A subspace approach to blind coil sensitivity estimation in parallel MRI

Background In parallel MRI, subsampled k-space data are simultaneously collected by multiple coils. Each coil introduces a sensitivity map (CSM) that is multiplied pointwise with the single image to be reconstructed. In ESPIRiT [1], for each pixel location in each coil, an eigen-decomposition is applied to small matrices to obtain CSMs. However, this approach can be time-consuming for larger imaging problems. Here, we exploit smoothness of the coil sensitivities in the image domain to model them as small finite impulse response (FIR) filters in k-space as in PRUNO [2]. Since pointwise-multiplication in image domain corresponds to convolution in k-space, parallel MRI problem can be expressed as a blind image deconvolution problem; consequently, a subspace approach [3] can be used to estimate the k-space coefficients of the CSMs.