Calibration-free Parallel Imaging Using Randomly Undersampled Multichannel Blind Deconvolution (MALBEC)

Jingyuan Lyu^{1}, Ukash Nakarmi^{1}, Yihang Zhou^{1}, Chaoyi Zhang^{1}, and Leslie Ying^{1,2}

A novel calibration-less parallel imaging technique is proposed. It is shown to be superior to SAKE in both theory and experiments.

[1] Shin, Peter J., et al. "Calibrationless parallel imaging reconstruction based on structured low-rank matrix completion." Magnetic Resonance in Medicine 72.4 (2014): 959-970.

[2] Majumdar, Angshul, Kunal Narayan Chaudhury, and Rabab Ward. "Calibrationless parallel magnetic resonance imaging: a joint sparsity model."Sensors 13.12 (2013): 16714-16735.

[3] Trzasko, Joshua D., and Armando Manduca. "Calibrationless parallel MRI using CLEAR." Signals, Systems and Computers (ASILOMAR), 2011 Conference Record of the Forty Fifth Asilomar Conference on. IEEE, 2011.

[4] Chen, Chen, Yeqing Li, and Junzhou Huang. "Calibrationless parallel MRI with joint total variation regularization." Medical Image Computing and Computer-Assisted Intervention–MICCAI 2013. Springer Berlin Heidelberg, 2013. 106-114.

[5] Kim, Tae Hyung, and Justin P. Haldar. "SMS-LORAKS: Calibrationless simultaneous multislice MRI using low-rank matrix modeling." Biomedical Imaging (ISBI), 2015 IEEE 12th International Symposium on. IEEE, 2015.

[6] Griswold, Mark A., et al. "Generalized autocalibrating partially parallel acquisitions (GRAPPA)." Magnetic resonance in medicine 47.6 (2002): 1202-1210.

[7] Lustig, Michael, and John M. Pauly. "SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space." Magnetic Resonance in Medicine 64.2 (2010): 457-471.

[8] Romberg, Justin, Ning Tian, and Karim Sabra. "Multichannel blind deconvolution using low rank recovery." SPIE Defense, Security, and Sensing. International Society for Optics and Photonics, 2013.

[9] Kim, Wan, et al. "Conflict-cost based random sampling design for parallel MRI with low rank constraints." SPIE Sensing Technology+ Applications. International Society for Optics and Photonics, 2015.

Figure 1. Illustration of multi-channel convolution in
k-space.

Figure
2. Illustration of rank 1 matrix $$${{\bf{X}}_{\bf{0}}}$$$
using a 1D example. It is formed as the outer product of two vectors. Each
observation $$${y_k}\left[ p \right]$$$ is a sum of the entries in $$${{\bf{X}}_{\bf{0}}}$$$ along
one of the skew diagonals of a submatrix of $$${{\bf{X}}_{\bf{0}}}$$$. The summations along
the arrows represent the linear equation $$$y = {\cal A}({{\bf{X}}_0})$$$.

Figure 3. Under-sampling pattern in k-space and the reconstruction results from SAKE,
Zero-filling, and the proposed MALBEC method.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

3232