to the reconstruction process. The noise amplification originates from the formulation of pMRI as an inverse problem and is characterized by the g-factor (1). Phase-constrained algorithms achieve a significant g-factor reduction by constraining all elements of the solution to be real-valued and are categorized into two formulations. In the original formulation, the SENSE reconstruction problem is split into realand imaginary parts and is referred to as phase-constrained (PC) SENSE (2,3,4). An alternative formulation utilizes conjugate k-space symmetry by generating virtual coils (VC) (5). The purpose of this work is to demonstrate by mathematical analysis that both formulations are equivalent.