As wED is a new approach to the ED reconstruction process, the OCTA scanning protocol for wED is the same as the aED [11,12]. The B scans were applied at the same locations a number of times. Therefore, each A-scan signal, X, would contain both the depth and temporal information, which can be presented by:

X=((Xm,n)m∈[1,L])n∈[1,N],

(1)

where L is the total depth of each A-scan, N is the number of acquisitions at the same scanning location, and m and n are both integers. After applying a window, the windowed signal W can be represented by:

Wk=((Xm,n)m∈[k,k+s))n∈[1,N];k=1,2,3,…, L−s,

(2)

where k is the window’s position, and s is the window size. The applied window would move from the first pixel towards the (L−s)th pixel. Since the temporal information is contained in W, the windowed signal can also be presented as:

Wk=[Wkstr, Wkflow, Wknoise],

(3)

where Wkstr is the structure component, Wkflow is the flow component, and Wknoise is the noise component, e.g., white noise. The aim of ED analysis is to extract Wkflow. When Wk is assumed to be Gaussian, the raw signals can be completely characterized by its correlation matrix, Rk, given by:

Rk=Rstr+Rflow+σnoise2I,

(4)

where Rstr is the structure correlation matrix, Rflow is the flow correlation matrix, σnoise2 is the noise variance, and I is the identity matrix [11,36,41]. The correlation matrix of the raw data can be estimated by: where H is the Hermitian transpose operation [11,12]. In this study, the structure component Wkstr was assumed to be the dominant component within the input data Wk. The dominant component can be separated by ED with the estimated raw data correlation matrix, which can be estimated by:

Rk^=EΛEH=∑i=1Nλ(i)e(i)e(i)H ,

(6)

where E=[e(1), e(2),…, e(N)] is the unitary matrix of N eigenvectors, and Λ=[λ(1), λ(2),…, λ(N)] is the diagonal matrix of N eigenvalues. The eigenvalues were sorted in descending order as the output of eigen-decomposition, pairing with the eigenvectors. More dominant components contribute to larger eigenvalues. Hence, the structure component was corresponding to the first Jth eigenvectors. Then, the flow component was extracted by:

Wkflow=[I−∑i=1Je(i)e(i)H]Wk,

(7)

where J is an integer between 1 and N [11,12]. The value of J can be manually set to a fixed value or automatically set based on the eigenvalues. In this study, the total number of acquisitions at the same location, N, was 4, while J was set to be a fixed value, 2. Lastly, the windowed flow signals were combined into one A-scan flow signal, which was calculated by:

Xflow=∑1L−sWkflowL−s.

(8)

By averaging the results from all windows, the final flow component was the wED OCTA result for each A-scan.

To summarise, wED applies a moving window to the OCTA data then the ED analysis to extract blood flow signals from static tissue signals. In order to utilize the best window size during the processing, an optimization process was applied in this study. In total, 20 datasets were selected, spanning all stages of wound healing. The method for evaluating the window sizes was to calculate the correlation coefficients between the windowed input data distribution and the fitted normal distribution. After applying 35 various window sizes from 5 to 175 pixels, the window size generating the best average correlation coefficient was selected to be used in the wED algorithm, which will be demonstrated in the Results section.