Impact of Coil Sensitivity Estimation on MRI reconstruction methods Combining Compressed Sensing and Parallel MRI

INTRODUCTION: Parallel MRI has been used widely to accelerate image acquisition [1,2]. Recently, application of compressed sensing (CS) to MRI has been proposed and showed great promise [3]. It is reported that combining parallel MRI and CS can enable further acceleration in MRI acquisition [4,5]. SparseSENSE directly applies CS to SENSE by using a random under-sampling pattern and a regularization term in the objective function [4]. DCS-SENSE serially concatenates distributed CS and SENSE, exploiting the inter-coil dependencies for the CS reconstruction [5]. In this study, we will investigate the performances of the two aforementioned methods and examine the impact of coil sensitivity estimation in each reconstruction technique. THEORY: The acquired k-space data in the l coil is given by yl = FΩSlu + nl, where u is the desired image, Sl is the sensitivity of the l coil, FΩ is the partial Fourier matrix, and nl is the observation noise. SparseSENSE minimizes the L1 norm of the reconstruction image in a sparsifying domain: min ||Wu||1 s.t. yl = FΩSlu for all 1≤l≤L (1), where W is the sparsifying transform operator. Thus it produces a single output image using measurements from all L coils. DCSSENSE first solves the CS problem for multiple coils producing L output images with reduced FOV, and uses these intermediate images as inputs to the SENSE reconstruction. The signal model for DCS-SENSE can be represented as yl = FΩ’ul + nl, where ul is the aliased image of l coil modulated by the coil sensitivity with reduced FOV. All aliased images are simultaneously reconstructed by: min ||C1||2+ ||C2||2+...+ |CN||2, s.t. yl = FΩ’ul for all 1≤l≤L (2), where Cn is the n row of [Wu1, Wu2, , WuL]. This assumes that the reconstructed aliased images are sparse in the transform domain and their nonzero coefficients are in the same coordinates. The final image is obtained by conventional SENSE reconstruction from aliased images ul’s and the coil sensitivity information. The coil sensitivity information is not utilized in the CS reconstruction of DCS-SENSE and only used in the SENSE reconstruction step.