76
L. Fang and S. Li
pression of patch x i can be achieved by storing the positions and values of non-zero
coefficients in α
s
i and the mean value of x i .
4.3 Sparsity Based Methods for the OCT Image
Reconstruction
4.3.1 Multiscale Sparsity Based Tomographic Denoising
(MSBTD)
4.3.1.1 Multiscale Structural Dictionary
As described in Sect. 4.2, a fundamental problem for the sparsity based denoising
model is the selection of the dictionary D. The popular sparsity based denoising
algorithms usually use the noisy image itself to train the dictionary (denoted as
D
Noise ) [28]. Though these kinds of methods can provide promising results for natural
images, the high level of noise in OCT images will negatively interfere with the
training process, degrade the quality of the trained dictionary, and subsequently lead
to a suboptimal denoising result. An ideal approach is to train the dictionary from
the noiseless image. Since in practice, such an ideal OCT image is not available, we
create a less noisy image Y
Ave , obtained from registering and averaging a sequence
of (e.g., T) repeated B-scans from a unique position (see Fig. 4.1). Compared with
the D
Noise , the dictionary trained on this averaged image, D
Ave , is less affected by
noise.
To compare the above two dictionary training strategy, we use the popular KSVD training algorithm [25] and the proposed MSBTD algorithm described in the
following subsection for the dictionary training. Figure 4.2 shows examples of the
dictionaries trained by the K-SVD algorithm on a low-SNR B-scan (see Fig. 4.3a) and
MSBTD algorithm on an averaged high-SNR image (see Fig. 4.3b, c), respectively.
As can be observed, compared with the D
Ave , the D
Noise is more affected by noise in
the OCT image. Therefore, unlike the work in [28], the proposed MSBTD algorithm
denoises each low-SNR image utilizing a dictionary learned from a nearby (or even
distant) averaged image. This learning strategy can reduce the noise disturbance in
the dictionary learning process, and thus is expected to enhance the denoising result,
without significantly increasing the image acquisition time.
On the other hand, the popular learning algorithms (e.g., K-SVD [28] and its
variants [19]) often learn a universal dictionary D on a large number of training
patches. Such a universal dictionary might be neither optimal nor efficient to represent
different kinds of structures in the retinal OCT images. Therefore, the proposed
MSBTD algorithm learns a set of subdictionaries
D
Str
k ∈ R
Q×Q
, k 1, 2, . . . , K,
each best fit a particular structure [35, 36]. This is achieved by first clustering the
training patches into K structural clusters using the k-means approach. The centroid
of each cluster (c k ∈ R
Q ) will be used in a later dictionary selection step. Then, the
L. Fang and S. Li
pression of patch x i can be achieved by storing the positions and values of non-zero
coefficients in α
s
i and the mean value of x i .
4.3 Sparsity Based Methods for the OCT Image
Reconstruction
4.3.1 Multiscale Sparsity Based Tomographic Denoising
(MSBTD)
4.3.1.1 Multiscale Structural Dictionary
As described in Sect. 4.2, a fundamental problem for the sparsity based denoising
model is the selection of the dictionary D. The popular sparsity based denoising
algorithms usually use the noisy image itself to train the dictionary (denoted as
D
Noise ) [28]. Though these kinds of methods can provide promising results for natural
images, the high level of noise in OCT images will negatively interfere with the
training process, degrade the quality of the trained dictionary, and subsequently lead
to a suboptimal denoising result. An ideal approach is to train the dictionary from
the noiseless image. Since in practice, such an ideal OCT image is not available, we
create a less noisy image Y
Ave , obtained from registering and averaging a sequence
of (e.g., T) repeated B-scans from a unique position (see Fig. 4.1). Compared with
the D
Noise , the dictionary trained on this averaged image, D
Ave , is less affected by
noise.
To compare the above two dictionary training strategy, we use the popular KSVD training algorithm [25] and the proposed MSBTD algorithm described in the
following subsection for the dictionary training. Figure 4.2 shows examples of the
dictionaries trained by the K-SVD algorithm on a low-SNR B-scan (see Fig. 4.3a) and
MSBTD algorithm on an averaged high-SNR image (see Fig. 4.3b, c), respectively.
As can be observed, compared with the D
Ave , the D
Noise is more affected by noise in
the OCT image. Therefore, unlike the work in [28], the proposed MSBTD algorithm
denoises each low-SNR image utilizing a dictionary learned from a nearby (or even
distant) averaged image. This learning strategy can reduce the noise disturbance in
the dictionary learning process, and thus is expected to enhance the denoising result,
without significantly increasing the image acquisition time.
On the other hand, the popular learning algorithms (e.g., K-SVD [28] and its
variants [19]) often learn a universal dictionary D on a large number of training
patches. Such a universal dictionary might be neither optimal nor efficient to represent
different kinds of structures in the retinal OCT images. Therefore, the proposed
MSBTD algorithm learns a set of subdictionaries
D
Str
k ∈ R
Q×Q
, k 1, 2, . . . , K,
each best fit a particular structure [35, 36]. This is achieved by first clustering the
training patches into K structural clusters using the k-means approach. The centroid
of each cluster (c k ∈ R
Q ) will be used in a later dictionary selection step. Then, the