4 Reconstruction of Retinal OCT Images with Sparse Representation
85
Fig. 4.7 Process for generating the HH and LL training images
Fig. 4.8 Selection of patches from the LL and HH images to construct their corresponding dictionaries
[25]. Then, we make the learned dictionary pair matched. In the dictionary learning
stage, the positions of the nonzero sparse coefficients determine the selected training
patches to update the atom [25]. Therefore, if the positions of non-zero coefficients
in
α
i
L ,L
Z
i1
are the same as that in
α
i
H,H
Z
i1
, the dictionary atoms in D L ,L and
D H,H will be updated with the spatially matched patch pairs [25] and thus D L ,L will
still match with D H,H in the learning process. Based on this, we modify the original
OMP algorithm [34], and propose a coupled OMP (COMP) algorithm to pursuit the
position matched coefficients
α
i
H,H
Z
i1
and
α
i
L ,L
Z
i1
. Since D H,H is unknown in
the image reconstruction phase, during the atom selection process, positions of the
selected atoms in D H,H should be the same as that of the chosen atoms in D L ,L . To
achieve this, we first employ the original OMP algorithm to seek the coefficient α
i
L ,L
of x
i
L ,L and preserve the index set of the selected atoms G. Then, we compute α
i
H,H
with the atoms set G