2.1.

Wavelet-Compounding Adaptive Noise Filter

Figure 1 shows a complete overview of the proposed wavelet-compounding adaptive noise filter (WCAN) method. The processing steps are wavelet transform, variance computation of the input and reference frames, adaptive variance compounding, weight computation, wavelet coefficient weighting, averaging, and inverse wavelet transform. The input to the algorithm is a set of $N$ OCT frames (${\mathrm{IF}}_1,{\mathrm{IF}}_2,\dots {\mathrm{IF}}_N$) and a set of $M$ reference OCT frames (${\mathrm{RF}}_1,{\mathrm{RF}}_2,\dots {\mathrm{RF}}_M$), with both sets acquired at consecutive positions. The reference frames could come from a homogeneous scattering sample independent of the input frames or from a homogeneous region of the set of input frames. This reference set should be collected as a prior step to the application of the method. The output of the algorithm is a single OCT denoised image. The terms “frame” and “image” from one side and the terms “method,” “filter,” and “algorithm” are used interchangeably in this paper. In the following paragraphs, we explain in detail each step of the method.

Fig. 1

Flow diagram of the wavelet-compounding adaptive noise algorithm. The acquired OCT input frames ${\mathrm{IF}}_1,{\mathrm{IF}}_2,\dots {\mathrm{IF}}_N$ represent the $N$ input noisy images for the algorithm. All images and the $M$ reference OCT frames ${\mathrm{RF}}_1,{\mathrm{RF}}_2,\dots {\mathrm{RF}}_M$ are wavelet decomposed in $L$ subbands. The variance of all subbands in the wavelet decomposition of the reference stack is computed. Using the subband variances, the weights of the detail coefficients for each subband are calculated based on the compounding of the previous variance computation and applied to each original detail coefficient. All denoised coefficients are then averaged in the wavelet domain before the inverse wavelet transform is calculated to obtain the final denoised OCT image, DOCT.

2.1.2.

Wavelet transform

All of the input images are decomposed by a wavelet transformation with a maximum decomposition level of $L$. The result of the transformation is a set of approximation coefficients $A_i^l$ and detail coefficients $C_{i,O}^l$, where $i$ is the frame number, $l$ is the decomposition level, and $O$ is the orientation or direction of the detail coefficient (horizontal, vertical, or diagonal). The wavelet transformation is computed using the 2D discrete stationary wavelet transform.⁴⁰ Figure 2 shows a representation of a 2D wavelet decomposition of an image with three levels, where $A$ contains the approximation coefficients and $C_{\text{Horizontal}}$, $C_{\text{Vertical}}$, and $C_{\text{Diagonal}}$ are the detail coefficients of each subband for the horizontal, vertical, and diagonal orientation, respectively.

Fig. 2

Representation of a 2D wavelet decomposition of an image using three levels.

2.1.7.

Data and OCT imaging systems

For the quantitative evaluation of the method, we used datasets representing four different environments, as specified in Table 1. Datasets Medical University of Vienna (MUW)-1, MUW-2, and MUW-3 each comprised 18 skin OCT volumes and were acquired via three different OCT image systems. MUW-1 and MUW-2 were custom designs from the Center for Medical Physics and Biomedical Engineering at the MUW. To assess the applicability of the method to a commercial device, the MUW-3 image dataset was acquired via a VivoSight OCT scanner (Michelson Diagnostics, Kent). The A2ASDOCT dataset is a public dataset comprising 17 retinal volumes from the A2ASDOCT study.⁵⁹ It was produced using a Bioptigen Inc (Research Triangle Park, North Carolina) spectral domain OCT imaging system²⁴ and involved 17 eyes from 17 subjects with and without nonneovascular age-related macular degeneration (AMD). Each set of images in this dataset comprises five frames of $900\times 450\text{pixels}$ from consecutive positions, each of which includes the fovea region. The main technical specifications of the imaging systems are summarized in Table 1. Table 2 gives additional details about the dermatological datasets (MUW-1, MUW-2, and MUW-3) and the retinal dataset (A2ASDOCT).

