Parallel imaging using multiple receiver coils has emerged as an effective tool to reduce imaging time in various MRI applications. Mathematically, the imaging equation can be expressed as a weighted Fourier transform, and the image reconstruction formula can be derived from Papoulis' generalized sampling theorem. Although perfect reconstructions can be obtained under ideal conditions, several signal processing problems exist in practical settings. This paper discusses some of these problems. Specifically, it analyzes the effect of data truncation, addresses the problem of estimating the coil sensitivity functions, and proposes a regularization scheme to cope with the ill-conditioned inverse problem associated with achieving high acceleration factors.