Image Reconstruction as Nonlinear Inverse Problem (NLINV)

In contrast to what many people believe, the most important improvement in MRI hardware is not the development of very high magnetic fields, but of multiple independent receive coils (and corresponding independent receive channels). This has led to completely new acquisition techniques such as parallel imaging and the adaptation of iterative algorithms for image reconstruction.

Iterative image reconstruction. The calculation starts with an initial image, computes the corresponding data, compares it with the measured data, and makes suitable adjustments to the image. Algorithms for iterative optimizations including regularization techniques are available from numerical mathematics but require modifications for MRI.

The idea of parallel imaging is to speed up the acquisition process by measuring less data. Because a conventional reconstruction of such data generates aliasing artifacts, the missing information must come from simultaneous acquisitions of several undersampled data sets with the use of multiple receive coils that exhibit different sensitivity profiles. This situation requires a new way of image reconstruction, which emerges as the solution of an inverse problem: if a direct image calculation is not possible because of a lack of sufficient data, then the process may be reversed by estimating an image that best matches the data of all coils.

Significant improvements in image quality (e.g., reduction of residual aliasing artifacts) are achieved by extending linear inverse techniques (GRAPPA, AutoSENSE), which are currently implemented on commercially available MRI systems, to a nonlinear inverse reconstruction. A most important advantage of such methods is the possibility to simultaneously (rather than sequentially) estimate the coil sensitivities and image content. On the hand other hand, the general utilization of nonlinear inverse reconstructions is still hampered by a considerably higher computational demand.

Comparison of linear inverse reconstructions (GRAPPA, AutoSENSE) with the proposed nonlinear reconstruction for the case of a 3D FLASH MRI acquisition (selected partition) with a 2D acceleration factor of 4 (2 × 2) and 16 × 16 reference lines in central k space.

For more details see Uecker et al: Image reconstruction by regularized nonlinear inversion - Joint estimation of coil sensitivities and image content. Magn Reson Med 60, 674-682 (2008) [Online Version]

For recent applications see Real-Time MRI in the applications section.

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