Table 1

Technical specifications of the OCT imaging systems used in the acquisition of the volumes in this study.

Parameter	MUW-155,56	MUW-257	MUW-3 (VivoSight)	A2ASDOCT (Bioptigen)58
System type	Swept-source frequency domain OCT	Spectral domain OCT	Multi-beam swept-source frequency domain OCT	Spectral domain OCT
Laser system	1340 nm	1320 nm	1305 nm Class 1	840 nm
A-line rate	200 kHz	47 kHz	10 kHz	17 kHz
Optical resolution	$19.5\mu \mathrm{m}$ (air) lateral $4.6\mu \mathrm{m}$ (air) axial	$15\mu \mathrm{m}$ (lateral) $7\mu \mathrm{m}$ (axial)	$<7.5\mu \mathrm{m}$ (tissue) lateral $<5\mu \mathrm{m}$ (tissue) axial	$10\mu \mathrm{m}$ (tissue) lateral $4.5\mu \mathrm{m}$ (tissue) axial
Field of view	$10\times 10\mathrm{mm}$	$7\times 3.5\mathrm{mm}$	$6\times 6\mathrm{mm}$	$6.7\times 6.7\mathrm{mm}$
Imaging depth	1.2 mm	2 mm	Between 1.2 and 2 mm, tissue dependent	2 mm

Table 2

Description of the datasets. The volumes of the three dermatological datasets were acquired and evaluated by experts from the Department of Dermatology at the MUW. The identified sample area (if available) is given in the fourth column. The results of the clinical assessments are given in the fifth column.

Dataset	Size (pixels)/number of B-scans	Volume ID	Sample area	Clinical evaluation
MUW-1	$1100\times 512/256$	1.1	Hand	Nevus araneus
		1.2	Back	Postsurgical scar
		1.3	Thigh	Normal skin
		1.4	Head	BCC
		1.5	Arm	BCC
MUW-2	$1000\times 680/256$	2.1	Palm	Normal skin
		2.2	—	Pityriasis
		2.3	Forearm	Normal skin
		2.4	Head	BCC
		2.5	Arm	Nevus
MUW-3	$1558\times 460/50$	3.1	Nose	BCC
		3.2	Chest	BCC
		3.3	Chest	BCC
		3.4	Palm	Normal skin
	$1298\times 460/50$	3.5	Fingertip	Normal skin
	$1038\times 460/50$	3.6	Back	Nevus
		3.7	Abdomen	Angioma
		3.8	Cheek	Folliculitis
A2ASDOCT	$900\times 450/5$	4.1–4.17	Fovea	10 from normal subjects and 7 from AMD subjects

The method requires the use of a reference set (${\mathrm{RF}}_1,{\mathrm{RF}}_2,\dots {\mathrm{RF}}_M$ in Fig. 1). The role of this reference is to characterize the speckle noise assuming, as stated by Zaki et al.,⁴³ that the variation in these uniform areas is determined by random noise. The calculation of the noise variance is based on Eq. 3 over a region of interest (ROI) selected from the reference frames. We used two strategies to calculate this variance. First, we used a homogeneous scattering phantom made of synthetic clay (Blu-Tak^®; Bostik, Wauwatosa, Wisconsin). This approach was tested with the MUW-1 OCT image system and the MUW-3 VivoSight device. Using the MUW-1 system, we acquired 512 -scans with dimensions of $512\times 219\text{pixels}$ from consecutive positions. Using the VivoSight device, we acquired 120 B-scans with dimensions of $1038\times 460\text{pixels}$ from consecutive positions.

In our second strategy, we selected a ROI in the same location (top or bottom) of the frames from both systems and computed the variances of the coefficients of four wavelet detail subbands. This involved selecting a homogeneous noisy ROI and computing the corresponding variance of the detail coefficients, considering all frames in the dataset. We selected the location of the ROI (top or bottom) to have enough data in the all frames of the volume. We used this strategy as an alternative approach for the MUW-2 and A2ASDOCT datasets, partly because a phantom was unavailable and partly to test an alternative approach to noise estimation. Figure 3 shows examples of the acquisition of the phantom and the selection of the ROIs for both strategies, and Table 3 summarizes the reference sets used for each OCT imaging system. We applied the same reference set to all volumes of each dataset (MUW-1, MUW-2, MUW-3, and A2ASDOCT).

Fig. 3

Examples of frames and ROIs (white rectangles) used to compute the noise variance required by the WCAN method. (a) First frame with size $512\times 219\text{pixels}$ for the phantom acquired via the MUW-1 image system. (b) First frame with size $1000\times 680\text{pixels}$ for Volume 2.1 (palm normal skin, see Table 2) acquired via the MUW-2 image system. (c) First frame with size $1038\times 460\text{pixels}$ for the phantom acquired via the VivoSight device. (d) First frame with size $900\times 450\text{pixels}$ for the first set in the A2ASDOCT dataset.

Table 3

Summary of the reference sets used in the application of the method WCAN for all of the datasets. M indicates the maximum number of frames in the reference set (RF1,RF2…RFM). The ROI Dimensions column refers to the size of the white rectangles shown in Fig. 3.

Dataset	Volume ID	Strategy	M	ROI dimensions	Figure
MUW-1	R.1	ROI phantom	512	$63\times 478$	Fig. 3a
MUW-2	R.2	ROI Vol 2.1	256	$112\times 993$	Fig. 3b
MUW-3	R.3	ROI phantom	120	$120\times 1009$	Fig. 3c
A2ASDOCT	R.4	ROI all frames	85	$153\times 885$	Fig. 3d

2.2.

Quantitative evaluation

We evaluated the efficacy of the algorithm, using common speckle-reduction performance metrics^41,43,44 via a comparison with different state-of-the-art methods. These quantitative metrics were the SNR, the contrast-to-noise ratio (CNR), and the equivalent number of looks (ENL), as expressed below.

SNR is defined in Eq. (11), where ${\mu }_I$ indicates the mean of the OCT image and ${\sigma }_I^2$ refers to the noise variance. In the definition of CNR [Eq. (12)], ${\mu }_b$ and ${\sigma }_b^2$ are the mean and variance for a background noise region, respectively, with ${\mu }_r$ and ${\sigma }_r^2$ being the mean and variance for all ROIs, respectively, including homogeneous and heterogeneous regions. ENL is a measure of the smoothness of a homogeneous ROI. In Eq (13), ${\mu }_h$ and ${\sigma }_h^2$ are the mean and variance of all $H$ homogeneous ROIs, respectively. Except for the SNR calculations, the remaining parameters were computed from the logarithmic OCT images.

To assess the overall influence of the quantitative metrics, we include two additional figure-of-merits (FOMs):⁴⁴

We compared the performance of the WCAN algorithm with respect to other state-of-the-art methods via two different approaches. First, we used 2D filters that have previously demonstrated excellent performance in OCT speckle reduction such as PNLM,³² complex wavelet based K-SVD (KSVD),⁴⁶ and noise adaptive wavelet thresholding (NAWT)⁴³ or in general image denoising (DNCNN).³⁴ Next, we used two 3D filters: i.e., the wavelet multiframe algorithm (WVMF)⁴⁵ and TNODE.⁴⁷ Table 4 gives sources for implementations of these methods. Figure 4 shows the process of evaluation for the various methods. All steps were performed over all frames in every dataset. The denoised OCT frames generated as outputs were compared using the SNR, CNR, and ENL performance metrics.

Table 4

State-of-the-art denoising software used in the assessment of the proposed method.

