  Parallel magnetic resonance imaging has served as an effective and widely
adopted technique for accelerating scans. The advent of sparse sampling offers
aggressive acceleration, allowing flexible sampling and better reconstruction.
Nevertheless, faithfully reconstructing the image from limited data still poses
a challenging task. Recent low-rank reconstruction methods exhibit superiority
in providing a high-quality image. However, none of them employ the routinely
acquired calibration data for improving image quality in parallel magnetic
resonance imaging. In this work, an image reconstruction approach named
STDLR-SPIRiT was proposed to explore the simultaneous two-directional
low-rankness (STDLR) in the k-space data and to mine the data correlation from
multiple receiver coils with the iterative self-consistent parallel imaging
reconstruction (SPIRiT). The reconstruction problem was then solved with a
singular value decomposition-free numerical algorithm. Experimental results of
phantom and brain imaging data show that the proposed method outperforms the
state-of-the-art methods in terms of suppressing artifacts and achieving the
lowest error. Moreover, the proposed method exhibits robust reconstruction even
when the auto-calibration signals are limited in parallel imaging. Overall the
proposed method can be exploited to achieve better image quality for
accelerated parallel magnetic resonance imaging.
