44
Z. Amini et al.
transforms like wavelet packets are placed in this group. Three parameters included
translation, duration and frequency are saved and studied in the third group models
like cosine packet transform. Finally, X-lets that involve scale, translation and angle
(or rotation) such as Curvelet, Contourlet, Wedgelet and Bandlet lie to the last group.
Besides, both of the spatial and transform models can be used as a deterministic,
stochastic, partial differential equation (PDE) based [24–26] or geometric models
[24, 27–29]. For example, using a deterministic model an image can be proposed as
a matrix while in statistical model image is proposed as a random field. In this base
for denoising problem average operator is obtained using first model while in the
context of second model denoising is converted to an estimation problem.
It is noteworthy that these models aren’t entirely distinct from each other and in
some cases they may have overlap. Combinations of these models results in new
image modeling frameworks such as using energy flow model [30] which is a PDEbased model in sparse domain [31] or Likewise combination of statistical model and
transform-based model [32]. Similarly the theory of multi-resolution representation
can be added on top of graph-based methods for using diffusion wavelet for image
modeling [33].
In particular about OCT images, the denoising methods have been categorized to
denoising methods before producing magnitude of OCT interference signal which
usually are hardware based methods, and denoising methods after producing magnitude of the OCT signal. Table 3.2 shows a review of proposed denoising methods
for OCT data [22].
Because of our limitation in access to hardware of devices and also to have an
investigation from modeling point of view, we focus more on the second group
denoising methods. Based on our classification in Fig. 3.2, these denoising methods
can be work in the spatial or transform domain. Some spatial models for decreasing
noise in OCT images are traditional methods such as low pass filters, linear smoothing, mean, median and wiener filters and using two one dimensional filters. However,
some advanced methods like non linear anisotropic filter [34, 35], directional filtering
[36, 37], complex diffusion [38], support vector machine (SVM) approach [39] and
adaptive vector-valued kernel function [40] are used in this domain. In the transform
based group, some data adaptive methods like PCA [41] and some non-data adaptive
models which are based on wavelets [42] [43], Curvelets [44], dual tree Complex
Wavelet [45–47], and wavelet diffusion [48] have been used for denoising.
Until now, the best results have been reported for the sparse data-driven methods [22], they improved the result of denoising by combination of DL and wavelet
thresholding.
In Table 3.3, various methods which used in OCT denoising are summarized
and also define that each of these methods lie on which group of image modeling
classification (based on Fig. 3.2). For example, “T-TD3” shows using DL model in
transform domain and “T-TNX11” indicates using wavelet.
Based on specific characteristics of OCT images and provided results of different
models mentioned in Table 3.3, it can be concluded that two more appropriate models
in denoising tasks on OCT images are statistical models and transform models. The
next sections are devoted to these two dominant models and the transform models
Z. Amini et al.
transforms like wavelet packets are placed in this group. Three parameters included
translation, duration and frequency are saved and studied in the third group models
like cosine packet transform. Finally, X-lets that involve scale, translation and angle
(or rotation) such as Curvelet, Contourlet, Wedgelet and Bandlet lie to the last group.
Besides, both of the spatial and transform models can be used as a deterministic,
stochastic, partial differential equation (PDE) based [24–26] or geometric models
[24, 27–29]. For example, using a deterministic model an image can be proposed as
a matrix while in statistical model image is proposed as a random field. In this base
for denoising problem average operator is obtained using first model while in the
context of second model denoising is converted to an estimation problem.
It is noteworthy that these models aren’t entirely distinct from each other and in
some cases they may have overlap. Combinations of these models results in new
image modeling frameworks such as using energy flow model [30] which is a PDEbased model in sparse domain [31] or Likewise combination of statistical model and
transform-based model [32]. Similarly the theory of multi-resolution representation
can be added on top of graph-based methods for using diffusion wavelet for image
modeling [33].
In particular about OCT images, the denoising methods have been categorized to
denoising methods before producing magnitude of OCT interference signal which
usually are hardware based methods, and denoising methods after producing magnitude of the OCT signal. Table 3.2 shows a review of proposed denoising methods
for OCT data [22].
Because of our limitation in access to hardware of devices and also to have an
investigation from modeling point of view, we focus more on the second group
denoising methods. Based on our classification in Fig. 3.2, these denoising methods
can be work in the spatial or transform domain. Some spatial models for decreasing
noise in OCT images are traditional methods such as low pass filters, linear smoothing, mean, median and wiener filters and using two one dimensional filters. However,
some advanced methods like non linear anisotropic filter [34, 35], directional filtering
[36, 37], complex diffusion [38], support vector machine (SVM) approach [39] and
adaptive vector-valued kernel function [40] are used in this domain. In the transform
based group, some data adaptive methods like PCA [41] and some non-data adaptive
models which are based on wavelets [42] [43], Curvelets [44], dual tree Complex
Wavelet [45–47], and wavelet diffusion [48] have been used for denoising.
Until now, the best results have been reported for the sparse data-driven methods [22], they improved the result of denoising by combination of DL and wavelet
thresholding.
In Table 3.3, various methods which used in OCT denoising are summarized
and also define that each of these methods lie on which group of image modeling
classification (based on Fig. 3.2). For example, “T-TD3” shows using DL model in
transform domain and “T-TNX11” indicates using wavelet.
Based on specific characteristics of OCT images and provided results of different
models mentioned in Table 3.3, it can be concluded that two more appropriate models
in denoising tasks on OCT images are statistical models and transform models. The
next sections are devoted to these two dominant models and the transform models