Ghost imaging has emerged as a promising technique, which is characterized by mitigating the adverse effects of atmospheric turbulence and scattering media, and has the potential to surpass the diffraction limitations. Meanwhile, its potential applications in remote sensing are highly anticipated. However, effective evaluation methods that can quantitatively assess the influence of various components within the imaging system on its performance should be proposed to facilitate the practical implementation of ghost imaging. Such methods can provide valuable support for the design and optimization of imaging systems. Currently, one area of research focuses on evaluating the influence of the observation matrix. Although commonly adopted evaluation methods that rely heavily on specific imaging scenarios and reconstructed images can accurately characterize the effect of the observation matrix based on image quality after reconstruction, they often fall short of independently assessing the system's overall performance. Therefore, it is essential to put forward a quantitative evaluation method prior to the reconstruction stages. Studies have indicated that information theory-based approaches hold promise in achieving this objective. Some researchers have evaluated the influence of factors such as the row number or the distribution type of the observation matrix on system performance by calculating the mutual information between signals received by bucket detectors and imaging scenes. Despite favorable results yielded by their methods, they encounter challenges such as difficulty in acquiring prior information or limited applicability. To this end, we explore a novel method for evaluating the performance of ghost imaging systems before the reconstruction process. This method employs communication system channel evaluation techniques to analyze and assess the observation matrix. By treating the observation matrix as a channel matrix, we derive the channel capacity of the sampling system and utilize it to evaluate the influence of the observation matrix on the system performance. Consequently, this approach addresses the limitations identified in previous studies.

Firstly, we establish an analogy between the ghost imaging system and the communication system, where the imaging scene information is considered as the information source, the M times sampling process as the channel, and the received signal of the bucket detector as the sink. At this juncture, the observation matrix assumes the role of the channel matrix, which constitutes a crucial component of the channel and can be analyzed by the channel evaluation method employed in communication systems. Subsequently, the M×N channels represented by the observation matrix undergo singular value decomposition, yielding R independent subchannels. Given that the interference during ghost imaging sampling primarily manifests as Gaussian white noise, we assume the channel to be a Gaussian channel. Consequently, the channel capacity of each subchannel can be determined by employing the formula for Gaussian channel capacity. The signal power during the sampling corresponds to that of the imaging scene information. Compared to temporal variations of the imaging scenes, the duration required for the M times sampling is relatively short. Thus, it is reasonable to assume that the overall power of the imaging scene information remains constant throughout the sampling. On the other hand, the noise power corresponds to the average power of Gaussian white noise, which is numerically equivalent to its variance. By substituting the signal power and noise power of each subchannel into the formula for Gaussian channel capacity and aggregating the results, we can obtain the total channel capacity of the ghost imaging sampling. Furthermore, the Bernoulli inequality is applied to establish a lower bound on the channel capacity value, and an approximate representation is employed. On this basis, we observe that the component associated with the signal power and noise power remains constant and nullifies during comparing the channel capacity of different observation matrices. Consequently, in practical applications, it is unnecessary to measure the total power of the imaging scene information and the average power of the Gaussian noise.

Based on the imaging simulation test encompassing 100 diverse imaging scenes, 20 distinct types of observation matrices, and 2 reconstruction algorithms, a comprehensive analysis is conducted by comparing the test results with the evaluation outcomes of image quality following imaging reconstruction. The findings indicate strong consistency between the effectiveness of our study in evaluating system performance before imaging and the validation results obtained by post-imaging. An imaging scene is selected, and the channel capacity variations for the sampling process and the MSE for reconstructed images are compared with the type of matrix element distribution. Then, it is evident that both exhibit identical dependence on the type of matrix element distribution at the same sampling ratio (Fig. 6). This consistency is observed in all imaging scenes. Additionally, by simulating the imaging process using a Bernoulli distribution matrix (p0=0.001) for a selected imaging scene, it is observed that the normalized channel capacity curve of the sampling process and the normalized inverse MSE curves of the reconstructed exhibit a high concordance degree, with R2 of 0.97606 and 0.95878 (Fig. 8). In the case of extending the imaging and fitting process to all 100 imaging scenes, it becomes apparent that the R2 values for the two reconstruction algorithms generally exceed 0.8 (Fig. 9).

The incorporation of information theory in this method facilitates an objective assessment of the transmission capability of the observation matrix for imaging scene information by utilizing the channel capacity of the sampling system. This approach enables independent and effective evaluation of system performance, disentangled from prior knowledge of the imaging scenes or reconstructed imaging results. The evaluation outcomes demonstrate robust consistency with the validation results obtained by post-imaging. Under constant sampling ratio, the mean squared error (MSE) of the reconstructed images and the channel capacity exhibit parallel dependency on the distribution type of matrix elements. Similarly, when the distribution type of matrix elements remains the same, the curves depicting the normalized channel capacity and the normalized inverse MSE as functions of the sampling times present a high concordance degree, with R2 values generally exceeding 0.8. Moreover, the simulation verification encompassing a diverse range of imaging scenes and observation matrices yields sound results. This further proves the applicability of the proposed method across various scales of imaging scenes and different types of ghost imaging systems, making it highly suitable for widespread implementation in common remote sensing scenarios.