Longitudinal Guided Super-Resolution Reconstruction of Neonatal Brain MR Images - Longitudinal Registration and Shape Modeling - page 65

at and , and
and are parameters cont
zation constant. We refer to
that the simultaneous consid
structural misalignments.
Fig. 2 illustrates the be
neonatal LR image by app
neonatal image, and then u
near a gyrus, we compute
LR image (Fig. 2A) and fo
rus structure in its neighbo
graded image. On the other
pattern (Fig. 2B). After com
map (Fig. 2C) that resemb
image (Fig. 2D). The com
reconstruction process. No
local weights are calculated
to the different contrast patt
The non-local mean ima
the neonatal HR image X :

are 3D patches of image centered at and ,
trolling the strength of the weights, and is the norm
o the obtained non-local mean image as , . N
deration of both LR and HR images increases robustnes

,
mali-
Note
ss to

nefit of using the longitudinal prior. We first simulat
plying Gaussian blurring and downsampling to a real
upsample it using spline-based interpolation. For a vo
its non-local similarity values in the interpolated neon
ound that its non-local weight map is dominated by the
orhood, which may be due to the blurring effect in the
r hand, the longitudinal HR image provides an informat
mbining these two sets of weights, we obtain a new wei
bles closely the results given by the original neonatal
mputed weight map would be very useful for guiding
te that, an advantage of our method is the proposed n
d based on the distance of patches, and thus will be rob
terns in the neonatal and longitudinal images .
ge is then used as a penalty term to guide the recovering

te a
HR
oxel
natal
gy-
de-
tive
ight
HR
the
non-
bust

g of

(5)

,

Fig. 2. Illustration of the prop
age after degradation process.
and shown in close-up view. T
of 7×7×7 are shown. The used
follow-up image. (C) is the com
image.

posed non-local weights. (A) shows a simulated neonatal LR
For the voxel marked by red, its local region is marked by gr
The non-local weights of that voxel with voxels in search dom
d image patch size is 3×3×3 for each voxel. (B) is its longitud
mbined weights from (A) and (B). (D) is the original neonatal

im-
reen
main
dinal
HR

2.3 Global and Local S Self-Similarity

We follow a previous stud
and local self-similarity in t
thus reformulated as follow

y [7] to add regularization terms for ensuring both glo
the estimated HR neonatal image. The proposed metho
ws:

obal
d is

min ,

(6)