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Parallel MRI using phased array coils can be viewed as an application of the multichannel sampling theory. Specifically, in the case of uniform 1-D undersampling, Papoulis' classical reconstruction formulas correspond well to the existing parallel MRI reconstruction algorithms, and a number of practical issues can be analyzed in this context. However, parallel MRI also presents several unique signal processing problems, whose solutions can help maximize the potential of parallel MRI for fast imaging. While existing parallel MRI methods were developed independently of the multichannel sampling theory, making such a connection may help develop more optimal methods for parallel MRI data acquisition and image reconstruction.