The SENSE-Isomorphism Theoretical Image Voxel Estimation (SENSE-ITIVE) Model for Reconstruction and Observing Statistical Properties of Reconstruction Operators
Format of Original
Journal of Magnetic Resonance Imaging
Original Item ID
doi: 10.1016/j.mri.2012.04.002; PubMed Central: PMCID 3443306
The acquisition of sub-sampled data from an array of receiver coils has become a common means of reducing data acquisition time in MRI. Of the various techniques used in parallel MRI, SENSitivity Encoding (SENSE) is one of the most common, making use of a complex-valued weighted least squares estimation to unfold the aliased images. It was recently shown in Bruce et al. [Magn. Reson. Imag. 29(2011):1267-1287] that when the SENSE model is represented in terms of a real-valued isomorphism,it assumes a skew-symmetric covariance between receiver coils, as well as an identity covariance structure between voxels. In this manuscript, we show that not only is the skew-symmetric coil covariance unlike that of real data, but the estimated covariance structure between voxels over a time series of experimental data is not an identity matrix. As such, a new model, entitled SENSE-ITIVE, is described with both revised coil and voxel covariance structures. Both the SENSE and SENSE-ITIVE models are represented in terms of real-valued isomorphisms, allowing for a statistical analysis of reconstructed voxel means, variances, and correlations resulting from the use of different coil and voxel covariance structures used in the reconstruction processes to be conducted. It is shown through both theoretical and experimental illustrations that the miss-specification of the coil and voxel covariance structures in the SENSE model results in a lower standard deviation in each voxel of the reconstructed images, and thus an artificial increase in SNR, compared to the standard deviation and SNR of the SENSE-ITIVE model where both the coil and voxel covariances are appropriately accounted for. It is also shown that there are differences in the correlations induced by the reconstruction operations of both models, and consequently there are differences in the correlations estimated throughout the course of reconstructed time series. These differences in correlations could result in meaningful differences in interpretation of results.
Bruce, Iain P.; Karaman, M. Muge; and Rowe, Daniel B., "The SENSE-Isomorphism Theoretical Image Voxel Estimation (SENSE-ITIVE) Model for Reconstruction and Observing Statistical Properties of Reconstruction Operators" (2012). Mathematics, Statistics and Computer Science Faculty Research and Publications. 263.
Accepted version. Magnetic Resonance Imaging, Vol. 30, No. 8 (October 2012): 1143-1166. DOI. © 2012 Wiley. Used with permission.
This is the peer reviewed version of the following article: "The SENSE-Isomorphism Theoretical Image Voxel Estimation (SENSE-ITIVE) Model for Reconstruction and Observing Statistical Properties of Reconstruction Operators," which has been published in final form here: DOI. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.