## 3 Proposed Algorithm  
The processing flowchart of the proposed method is shown in Figure 5. The algorithm consists of the following steps:  
Firstly, the logarithmic transformation technique is used to transform the time-series images into logarithmic images, which are then sorted by azimuth time to form a sequence of logarithmic images. This sequence consists of \(n\) images, each of size M \(\times\) N pixels, and can be represented by a 3D array \(f\{log[I]\}\) of dimensions \(n\times\) N \(\times\) M, where the \(k\)_-th_ layer represents the \(k\)_-th_ image, and each layer contains M \(\times\) N pixel values. It can be expressed as:  
\[f\{\log[I]\}=\{\log[I(i,j,k)],i=1,2,\ldots M;j=1,2,\ldots N;k=1,2,\ldots n\} \tag{1}\]  
In the formula, \(log[I(i,j,k)]\) represents the pixel value located in the \(i\)_-th_ row and \(j\)_-th_ column of the \(k\)_-th_ image in the logarithmic image sequence. Next, the sequence of logarithmic images is preprocessed, including image registration, image filtering, and radiometric correction. The speckle noise in SAR image seriously affects the accuracy of change detection, so it needs to be processed. The mean filtering method can be used to filter out the speckle noise in SAR images so as to improve the image quality. Image registration aligns the two images so that the corresponding points in the two images have the same coordinates. Radiation correction is a technique used to correct the radiation distortion in SAR images due to the beam illumination variation. Its purpose is to make the values of the corresponding pixels of each image in the image sequence consistent so that the user can obtain the stable parts of all images. Among them, SAR-SIFT image registration is a critical preprocessing step. The preprocessed logarithmic image sequence can be represented as follows:  
\[f\{\log[\vec{I}]\}=\{\log[\vec{I}(i,j,k)],i=1,2,\ldots M;j=1,2,\ldots N;k=1,2, \ldots n\} \tag{2}\]  
In the formula, \(log[\vec{I}]\) represents the registered image sequence. The steps of SAR-SIFT imag registration technology are detailed in Section 3.1. Then, a median filter is applied along the image index dimension of the registered image sequence, whereby for each pixel, the grayscale values across multiple images are  
Figure 5: Overall flowchart of the algorithm. sorted, and the middle value is taken as the corresponding grayscale value in the static background, resulting in the unchanged part. The median filtering is the key concept used in the Background Subtraction method. It is used for extracting the unchanged part (background) from the reregistered image sequence. Since the image sequence consists of repeated pass observation data, the unchanged parts like buildings present as stable pixel values and have less variation along the index of the images. Meanwhile, the pixels with changes like cars leaving or moving into the frame present as high value or low value variations on the stable pixel value curve. Therefore, the median filtering can filter those high or low values caused by the changes and output the stable background, which we can use to obtain the unchanged parts in all the images. \[\log[B(i,j)]=\text{median}\Bigg{\{}\bigcup_{k=1}^{n}\log[\hat{I}(i,j,k)] \Bigg{\}} \tag{3}\]  
In the formula, \(B(i,j)\) represents the pixel intensity value located in the \(i\)-\(th\) row and \(j\)-\(th\) column of the static background, and median refers to the operation of taking the median value. After obtaining the static background, the image sequence that contains the changed part is obtained by subtracting the static background from the original registered image sequence. \[\log[F(i,j,k)]=\log[\hat{I}(i,j,k)]-\log[B(i,j)] \tag{4}\]  
In the formula, \(log[F(i,j,k)]\) represents the pixel intensity value located in the \(i\)-\(th\) row and \(j\)-\(th\) column of the \(k\)-\(th\) image that contains the changed part. Meanwhile, to exclude other interfering areas, a binary mask is applied on the image sequence to retain only the region of interest.