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We compare here two approaches to reconstruct sub-sampled partial Fourier MRI data acquired with multiple receiver coils. The first approach combines homodyne detection with SENSE-like reconstructions. The second approach employs separate regularization of the real and imaginary components (two-parameters) of the parallel MRI linear system to constrain the magnitude of phase variation in the reconstructed image. We show that both methods robustly reconstruct images from several sampling patterns. The dominant difference is the number of symmetric lines of k-space needed to provide high quality reconstructions. The two parameter approach can reconstruct good images using only two whereas the homodyne approach requires significantly more. We present a method for automatic selection of the two parameters, and results from both high resolution and low contrast phantom data.