• joint estimation;
  • SENSE;
  • self calibration;
  • variable density acquisition;
  • sensitivity estimation


Parallel magnetic resonance imaging (pMRI) using multichannel receiver coils has emerged as an effective tool to reduce imaging time in various applications. However, the issue of accurate estimation of coil sensitivities has not been fully addressed, which limits the level of speed enhancement achievable with the technology. The self-calibrating (SC) technique for sensitivity extraction has been well accepted, especially for dynamic imaging, and complements the common calibration technique that uses a separate scan. However, the existing method to extract the sensitivity information from the SC data is not accurate enough when the number of data is small, and thus erroneous sensitivities affect the reconstruction quality when they are directly applied to the reconstruction equation. This paper considers this problem of error propagation in the sequential procedure of sensitivity estimation followed by image reconstruction in existing methods, such as sensitivity encoding (SENSE) and simultaneous acquisition of spatial harmonics (SMASH), and reformulates the image reconstruction problem as a joint estimation of the coil sensitivities and the desired image, which is solved by an iterative optimization algorithm. The proposed method was tested on various data sets. The results from a set of in vivo data are shown to demonstrate the effectiveness of the proposed method, especially when a rather large net acceleration factor is used. Magn Reson Med 57:1196–1202, 2007. © 2007 Wiley-Liss, Inc.