Fig. 4

(a) Process used for the evaluation of all methods with all datasets. Each volume in the study was divided into blocks of $N$ frames. For each block, all filters were applied and the evaluation metrics were computed. Finally, all blocks were combined and the improved version of each volume and each filter was created. (b) Details of the process for each block. The compounding of each block with $N$ initial frames (${\mathrm{IF}}_1,\dots {\mathrm{IF}}_N$) was performed using WCAN, WVMF, TNODE, and MEAN. The output of the MEAN was applied to the methods KSVD, NAWT, PNLM, and DNCNN. The output frames from each method (${\mathrm{OF}}_{\mathrm{WCAN}}$, ${\mathrm{OF}}_{\mathrm{WVMF}}$, ${\mathrm{OF}}_{\mathrm{TNODE}}$, ${\mathrm{OF}}_{\mathrm{KSVD}}$, ${\mathrm{OF}}_{\mathrm{NAWT}}$, ${\mathrm{OF}}_{\mathrm{PNLM}}$, and ${\mathrm{OF}}_{\mathrm{DNCNN}}$), as applied to all frames, were used in the quantitative assessment. The normalized value of the metrics (SNR Norm, CNR Norm, ENL Norm, and FOM) were calculated with respect to the maximum value of each metric from the output frames. We used these normalized values for all volumes in comparing the quantitative assessments for all filters.

3.1.

Parameter Assessment

Before applying the method to all datasets and comparing it with the state-of-the-art filters, we evaluated the impact of the two main parameters of the algorithm, i.e., $k$ [the threshold parameter in Eq. (3)] and $N$ (the number of frames to consider in the compounding process). We used Volume 2.1 (see Table 2) and the reference frames from Volume R.2 (Table 3) for this purpose in the two experiments outlined in Fig. 5.

Fig. 5

Process followed for the assessment of the parameters $k$ and $N$ using Volume 2.1 from the MUW-2 dataset and the reference frames from Volume R.2. (a) Evaluation of the parameter $k$ with $N=3$ for values of $k$ from 0.3 to 1.4 in steps of 0.1. We divided the volume into blocks of three frames and applied WCAN for each $k$ value. After calculating the quantitative metrics, we compared the resulting FOMs of the enhanced frames for consecutives values of $k$. (b) Evaluation of the parameter $N$ with $k=1$ for values of $N$ from 2 to 6. For each $N$ value, we divided the volume into blocks of $N$ frames and applied WCAN with $k$ set to 1. After calculating the quantitative metrics, we compared the resulting FOM of the enhanced frames for consecutives values of $N$.

First, we varied the parameter $k$ from 0.3 to 1.5 in steps of 0.1, with $N$ set to 3. In the second experiment, we varied the parameter $N$ from 2 to 6, with $k$ set to 1.0. After applying the WCAN method in both cases, we calculated the quantitative metrics (SNR, CNR, and ENL) and the resulting $FO{M}_{SUM}$ (only FOM for the rest of this section). We then computed the difference in the FOM values for each enhanced frame for two consecutive values of $k$ (such as $k=0.4$ and 0.3) and $N$ (such as $N=3$ and $N=2$). This process generated a set of FOM-value differences $\mathrm{\Delta }FO{M}_K$ for each pair of consecutive $k$ values and a set of $\mathrm{\Delta }FO{M}_N$ for each pair of consecutive $N$ values.

Figure 6 gives the main results and some examples of the application of the WCAN method to Volume 2.1. We observe that the improvement in the quantitative metrics reaches a maximum between $k=0.8$ and 0.9, with a mean improvement in FOM of 0.213, and any further increase in $k$ decreases the incremental improvement. Note that this does not imply that $k=0.9$ is the optimal value to use but that $k=0.9$ is the value for which we have the greatest improvement with respect to the previous value of $k$. Although increasing the value of $k$ always produces a quantitative improvement in the image, there are diminishing returns from increasing $k$ beyond $k=0.9$. We can observe the same trend for the parameter $N$, the maximum mean improvement of FOM, i.e., $\mathrm{\Delta }FO{M}_N=0.229$, occurs between $N=4$ and $N=3$. The image examples in Fig. 6 show how increases in $N$ and $k$ produce better noise reduction in the resultant image. One of the main advantages of the proposed method is that it is easily adaptable to very different OCT settings by simply adjusting these two parameters.

