# SEAIS: Secure and Efficient Agricultural Image Storage Combining Blockchain and Satellite Networks
## 4 System Design and Methodology
### Satellite Imaging and Pre-Processing  
In remote farmland or extreme environments, traditional smart devices and drones often cannot effectively monitor fields and generate real-time images. The satellite network can regularly capture images of fields, providing a continuous data stream, as it has a wide coverage area and is unaffected by environmental factors. The transmitted image data includes raw image signals and various environmental noises. To ensure data integrity and reliability, we propose the following mathematical model and data processing scheme, as shown in Equation (1):  
\[I_{raw}(x,y,\lambda)=R_{sat}(x,y,\lambda)+A(x,y,\lambda)+N(x,y,\lambda), \tag{1}\]  
where \(I_{raw}(x,y,\lambda)\) represents the raw image signal at pixel \((x,y)\) and wavelength \(\lambda\), \(R_{sat}(x,y,\lambda)\) is the ground reflectance at pixel \((x,y)\) and wavelength \(\lambda\), \(A(x,y,\lambda)\) is atmospheric noise and absorption effects, and \(N(x,y,\lambda)\) represents the sensor noise. To simplify calculations, we combine atmospheric and sensor noise, as shown in Equations (2) and (3). \[I_{raw}(x,y,\lambda)=R_{sat}(x,y,\lambda)+N^{\prime}(x,y,\lambda), \tag{2}\]  
\[N^{\prime}(x,y,\lambda)=A(x,y,\lambda)+N(x,y,\lambda) \tag{3}\]  
In this model, we assume that atmospheric noise, such as humidity, temperature fluctuations, and aerosol presence, remains relatively stable over the course of transmission. These environmental factors can impact noise estimation, particularly in dynamic or extreme conditions, but we assume their influence to be consistent in our modeling. Furthermore, the sensor noise \(N(x,y,\lambda)\) is modeled under typical satellite sensor conditions, with minimal external interference such as radiation or equipment malfunctions. One limitation of this model is that it assumes a uniform distribution of noise across the entire image, without explicitly accounting for severe atmospheric disturbances like heavy rainfall or dust storms, which could cause localized variations in communication quality. After capturing the images, they need to be transmitted to a local server or cloud server for preprocessing. We assume no channel interference between satellites and servers, and that the bandwidth \(B\) remains constant throughout the transmission process. Additionally, the model assumes that interference power \(I_{c}\) is minimal and stable, without considering potential atmospheric disturbances or signal disruptions caused by multipath effects. The transmission delay \(T_{c}\) is assumed to be fixed. Therefore, the image transmission model is idealized and does not consider more complex scenarios such as multi-satellite communications or changing environmental conditions. This introduces limitations in real-world applications, where factors like rain, snow, and dust storms could degrade communication quality. According to [PERSON]'s formula, the data transmission model is given, with the channel capacity \(C\) expressed in Equation (4). Assuming that the raw image data volume is \(D\), the transmission time \(T_{trans}\) is given in Equation (5). \[C=B\log_{2}(1+\frac{L_{t}G_{c}}{N_{0}B+I_{c}}), \tag{4}\]  
\[T_{trans}=\frac{D}{C}+T_{l} \tag{5}\]  
In the above equations, \(B\) is the channel bandwidth, \(P_{t}\) is the transmission power of the device, \(G_{c}\) denotes the noise power spectral density, \(N_{0}\) represents the average co-channel interference power, and \(T_{c}\) is the transmission delay. To ensure data transmission integrity, we use a cyclic redundancy check (CRC) to verify data packets. During transmission,each data packet includes a checksum, and the receiver uses this checksum for integrity verification. Given the raw data sequence \(M(d)\) and the generating polynomial \(P(d)\), the data sequence with the appended checksum \(S(d)\) is calculated from Equation (6), where \(n\) denotes the length of the checksum and \(U(d)\) is the remainder and satisfies Equation (7).