Yu Y. Li^{1,2}

In the presented work, a compressed sensing approach is introduced to calibrate k-t space parallel imaging reconstruction. This approach removes the need for calibration data and improves image reconstruction using data sparsity associated with narrow bandwidth of physiological motion signals. The new approach is used to enable real-time neonatal chest MRI. It is experimentally demonstrated that real-time imaging can provide high-quality cardiac and pulmonary images for improved clinical diagnosis in premature babies.

Figure 1 illustrates a correlation imaging model ^{1,2}. In correlation imaging, correlation functions may be estimated from
a set of fully-sampled calibration data, e.g., auto-calibration signals (ACS).
This may lead to a method equivalent to either GRAPPA or SENSE that has been
found insufficient for real-time imaging. The presented work introduces a compressed
sensing approach to estimating correlation functions. This can remove the need
for calibration data and improve image reconstruction using data
correlation associated with data sparsity. As a result, a gain in imaging
acceleration can be achieved, making it possible to collect real-time neonatal
chest MRI data. The proposed approach is formulated as follows:

Minimize
|| ** P_{s}** (

Subject
to **1). **Reconstructed data ** x** satisfies correlation imaging model
in Figure 1; and

where ** P_{s}** represents data undersampling in k-space
and

**Step 1**: Correlation functions are calculated from all available data (collected and reconstructed) in k-t space as
in Figure 1. The estimated correlation functions are transformed to Fourier
space. The sparsity constraint is applied by setting the Fourier spectra to be
zeroes outside of the frequency range of cardiac and respiratory motion signals.
The modified Fourier spectral are then transformed to the original space by inverse Fourier transform and used as the final
correlation functions.

**Step 2**: The linear equations are formed from the
estimated correlation functions and used to resolve the reconstruction
operators for image reconstruction from the collected data as in Figure 1. The
reconstructed data are modified by data fidelity constraint, i.e., they are
equal to the collected data at the sampling k-t space positions. The modified
data are used to estimate correlation functions for the next iteration.

To demonstrate real-time neonatal chest MRI, 5 neonatal volunteers (2 weeks to 2 months of age and <2.5kg of weight) were scanned with free-breathing and without sedation. Cardiac CINE imaging data were collected in real-time for ~25 seconds with a temporal resolution of 48 milliseconds (FOV 16cm, matrix 128×128, TR/TE 3.7/1.1 ms, slice thickness 5 mm, flip angle 45°). A set of data collected with k-space segmentation (8 phase encoding lines per segment) was used as references. Real-time lung images were collected for ~40 seconds with a temporal resolution of 123 milliseconds (FOV 16cm, matrix 192×192, slice thickness 6mm, flip angle 10°). A set of static lung images collected with a 3D fast gradient echo sequence with the same acquisition parameters was used as references.

1. Li, Y et al., MRM 2012, 68:2005-2017.

2. Li, Y et al., MRM 2015, 74(6): 1574-1586.

3. Bauman, G et al., MRM 2009, 62: 656-664.

Figure 1. Correlation imaging
model ^{1,2} gives a mathematical description for general parallel imaging. The model
may generate either SENSE-like or a GRAPPA-like reconstruction depending on how
correlation functions are estimated.

Figure 2. (a) Real-time
cardiac imaging provides better dynamic contrast between systolic and
diastolic phases than k-space segmentation. The temporal trajectory plot also shows
that real-time imaging gives a higher speed than cardiac (fast wave)
and respiratory (slow wave) motion. (b) The Fourier transform of the collected
center k-space lines show that the data are sparse in Fourier domain (signals
are concentrated within the respiratory and cardiac frequency bands). This
frequency sparsity is used to estimate k-t space correlation functions with
compressed sensing in correlation imaging model.

Figure 3. Compared with static imaging (upper-left), real-time
lung imaging (lower-left) gives higher signals within the lung parenchyma.
The Fourier spectrum (lower-right) shows the spectral peaks at the respiratory
and cardiac frequencies. They can be used to generate ventilation- and
perfusion-weighted images (upper-right) ^{3}. These spectra also
demonstrate the frequency sparsity of k-t space data. The frequency sparsity can
be used to estimate correlation functions with compressed sensing in
correlation imaging model.