Fig. 6

Results of the evaluation of the parameters $k$ and $N$ for the WCAN method, using the Volume 2.1 from the MUW-2 dataset and the reference frames from Volume R.2. (a) FOM for consecutive $k$ values from 0.3 to 1.5. (b) Improvement in the FOM metric for consecutive $k$ values from 0.3 to 1.5. The horizontal axis represents consecutive pairs of values for $k$. The vertical axis represents the FOM differences over all frames in the volume for consecutive pairs of values for $k$. (c) FOM for consecutive $N$ values from 2 to 6. (d) Improvement in FOM metric for consecutive $N$ values from $N=2$ to $N=6$. The horizontal axis represents consecutive pairs of values for $N$. The vertical axis represents the FOM differences over all frames in the volume for consecutives pairs of values for $N$. (e) Examples of the application of the WCAN method for different combinations of $k$ and $N$ in the ROI marked as a white box in the top-left raw noisy OCT image.

To find appropriate values of $k$ and $N$ for the quantitative assessment, we used the first volume in each dataset (Volume IDs 1.1, 2.1, 3.1, and 4.1 for the MUW-1, MUW-2, MUW-3, and A2ASDOCT datasets, respectively, in Table 2 and the references frames with Volumes IDs R.1, R.2, R3, and R.4 I in Table 3). Table 5 gives the final values chosen for each dataset, having been determined empirically as a suitable balance between performance metric improvement, qualitative visual quality, and execution time.

Table 5

Parameters used in the assessment of the WCAN method for each dataset. N is the number of frames considered at consecutive positions in the compounding process. k is the adjustment parameter for the thresholding process. The number of decomposition levels, L, was set to four for all datasets.

We also evaluated the influence of the wavelet family in the calculation of 2D discrete stationary wavelet transform. We tested the wavelets families Haar, Daubechies (db1-db10), Symlets (sym2-sym8), Coiflets (coif1-coif5), and BiorSplines (bior1.1, bior1.3, bior1.5, bior2.2, bior2.4, bior2.6, bior2.8, bior3.1, bior3.3, bior3.5, bior3.7, bior3.9, bior4.4, bior 5.5, and bior6.8) using the Volume ID 2.1 and the reference set R.2 of Table 3. The Table 6 presents the results of the wavelet with the best performance in each family. As we can observe, the Haar wavelet shows the best performance and was the wavelet selected for the rest of the experiments.

Table 6

Quantitative evaluation of the wavelet families Haar, Daubenchies, Symlets, Coiflets and BiorSplines, considering the Volume ID 2.1 and the reference set R.2 from Table 3. The results show the mean ± standard deviation of the improvement with respect to the initial metrics presented in Table S1 in the Supplementary Material (raw images).

3.2.

Quantitative Evaluation

We now present the results of our quantitative evaluation of the application of the compared methods to the complete stack of frames for all four datasets in this study. In the evaluation, we used the same ROIs for all frames in the same volume to maintain a consistent reference (Fig. 7 shows one frame with the ROIs used for Volume 1.1). The detailed values of the metrics for all datasets are included in Tables S2–S7 in the Supplementary Material. In Tables 7Table 8Table 9–10 and Fig. 8, we present the aggregate results. Tables 7Table 8Table 9–10 show the mean ± standard deviation of the improvement with respect to the initial metrics presented in Table S1 in the Supplementary Material (raw images). The values corresponding to the best performance for the individual metrics and for the FOMs are shown in bold.

Fig. 7

OCT raw image and ROIs used for the calculation of the quality metrics. The white rectangular region was used for the noise estimation; the red rectangles represent the homogeneous regions ($H=3$) used to calculate ENL, and the green rectangles represent the nonhomogeneous regions. The sum of both individual metrics is used to calculate the CNR ($R=6$).

Table 7

Quantitative evaluation for the MUW-1 dataset, considering the results of the application of all filters to Volumes 1.1–1.5 (see Table 2) and the reference frames R.1 (see Table 3). The compounding was performed using three B-scans per position.

Table 8

Quantitative evaluation for the MUW-2 dataset, considering the results of the application of all filters to Volumes 2.1–2.5 (see Table 2) and the reference frames R.2 (see Table 3). The compounding was performed using three B-scans per position.

Table 9

Quantitative evaluation for the MUW-3 dataset, considering the results of the application of all filters to Volumes 3.1–3.8 (see Table 2) and the reference frames R.3 (see Table 3). The compounding was performed using two B-scans per position.

Table 10

Quantitative evaluation for the A2ASDOCT dataset, considering the results of the application of all filters to the 17 retinal sets (see Table 2) and the reference frame R.4 (see Table 3). The compounding was performed using four B-scans per position.

Fig. 8

Value distribution for the different metrics of the quantitative evaluation of all datasets used in the study (see Table 2). The proposed WCAN method is shown in the rightmost column within the red box. (a) $FO{M}_{SUM}$ calculated using Eq. (14). (b) $FO{M}_{MIN}$ calculated using Eq. (15). (c) SNR Norm calculated using Eq. (11) and normalized with respect to the maximum value of the metric for each denoised frame. (d) CNR Norm calculated using Eq. (12) and normalized with respect to the maximum value of the metric for each denoised frame. (e) ENL Norm calculated using Eq. (13) and normalized with respect to the maximum value of the metric for each denoised frame. (f) Order of the datasets for each method.

To facilitate comparison between metrics, we used the normalized value of each metric, calculated from the maximum values for all filtered images in each group of frames [see Fig. 4(b)]. We can then refer to metric values corresponding to the best filtered output for each group of frames to make fair comparisons across the volume. We should first note that the best results across all datasets were accomplished by WCAN, with the highest values for $FO{M}_{SUM}$ and standard deviations between the smallest (MUW-3) and the second smallest (MUW-1, MUW-2, and A2ASDOCT). We have the same situation with the metric $FO{M}_{MIN}$, where WCAN presents the highest values. The TNODE algorithm had the second-best performance across all datasets. WCAN was also the best option, in most cases, when considering each metric separately. It returned the best CNR and ENL results for all datasets (except for MUW-1, where it had the second highest ENL). WCAN had the best SNR score for MUW-1, was second for MUW-2, and third for MUW-3 and A2ASDOCT.

Another notable aspect of the WCAN results is its consistent performance with very different OCT image settings, image samples, and locations on the skin (see Table 2) and retina. As is clear from Figs. 8(a) and 8(b), other filters such as PNLM and KSVD perform very differently for the retina dataset (A2ASDOCT) than for the skin datasets (MUW-1, MUW-2, and MUW-3).

Figure 9 shows the significant differences in the OCT images generated by applying the state-of-the-art methods to Volume 1.1 and the reference frames R.1. Videos S1–S4 (see Figs. 13–16 in the Appendix) show the results of the application of the method over frames of the datasets MUW-1, MUW-2, MUW-3, and A2SDOCT.

Fig. 9

Comparison of the application of speckle reduction methods in a frame with $1100\times 512\text{pixels}$ from Volume 1.1 using three B-scans at consecutive positions and the reference frames R.1. (a) Raw OCT image with a detailed ROI. The remainder of the image is the filtered OCT image after applying the method. (b) Proposed WCAN method. (c) TNODE method. (d) PNLM method. (e) NAWT method. (f) WVMF method. (g) KSVD method. (h) DNCNN method.

Simple averaging was also evaluated. We used three volumes from datasets MUW-1, MUW-2, and MUW-3, where we have enough frames to perform the experiment in each volume. In particular, we considered Volumes ID 1.1, 2.1, 3.1 (Table 2) and the reference sets R.1, R.2, and R.3 of Table 3, respectively. We applied the WCAN method to each volume using the parameters previously identified in Table 5. In particular, we applied the WCAN to the three first frames of Volume ID 1.1 and 2.1 with $k=1$ and to the first two frames of Volume ID 3.1 with $k=1.1$. Then, we performed the average of $N$ frames iteratively until the metric $FO{M}_{SUM}$ of averaging frames improved the metric of WCAN previously calculated. The results showed that to improve WCAN we needed to average 12, 27, and 13 frames for the Volumes ID 1.1, 2.1, and 3.1, respectively.

Figure 10 shows an analysis of some examples of the WCAN algorithm’s performance with skin images corresponding to frames of the MUW-2 and MUW-3 datasets. The first sample (Volume 2.4) provides information about a superficial BCC on the head. In Figs. 10(a) and 10(b), speckle reduction using WCAN [Fig. 10(b)] enables a stronger identification of the skin layers (marked with digits 1–3) than does the raw image [Fig. 10(a)]. In addition, the stratum corneum layer and the epidermis–dermis interface are more clearly distinguished. The boundaries and contrast are also enhanced, shown by comparing the area enclosed by the blue ellipse and the red arrows in the zoom-in boxes in the raw image [Fig. 10(a)] and after filtering [Fig. 10(b)]. The second example (Volume 3.8) shows a cheek with folliculitis. Figures 10(c) and 10(d) show a sharper difference between the regions indicated by the blue line and the red arrows and the structure indicated by the green arrow in the zoom-in boxes.

Fig. 10

Comparison of the application of the WCAN method to frames from the MUW-2 and MUW-3 datasets. (a) Raw OCT skin image from a $1000\times 680\text{pixel}$ sample of a head affected by BCC (Volume 2.4). Two detail ROIs are identified by white rectangular boxes. The digits 1, 2, and 3 in the image identify the stratum corneum, epidermis, and dermis layer, respectively. The blue ellipse and red arrows indicate regions that show the contrast enhancement obtained by filtering the raw image. (b) WCAN image processed using three consecutive frames from Volume 2.4, starting from the a frame. (c) Raw OCT skin image from a $1038\times 460\text{pixel}$ sample of a cheek with folliculitis (Volume 3.8). Two zoom-in ROIs are identified by white rectangular boxes. The blue line and the red and green arrows identify different areas affected by speckle reduction after application of the proposed method. (d) WCAN image processed using two consecutive frames from Volume 3.8 starting from the c frame.

Figure 11 enables qualitative comparisons for a retinal image from the A2ASDOCT database after applying each of the denoising methods in the study. Figure 11 shows that the WCAN algorithm gives significant noise suppression, which enables clear identification of the boundaries between retinal layers.

Fig. 11

Comparison of the application of speckle reduction methods in a $900\times 450\text{-}\text{pixel}$ frame from Volume 4.1 using four B-scans at consecutive positions. (a) Raw OCT image and a detail ROI used for the qualitative comparison of all methods. (b) Proposed WCAN method. (c) TNODE method. (d) PNLM method. (e) KSVD method. (f) WVMF method.

Finally, to assess the computation time for the various algorithms we applied all methods of the study to 20 scaled versions of the first two frames of Volume ID 1.1. For the WCAN method we used $k=1$ and the reference frames R.1 from Table 3. The original size of the volume was two frames with $1100\times 512\text{pixels}$. We used scales from 0.1 to 4 in steps of 0.2 (20 scales in total) to resize the frames. For each scale we applied all of the methods and calculated the execution time using the method timeit of Matlab. In Fig. 12 we present the results. As shown in Fig. 12(a) the application of the WCAN method requires less execution time than the other pure compounding alternatives such as TNODE and WVMF. The PNLM and NAWT methods presented the best performance among all of the algorithms tested [Fig. 12(b)]. Finally, to estimate the computational complexity of the algorithm, we applied a basic fitting of the performance metrics of WCAN, resulting a linear polynomial function of the type $y=p1*x+p2$ with $p_1=0.0087$, $p_2=0.0086$, and the norm of residuals equaling 0.699. So we can estimate that the time complexity of the method is linear. The tests were executed in Matlab 2018b (MathWorks, Inc.) on a personal computer (Intel 3.3 GHz CPU, 32 GB memory).

Fig. 12

Comparison of the computation time in seconds of all methods of the study (WCAN, TNODE, WVMF, PNLM, NAWT, KSVD, and DNCNN). The parameter $N^{*}$ represents the total number of the pixels considered in each test ($1100\times 512\times 2\times \text{scale}$) normalized with respect to the smallest one ($1100\times 512\times 2\times 0.1$). (a) Computation time comparison of WCAN with respect to the compounding methods TNODE and WVMF. (b) Computation time comparison of WCAN with respect to PNLM, NAWT, KSVD, and DNCNN methods.