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. 2012 Jan;67(1):34-41.
doi: 10.1002/mrm.22964. Epub 2011 Jun 27.

Parallel imaging with nonlinear reconstruction using variational penalties

Florian Knoll  1 , Christian Clason, Kristian Bredies, Martin Uecker, Rudolf Stollberger
Affiliations

Parallel imaging with nonlinear reconstruction using variational penalties

Florian Knoll et al. Magn Reson Med. 2012 Jan.

Abstract

A new approach based on nonlinear inversion for autocalibrated parallel imaging with arbitrary sampling patterns is presented. By extending the iteratively regularized Gauss-Newton method with variational penalties, the improved reconstruction quality obtained from joint estimation of image and coil sensitivities is combined with the superior noise suppression of total variation and total generalized variation regularization. In addition, the proposed approach can lead to enhanced removal of sampling artifacts arising from pseudorandom and radial sampling patterns. This is demonstrated for phantom and in vivo measurements.

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Figures

Figure 1
Figure 1
Comparison of IRGN (left) and IRGN-TV (right) for pseudorandom subsampling of a water phantom. Top: acceleration factor R = 4, βmin = 0; bottom: R = 10, βmin = 5 · 10−3.
Figure 2
Figure 2
Comparison of IRGN (first row) and IRGN-TV (second row) for retrospective pseudorandom subsampling (βmin = 0). From left: fully sampled acquisition, acceleration factors R = 4, R = 6, R = 8. difference images to the fully sampled SOS reconstruction are shown for IRGN (third row) and IRGN-TV (fourth row) and are rescaled individually for IRGN and IRGN-TV to allow better depiction of the pixel differences.
Figure 3
Figure 3
Magnified detail of Figure 2.
Figure 4
Figure 4
Comparison of IRGN-TV to TV filtering of conventional IRGN reconstructions for pseudorandom subsampling with R = 6 (top, same data as Fig. 2) and accelerated in-vivo imaging with R = 4 (bottom). For TV filtering, optimal regularization parameters were identified by visual inspection: β1∗=5⋅10−3 (left, for T2 weighted TSE data) and β2∗=1.5⋅10−2 (middle, for FLASH data). Both results for IRGN-TV (right) were obtained using the same parameter set, esp. βmin = 0.
Figure 5
Figure 5
Comparison of IRGN (left) and IRGN-TV (right) for radial sampling of a phantom (25 spokes, βmin = 5 · 10−3). Shown are two slices.
Figure 6
Figure 6
Comparison of IRGN (left) and IRGN-TV (middle) for radial sampling of a human heart (βmin = 5·10−3). Top: 25 spokes. Highlighted are structures with little signal intensity that can be lost due to strong TV regularization. Middle: 21 spokes. Highlighted are structures of similar size but slightly higher signal intensity that are preserved even in case of TV regularization. Bottom: 19 spokes. The plots on the right show signal intensities across a horizontal line, indicated in the top row of the reconstruction results. The ability of IRGN-TV to preserve sharp edges is highlighted in the plot of the reconstruction from 19 spokes. The arrow marks the sharp boarder of the ventricle, which is depicted equally well with IRGN and IRGN-TV. The undesired loss of a small structure is highlighted in the plot of the reconstruction from 21 spokes. The plot crosses two adjacent vessels, which are both represented in the IRGN solution, but only the left one appears in the IRGN-TV reconstruction.
Figure 7
Figure 7
Comparison of IRGN-TV and IRGN-TGV for phantom data (top: pseudorandom sampling; bottom: radial sampling; both: βmin = 5 · 10−3). Left: IRGN-TV (magnified details from Figs. 1, R = 10 and 5). Modulations from the coil sensitivities lead to pronounced staircasing artifacts from TV regularization. Right: IRGN-TGV. Staircasing artifacts are completely removed for TGV regularization.
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References

    1. Bauer F, Kannengiesser S. An alternative approach to the image reconstruction for parallel data acquisition in MRI. Math Meth Appl Sci. 2007;30:1437–1451.
    1. Ying L, Sheng J. Joint image reconstruction and sensitivity estimation in SENSE (JSENSE) Magn Reson Med. 2007;57(6):1196–1202. - PubMed
    1. Uecker M, Hohage T, Block KT, Frahm J. Image reconstruction by regularized nonlinear inversion – joint estimation of coil sensitivities and image content. Magn Reson Med. 2008;60(3):674–682. - PubMed
    1. Uecker M, Karaus A, Frahm J. Inverse reconstruction method for segmented multishot diffusion-weighted MRI with multiple coils. Magn Reson Med. 2009;62(5):1342–1348. - PubMed
    1. Sodickson DK, Manning WJ. Simultaneous acquisition of spatial harmonics (SMASH): fast imaging with radiofrequency coil arrays. Magn Reson Med. 1997;38(4):591–603. - PubMed

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