4 Reconstruction of Retinal OCT Images with Sparse Representation
83
to the case of MSR and CNR in Table 4.1, we observe that the MSBTD method also
delivers the best results in the PSNR. Furthermore, we note that although the PSNR
of the K-SVD is close to that of the MSBTD method, two clinical experts preferred
the visual outcome of the MSBTD method, as illustrated in Fig. 4.6.
4.3.2 Sparsity Based Simultaneous Denoising
and Interpolation (SBSDI)
As described in the Sect. 4.2, Yang et al., introduced a sparsity based interpolation
method for the nature images [29]. However, unlike the natural images, the real
obtained low resolution OCT image is interfered by very high levels of noise. In this
subsection, we introduce a novel SBSDI method, which can simultaneously denoise
and interpolate OCT images.
4.3.2.1 Low-Resolution-Low-SNR and High-Resolution-High-SNR
Dictionary Pair and Mapping Training
Inspired by the machine learning based approaches [29, 45, 46], the objective of the
proposed SBSDI method is to obtain the relationship between two feature spaces:
low-resolution-low-SNR (LL) space χ L ,L and ideal high-resolution-high-SNR (HH)
space χ H,H from a large number of training samples. After the relationship is
obtained, we can reconstruct the ideal HH image Y H,H ∈ χ H,H using the observed
LL image Y L ,L ∈ χ L ,L .
Dictionary and Mapping Training
To create HH images as the ideal training datasets, we first adopt a customized
scanning pattern to acquire a number of repeated densely sampled B-scans from
nearly the same position. Then, we register and average all these images to obtain
the ideal HH image [47]. In the densely acquired B-scans, we randomly select a single
noisy yet still high resolution frame and downsample this noisy frame to create the
related LL image. The process for generating the HH and LL training images is
illustrated in Fig. 4.7.
We link the LL and HH spaces by establishing a relationship between their related
dictionary atoms and sparse coefficients. Instead of enforcing the equality restriction on the sparse coefficients [29], we require the dictionaries (denoted as D L ,L
and D H,H ) for the two feature spaces to be strictly matched. That is, the selected
dictionary atoms for reconstructing the LL image strictly correspond to the counterpart atoms for recovering the HH image. To meet this, we can directly extract a
large number of spatially matched LL and HH patches from training image pairs
(Fig. 4.8). However, sparse coding over the dictionary with large number of samples
will create very high computational cost. To achieve a more compact representation, we can train the dictionary pair on a large number of extracted training patches
83
to the case of MSR and CNR in Table 4.1, we observe that the MSBTD method also
delivers the best results in the PSNR. Furthermore, we note that although the PSNR
of the K-SVD is close to that of the MSBTD method, two clinical experts preferred
the visual outcome of the MSBTD method, as illustrated in Fig. 4.6.
4.3.2 Sparsity Based Simultaneous Denoising
and Interpolation (SBSDI)
As described in the Sect. 4.2, Yang et al., introduced a sparsity based interpolation
method for the nature images [29]. However, unlike the natural images, the real
obtained low resolution OCT image is interfered by very high levels of noise. In this
subsection, we introduce a novel SBSDI method, which can simultaneously denoise
and interpolate OCT images.
4.3.2.1 Low-Resolution-Low-SNR and High-Resolution-High-SNR
Dictionary Pair and Mapping Training
Inspired by the machine learning based approaches [29, 45, 46], the objective of the
proposed SBSDI method is to obtain the relationship between two feature spaces:
low-resolution-low-SNR (LL) space χ L ,L and ideal high-resolution-high-SNR (HH)
space χ H,H from a large number of training samples. After the relationship is
obtained, we can reconstruct the ideal HH image Y H,H ∈ χ H,H using the observed
LL image Y L ,L ∈ χ L ,L .
Dictionary and Mapping Training
To create HH images as the ideal training datasets, we first adopt a customized
scanning pattern to acquire a number of repeated densely sampled B-scans from
nearly the same position. Then, we register and average all these images to obtain
the ideal HH image [47]. In the densely acquired B-scans, we randomly select a single
noisy yet still high resolution frame and downsample this noisy frame to create the
related LL image. The process for generating the HH and LL training images is
illustrated in Fig. 4.7.
We link the LL and HH spaces by establishing a relationship between their related
dictionary atoms and sparse coefficients. Instead of enforcing the equality restriction on the sparse coefficients [29], we require the dictionaries (denoted as D L ,L
and D H,H ) for the two feature spaces to be strictly matched. That is, the selected
dictionary atoms for reconstructing the LL image strictly correspond to the counterpart atoms for recovering the HH image. To meet this, we can directly extract a
large number of spatially matched LL and HH patches from training image pairs
(Fig. 4.8). However, sparse coding over the dictionary with large number of samples
will create very high computational cost. To achieve a more compact representation, we can train the dictionary pair on a large number of extracted training patches