Noise reduction of OCT images is important, especially background and speckle noise reduction. Image patch space is not a ball-like Euclidean space. Using the Mahalanobis distance to characterize the patch covariance matrix could be a better choice for patch similarity measurement, as described in [
30]. The external patch prior guided internal clustering and morphological analysis (E2PGICMA)-based noise removal method was proposed. Some in vivo experiments were conducted to acquire OCT images of normal skin tissues. We computed the quantitative noise removal parameters and visualized the results of denoised OCT images through two-dimensional visualization and denoised A-scan lines.
2.3. Noise Reduction Algorithm Based on E2PGICMA
The E2PGICMA algorithm was conducted to remove the speckle and background noise of OCT images. The method is developed based on the external patch prior guided internal similarity clustering algorithm [
30]. The procedure is as Algorithm 1. The quadratic optimization problem can be solved in closed form (Equation (1)),
where
λ is a positive constant,
l is the alternating times,
Rk is a matrix which extracts the
k-th patch from
x,
is the low-rank matrixes, and
y is a noisy OCT image.
After obtaining an improved estimate of the unknown image xl+1, the noise standard deviation σ can be updated by utilizing the feedback of the filtered noise. The updated σ is then used to improve the estimate xl+2. Such a process is iterated until convergence. The total procedure of the proposed algorithm was as follows:
First, a reasonable scaling factor γ was chosen to control the re-estimation of noise variance.
Second, the optimization process was conducted by updating the standard deviation (σ) to improve the unknown image x.
Finally, the despeckled OCT images were output for further processing and were used to remove the background.
The despeckled OCT image was histogram-equalized. The gray threshold for the binarization of a whole OCT image was chosen automatically by the
Otsu algorithm. This method was implemented through function ‘
graythresh’ and ‘
im2bw’ in MATLAB. It can acquire the threshold for minimizing the in-class variance of the threshold black and white pixels. The global threshold can be used in conjunction with imbinarize to convert grayscale images into binary images. Then, a 5 × 5 mask was applied to implement the median filtering of an OCT image. The region-filling operation was conducted to fill the hole in the binarized OCT image. This procedure is shown in
Figure 2a. The upper surface was searched and saved by comparison with the gray threshold. The gray value of the binarized OCT image ranges from 0 to 255. Here, we chose the 70 as the gray threshold. Then, the upper surface was smoothed through the median filtering method. The pixels located above the upper surface were set as zero. The useful information depth was approximately 1.5 mm; hence, the 150-pixel-depth OCT image below the upper boundary was acquired and flattened.
Algorithm 1: Proposed algorithm for denoising of OCT images |
1. Input: noisy image y, noise standard deviation σ, learned GMM model parameter Θ’ and K. |
2. Initialization: |
(1) Choose a reasonable scaling factor γ for controlling the re-estimation of noise variance; |
(2) Initialize x0 = y; σ0 = σ. |
3. Optimization and Compute xl via Equation (1); |
4. Update σl, such that (σl)2 = γ(σ2 − ). |
5. Beginning the background reduction |
(1) Input the speckle-reduced OCT image, |
(2) Image binarization with Ostu algorithm, |
(3) Region filling (Mask: 5 × 5) and finding the upper boundary of OCT image, |
(4) Reset the gray level above the upper boundary of the OCT image to zero. |
6. Output: denoised image x. |
The noise reduction procedure was as follows: the involved parameters
λ (positive constant) and
γ (reasonable scaling factor) in the proposed algorithm were set to 0.18 and 0.67, respectively. According to experimental experience [
36], the patch size was set to 7 × 7, 8 × 8, 9 × 9 and 10 × 10 for σ ≤ 20, 20 < σ ≤ 40, 40 < σ ≤ 60 and σ > 60, respectively.
2.4. Validation for the Noise Reduction of OCT Images
For qualitative evaluation, the filtered images, and the view of textures in enlarged regions are provided in visual B-scan OCT images, making the comparison more comprehensive and directed. Visual A-scan lines of original, ground truth and denoised OCT images were provided, making the comparison of these methods more comprehensive and purposeful. The execution time was also recorded and compared. Expert observers manually reviewed all denoised single-frame B-scan images.
For quantitative evaluation of the performance of noise reduction, five other metrics were used to quantify the image quality, including the global signal-to-noise ratio (SNR), the peak signal-to-noise ratio (PSNR), the cross-correlation (XCOR), the equivalent number of looks (ENL), and the average contrast-to-noise ratio (CNR). Equations (2) and (3) show that the SNR and PSNR act as indicators of speckle reduction, and higher values indicate better quality. Equation (4) shows that XCOR depicts the similarity between the despeckled image
and the reference image
; a larger value implies that the recovered image is more like the reference image. The ENL measures the smoothness of the filtering results in the homogeneous regions (Equation (5)); higher values indicate better speckle reduction. CNR is a measurement of the contrast between the foreground objects and the noisy background regions (Equation (6)). As an indicator of improving contrast and preserving structures, a higher CNR value means that the image features are more separated from the OCT image background. Since there are no ideal ‘noiseless’ OCT images available, we use the averaged B-scan images as a noiseless approximation (ground truth). These metrics are, respectively defined as:
where
is the recovered image concerning its ground truth image
I.
N is the total number of pixels, and
MAX is the maximum intensity of the images.
μn and
σn are the mean value and variance of the background regions in the linear magnitude image,
μh and
σh are the mean and variance of the
hth homogenous regions of interest (ROI), and
μr and
σr are the mean and variance of the
rth ROI in the homogenous and nonhomogenous regions, respectively.
Furthermore, the structure similarity (SSIM) [
37] index was designed by modeling any image distortion as a combination of three factors, namely, the loss of correlation
s(
I,
), the luminance distortion
l(
I,
), and the contrast distortion
c(
I,
). The metric (Equation (7)) measures the similarity between a reference image and a denoised image.
where,
Edge Preservation index (
EPI) (Equation (9)) shows the degree of edge blurring inside the
ROI based on the methods discussed in [
38]. The closer the
EPI is to 1, the better the edge preservation.
where,
∇2I0 and
∇2I represent the Laplacian operator (
∇2) performed on the noisy image (
I0) and the filtered image (
I) in the
eth nonhomogenous
ROI, respectively.
I0,
I,
∇2I0, and
∇2I are the means of
I0,
I,
∇2I0, and
∇2I over 3 × 3 neighborhoods, respectively.
Moreover, we calculated the noise-reduction ratio (NRR) (Equation (10)) to compute the noise reduction index to evaluate the noise removal effect of the presented method. The NRR is defined as in Equation (10):
where
and
are the intensities of the removed noise and the original image, respectively. This indicator indicates that higher values indicate a better effect of speckle and background reduction.
In vivo normal skin tissues were imaged using an SS-OCT system. Then, 200 B-scan OCT images were denoised, analyzed with the proposed denoised method, and used to validate the performance of NRR and the visual effect of noise reduction. Furthermore, these OCT images were visualized through ray-tracing rendering and the 3-D visualization method. We qualitatively evaluated the effect of noise reduction by viewing the inner structural characteristics of OCT images. This method was processed on a laptop with an Intel (Santa Clara, CA, USA) Core i5-7500 CPU (3.40 GHz).