3 Speckle Noise Reduction and Enhancement for OCT Images
51
3.4 Data Adaptive—Transform Models for OCT Denoising
As mentioned in Sect. 3.2, in non-parametric (data adaptive) methods, the basis is
extracted regarding each dataset and there is no parameter to be selected. Single scale
and multi scale non-parametric models may be subcategorized for more detail. Single
scale models include PCA, ICA, diffusion maps and dictionary learning methods.
Diffusion wavelets and complex wavelet transform along with dictionary learning
are instances for multi scale models [22].
Nonparametric representations are relatively new in OCT denoising [43, 53, 54],
but they have specific properties which makes them appropriate for this task. They
are acquired from the data (better fit to OCT data), applicable on higher dimensional
data (adaptable to 3D OCT data), and able to provide multi scale representation (to
match different anatomical properties of OCT).
One sample denoising method on OCT, with focus on nonparametric models is
elaborated below [16]. The method incorporates dictionary learning to improve the
performance of available wavelet-thresholding. To do so, dictionaries are learned
from the data instead of applying ready-to–use basis functions. Furthermore, conventional start dictionary (discrete cosine transform) is replaced by dual tree complex
wavelet to take advantage of its shift invariant properties. Three dimensional versions
of the method are also introduced to be applied on 3D volumes of OCT.
3.4.1 Conventional Dictionary Learning
Dictionary learning in denoising of OCT was first proposed in [54, 55] by learning
a sparse dictionary from a selected number of higher signal-to-noise ratio (SNR)
B-scans and using such dictionaries for denoising of low-SNR B-scans. The main
problem in this work was need for high-SNR slices which are not accessible in most
of available datasets.
In this section, K-SVD algorithm [56] is applied on OCT data. For construction
of sparse land, each data (x) can be represented over a redundant dictionary matrix
D ∈ ∈
n×k (with k > n):
ˆ
α arg min α Dα − x
2
2 subject to α 0 < t
(3.6)
for a defined value of t. Having a noisy version of x named y, the maximum a
posteriori (MAP) estimator for denoising the data is built by solving:
ˆ
α arg min α Dα − y
2
2 + μα 0
(3.7)
In K-SVD, the algorithm iterates in two stages to solve the above equation [56,
57] and the dictionary D can be learned on patches extracted from the image. In the
first stage, D is supposed to be unknown, and similar to [56]:
51
3.4 Data Adaptive—Transform Models for OCT Denoising
As mentioned in Sect. 3.2, in non-parametric (data adaptive) methods, the basis is
extracted regarding each dataset and there is no parameter to be selected. Single scale
and multi scale non-parametric models may be subcategorized for more detail. Single
scale models include PCA, ICA, diffusion maps and dictionary learning methods.
Diffusion wavelets and complex wavelet transform along with dictionary learning
are instances for multi scale models [22].
Nonparametric representations are relatively new in OCT denoising [43, 53, 54],
but they have specific properties which makes them appropriate for this task. They
are acquired from the data (better fit to OCT data), applicable on higher dimensional
data (adaptable to 3D OCT data), and able to provide multi scale representation (to
match different anatomical properties of OCT).
One sample denoising method on OCT, with focus on nonparametric models is
elaborated below [16]. The method incorporates dictionary learning to improve the
performance of available wavelet-thresholding. To do so, dictionaries are learned
from the data instead of applying ready-to–use basis functions. Furthermore, conventional start dictionary (discrete cosine transform) is replaced by dual tree complex
wavelet to take advantage of its shift invariant properties. Three dimensional versions
of the method are also introduced to be applied on 3D volumes of OCT.
3.4.1 Conventional Dictionary Learning
Dictionary learning in denoising of OCT was first proposed in [54, 55] by learning
a sparse dictionary from a selected number of higher signal-to-noise ratio (SNR)
B-scans and using such dictionaries for denoising of low-SNR B-scans. The main
problem in this work was need for high-SNR slices which are not accessible in most
of available datasets.
In this section, K-SVD algorithm [56] is applied on OCT data. For construction
of sparse land, each data (x) can be represented over a redundant dictionary matrix
D ∈ ∈
n×k (with k > n):
ˆ
α arg min α Dα − x
2
2 subject to α 0 < t
(3.6)
for a defined value of t. Having a noisy version of x named y, the maximum a
posteriori (MAP) estimator for denoising the data is built by solving:
ˆ
α arg min α Dα − y
2
2 + μα 0
(3.7)
In K-SVD, the algorithm iterates in two stages to solve the above equation [56,
57] and the dictionary D can be learned on patches extracted from the image. In the
first stage, D is supposed to be unknown, and similar to [56]: