Longitudinal Guided Super-Resolution Reconstruction of Neonatal Brain MR Images - Longitudinal Registration and Shape Modeling - page 67

Algorithm 1. Longitudinal Guided Super-Resolution Reconstruction of Neonatal
Images
Input : Low-resolution neonatal image T , high-resolution longitudinal image L
Initialize the desired high-resolution neonatal image X by upsampling T with
spline-based interpolation . Set redundant variables 0 , 0 , 1,2,3 .
Repeat
Update , using non-local weights computed from X and L;
Repeat
Update based on Eq. (8) using gradient descent;
Update based on Eq. (9) using Singular Value Thresholding (SVT) [14];
Update based on Eq. (10);
End
Until iteration difference in the cost function (Eq. (7)) is less than ;
End
Output: Reconstructed high-resolution neonatal image X ;

3 Experiments

3.1 Data

A total of 28 healthy infants (11 males and 17 females) were used in this study. They
were firstly scanned at birth, and a follow-up scan was performed at 2 years of age. A
Siemens head-only 3T scanner was used with a circular polarized head coil. T2 im-
ages were acquired with 58 axial slices at the resolution of 1.25×1.25×1.95 mm 3 . T1
images were also acquired with 144 sagittal slices at the resolution of 1×1×1 mm 3 .
All images were preprocessed using a standard image-processing pipeline, includ-
ing bias correction and skull stripping [15]. T2 images were linearly aligned to their
corresponding T1 images. The longitudinal follow-up images were also aligned to
their neonatal images using affine registration followed by nonlinear diffeomorphic
demons registration [16].

3.2 Experimental Setting

For evaluation of the proposed method, we simulated a group of neonatal LR
images (Fig. 3) by applying blurring and downsampling operators to the original
neonatal images. Images reconstructed by the proposed method were compared with
the respective original images serving as ground-truth. Specifically, blurring was
performed using a Gaussian kernel with standard deviation of 1 voxel. Downsampling
was carried out by averaging every 8 voxels in an image, to simulate the partial vo-
lume effect. Signal-to-noise ratio (SNR) was used to compare the recovered image