4 Reconstruction of Retinal OCT Images with Sparse Representation
93
Fig. 4.13 Clinical OCT scan patterns sample the field-of-view, to avoid missing small abnormalities, and thus result in highly correlated neighboring B-scans. a Summed-voxel projection [55] en
face SDOCT image of a non-neovascular age-related macular degeneration (AMD) patient from
the Age-Related Eye Disease Study 2 (AREDS2) Ancillary SDOCT (A2A SDOCT) [52]. b Three
B-scans acquired from adjacent positions. The red rectangular regions are zoomed into show the
differences between these neighboring scans
Structural Dictionary Construction
We learn the appropriate overcomplete dictionary of basis functions from a set
of high-quality training data. The high-quality training data is obtained by capturing, registering, and averaging repeated low-SNR B-scans from spatially very close
positions [56]. In addition, typical clinical OCT images may contain many complex
structures (e.g. retinal OCT scans show different layers and pathologies such as cysts
[54]) and thus one universal dictionary D might not be optimal for representing these
varied structures. Therefore, following our previous works in [5, 26], we learn H
sets of structural sub-dictionaries
D
structural
h
∈ R
q×n
, h 1, . . . , H , each designed
to represent one specific type of structure. This is achieved by first adopting the kmeans approach to divide the training patches into H clusters. For each cluster h, one
sub-dictionary D
structural
ˆ
h
t
i
is learned by the K-SVD algorithm [25] and one centroid
c h ∈ R
q patch is also obtained by the k-means approach.
3D Adaptive Sparse Decomposition
Firstly, we search for the structural sub-dictionary that is most suitable to represent
each test patch (x
t
i ). We use the Euclidian distance between the patch and the subdictionary centroid c h for selecting the appropriate sub-dictionary D
structural
ˆ
h
t
i
:
ˆ
h
t
i arg min
h
t
i
c h − x
t
i
2
2
, t 1, . . . , T, and h 1, . . . , H.
(4.18)
93
Fig. 4.13 Clinical OCT scan patterns sample the field-of-view, to avoid missing small abnormalities, and thus result in highly correlated neighboring B-scans. a Summed-voxel projection [55] en
face SDOCT image of a non-neovascular age-related macular degeneration (AMD) patient from
the Age-Related Eye Disease Study 2 (AREDS2) Ancillary SDOCT (A2A SDOCT) [52]. b Three
B-scans acquired from adjacent positions. The red rectangular regions are zoomed into show the
differences between these neighboring scans
Structural Dictionary Construction
We learn the appropriate overcomplete dictionary of basis functions from a set
of high-quality training data. The high-quality training data is obtained by capturing, registering, and averaging repeated low-SNR B-scans from spatially very close
positions [56]. In addition, typical clinical OCT images may contain many complex
structures (e.g. retinal OCT scans show different layers and pathologies such as cysts
[54]) and thus one universal dictionary D might not be optimal for representing these
varied structures. Therefore, following our previous works in [5, 26], we learn H
sets of structural sub-dictionaries
D
structural
h
∈ R
q×n
, h 1, . . . , H , each designed
to represent one specific type of structure. This is achieved by first adopting the kmeans approach to divide the training patches into H clusters. For each cluster h, one
sub-dictionary D
structural
ˆ
h
t
i
is learned by the K-SVD algorithm [25] and one centroid
c h ∈ R
q patch is also obtained by the k-means approach.
3D Adaptive Sparse Decomposition
Firstly, we search for the structural sub-dictionary that is most suitable to represent
each test patch (x
t
i ). We use the Euclidian distance between the patch and the subdictionary centroid c h for selecting the appropriate sub-dictionary D
structural
ˆ
h
t
i
:
ˆ
h
t
i arg min
h
t
i
c h − x
t
i
2
2
, t 1, . . . , T, and h 1, . . . , H.
(4.18)