42
Z. Amini et al.
Leading to the well known high speckle contrast C 1 of fully developed
polarized speckle; σ I s is the standard deviation of I s .
Second order statistics of speckle is concerned with their temporal or spatial
structure. A standard means to describe such properties are correlation functions. The
characteristic depth extension of speckle in the OCT signal, e.g. can be estimated as
correlation length of its intensity fluctuations. We assume statistically independent
backscattered wavelets. In this case the intensity correlations can be obtained from
the amplitude correlation G(τ ) by [15]
I (t)I (t + τ I (t)
2 [1 + |G(τ )|
2 ].
(3.5)
Since the spectrum of light scattered back from the sample has approximately the
same spectrum as the probe beam, the correlation length of its intensity fluctuations
can be estimated by the corresponding coherence length I c . In fact the real situation
in OCT can be more complex: first, because of the reference beam we do not have
fully developed speckle in OCT. Second, light backscattered at specularly reflecting
interfaces does not generate speckle. Third, due to absorption, backscattered light
can have a modified spectrum.
3.2 OCT Image Modeling
OCT images produce enormous amount of information of retina that interpretation
of them with simple observation and common methods is generally impossible. So,
some automatic systems for analyzing medical images are needed to decrease the
amount of great information and help doctors for interpretation of them. In this
regard, modeling of images can be known as a core of many processes. As soon as
we determine a reliable model for OCT images, the rest of the processes may be
explored more correctly.
It is understood that contrast enhancement and noise reduction algorithms for
OCT images are also obtained based on the proposed model for image. In this base,
Fig. 3.2 shows a classification of image modeling methods [16]. According to this
classification, denoising methods such as other image processes may be studied in
spatial domain or transform representations. The latter may also be subcategorized
into parametric (non data adaptive) and non parametric (data adaptive) methods.
In data adaptive models basis functions of transform are directly defined by data.
Algorithms such as Principle Component Analysis (PCA) [17], Independent Component Analysis (ICA) [18–20] and Dictionary Learning (DL) [21] lie in the data
adaptive subgroup. In the other branch, we have some models in the frequency domain
such as Fourier and Discrete Cosine transform (DCT) and some others involve different X-lets. These X-lets themselves can be subdivided into some groups based on their
definition’s space. A summarized table about various atomic representation methods
and their parameters is given in Table 3.1 [16, 22]. Based on Fig. 3.2, scale-translation
transforms like wavelets take place in the first group of these X-lets [23]. In the second group frequency is also added to the scale and translation parameters; some
Z. Amini et al.
Leading to the well known high speckle contrast C 1 of fully developed
polarized speckle; σ I s is the standard deviation of I s .
Second order statistics of speckle is concerned with their temporal or spatial
structure. A standard means to describe such properties are correlation functions. The
characteristic depth extension of speckle in the OCT signal, e.g. can be estimated as
correlation length of its intensity fluctuations. We assume statistically independent
backscattered wavelets. In this case the intensity correlations can be obtained from
the amplitude correlation G(τ ) by [15]
I (t)I (t + τ I (t)
2 [1 + |G(τ )|
2 ].
(3.5)
Since the spectrum of light scattered back from the sample has approximately the
same spectrum as the probe beam, the correlation length of its intensity fluctuations
can be estimated by the corresponding coherence length I c . In fact the real situation
in OCT can be more complex: first, because of the reference beam we do not have
fully developed speckle in OCT. Second, light backscattered at specularly reflecting
interfaces does not generate speckle. Third, due to absorption, backscattered light
can have a modified spectrum.
3.2 OCT Image Modeling
OCT images produce enormous amount of information of retina that interpretation
of them with simple observation and common methods is generally impossible. So,
some automatic systems for analyzing medical images are needed to decrease the
amount of great information and help doctors for interpretation of them. In this
regard, modeling of images can be known as a core of many processes. As soon as
we determine a reliable model for OCT images, the rest of the processes may be
explored more correctly.
It is understood that contrast enhancement and noise reduction algorithms for
OCT images are also obtained based on the proposed model for image. In this base,
Fig. 3.2 shows a classification of image modeling methods [16]. According to this
classification, denoising methods such as other image processes may be studied in
spatial domain or transform representations. The latter may also be subcategorized
into parametric (non data adaptive) and non parametric (data adaptive) methods.
In data adaptive models basis functions of transform are directly defined by data.
Algorithms such as Principle Component Analysis (PCA) [17], Independent Component Analysis (ICA) [18–20] and Dictionary Learning (DL) [21] lie in the data
adaptive subgroup. In the other branch, we have some models in the frequency domain
such as Fourier and Discrete Cosine transform (DCT) and some others involve different X-lets. These X-lets themselves can be subdivided into some groups based on their
definition’s space. A summarized table about various atomic representation methods
and their parameters is given in Table 3.1 [16, 22]. Based on Fig. 3.2, scale-translation
transforms like wavelets take place in the first group of these X-lets [23]. In the second group frequency is also added to the scale and translation parameters; some