4 Reconstruction of Retinal OCT Images with Sparse Representation
89
We first tested a compressive sampling method [51] on both randomly and regularly subsampled synthetic datasets to examine the random sampling scheme advocated in [12, 13]. As can be observed in Fig. 4.11, random sampling had insignificant
benefits over the conventional regularly sampling scheme for our application. Therefore, we apply the regular sampling for both the synthetic and real experimental
datasets. In these experiments, we compared our proposed SBSDI method with four
competing approaches: Tikhonov [15], Bicubic, BM3D [40] +Bicubic and ScSR
[29]. The BM3D+Bicubic method is a combination of the state-of-the-art denoising
algorithm BM3D with the bicubic interpolation approach. The ScSR method utilizes
the joint dictionary learning operation to train the LL and HH dictionaries from the
related LL and HH training patches, without considering the correlations from 3D
nearby slices.
In these experiments, the parameters of the proposed method were empirically
selected and kept unchanged for all images in both synthetic and real experimental datasets. Since most of the similar structures in SDOCT images lay along the
horizontal direction, the patch size was chosen to be 4 × 8 and 4 × 16 pixel wide
rectangles for 50 and 75% data missing, respectively. As the patch size becomes bigger, our algorithm will remove the noise more efficiently, but may result in stronger
smoothing and the loss of image detail. We set the number of nearby slices for the
joint operation to 4 (2 slices above and 2 slices below the current processed image,
respectively). Slices that are far distant from the target B-scan being processed have
not been added since they often have different image content. In the clustering stage,
the cluster number f in the detailed group and v in the smooth group were set to
70 and 20, respectively. As the detailed group has more complex structures than the
smooth group, the f number of the detailed group is larger than that of the smooth
group. From each cluster, 500 vectors were selected to construct the initial structural
sub-dictionary. The sparsity level T for both COMP and SOMP algorithms were set
to 3. We select the iteration number J in the dictionary learning process to 10, which
almost reaches convergence in our learning problem. We select the parameters β in
(11) and h in (16) to 0.001, 12, and 80, respectively.
For the synthetic datasets, the low-SNR-high-resolution datasets previously utilized in the Sect. 4.3.2.3 were also used here. As described in Sect. 4.3.2.3, these
datasets were acquired from 28 eyes of 28 subjects with and without non-neovascular
age-related macular degeneration (AMD). For each patient, we acquired two sets of
SDOCT scans. The first scan was a volume containing the retinal fovea with 1000
A-scans per B-scan and 100 B-scans per volume. The second scan was centered at
the fovea with 1000 A-scans per B-scan and 40 azimuthally repeated B-Scans. We
selected the central foveal B-scan within the first volume and further subsampled
this scan with both random and regular patterns, to create simulated LL test images
(e.g. Fig. 4.11a, c). The set of azimuthally repeated B-scans was registered using the
StackReg image registration plug-in [41] for ImageJ to construct the HH averaged
image (e.g. Fig. 4.11j). In the 28 datasets, 18 LL and HH pairs from 18 different
datasets were randomly selected to test the performance of the proposed method,
while the remaining 10 LL and HH pairs were used to train the dictionaries and the
mapping functions. The constructed dictionaries and mapping functions were also
89
We first tested a compressive sampling method [51] on both randomly and regularly subsampled synthetic datasets to examine the random sampling scheme advocated in [12, 13]. As can be observed in Fig. 4.11, random sampling had insignificant
benefits over the conventional regularly sampling scheme for our application. Therefore, we apply the regular sampling for both the synthetic and real experimental
datasets. In these experiments, we compared our proposed SBSDI method with four
competing approaches: Tikhonov [15], Bicubic, BM3D [40] +Bicubic and ScSR
[29]. The BM3D+Bicubic method is a combination of the state-of-the-art denoising
algorithm BM3D with the bicubic interpolation approach. The ScSR method utilizes
the joint dictionary learning operation to train the LL and HH dictionaries from the
related LL and HH training patches, without considering the correlations from 3D
nearby slices.
In these experiments, the parameters of the proposed method were empirically
selected and kept unchanged for all images in both synthetic and real experimental datasets. Since most of the similar structures in SDOCT images lay along the
horizontal direction, the patch size was chosen to be 4 × 8 and 4 × 16 pixel wide
rectangles for 50 and 75% data missing, respectively. As the patch size becomes bigger, our algorithm will remove the noise more efficiently, but may result in stronger
smoothing and the loss of image detail. We set the number of nearby slices for the
joint operation to 4 (2 slices above and 2 slices below the current processed image,
respectively). Slices that are far distant from the target B-scan being processed have
not been added since they often have different image content. In the clustering stage,
the cluster number f in the detailed group and v in the smooth group were set to
70 and 20, respectively. As the detailed group has more complex structures than the
smooth group, the f number of the detailed group is larger than that of the smooth
group. From each cluster, 500 vectors were selected to construct the initial structural
sub-dictionary. The sparsity level T for both COMP and SOMP algorithms were set
to 3. We select the iteration number J in the dictionary learning process to 10, which
almost reaches convergence in our learning problem. We select the parameters β in
(11) and h in (16) to 0.001, 12, and 80, respectively.
For the synthetic datasets, the low-SNR-high-resolution datasets previously utilized in the Sect. 4.3.2.3 were also used here. As described in Sect. 4.3.2.3, these
datasets were acquired from 28 eyes of 28 subjects with and without non-neovascular
age-related macular degeneration (AMD). For each patient, we acquired two sets of
SDOCT scans. The first scan was a volume containing the retinal fovea with 1000
A-scans per B-scan and 100 B-scans per volume. The second scan was centered at
the fovea with 1000 A-scans per B-scan and 40 azimuthally repeated B-Scans. We
selected the central foveal B-scan within the first volume and further subsampled
this scan with both random and regular patterns, to create simulated LL test images
(e.g. Fig. 4.11a, c). The set of azimuthally repeated B-scans was registered using the
StackReg image registration plug-in [41] for ImageJ to construct the HH averaged
image (e.g. Fig. 4.11j). In the 28 datasets, 18 LL and HH pairs from 18 different
datasets were randomly selected to test the performance of the proposed method,
while the remaining 10 LL and HH pairs were used to train the dictionaries and the
mapping functions. The constructed dictionaries and mapping functions were also