结合成像模型,从数学角度分析了噪声对重构结果的影响,结合POCS算法,仿真了常见成像模型中噪声对重构结果的影响。通过MATLAB软件仿真获取低分辨率图像序列集,并对低分辨率图像施加噪声获取带有噪声的低分辨率图像集,再借助算法获取高分辨率图像。根据实际情况的不同,分别仿真分析了不同程度的高斯噪声和乘性噪声以及椒盐噪声对最终重构结果的影响。研究结果表明:不论何种噪声,其对重构结果的影响趋势基本一致,即较小噪声对于重构结果影响较小,但随着噪声的增加,图像质量严重退化,重构结果中信噪比相对于原始图像下降更快,图像质量更差;另一方面在相同的信噪比情况下,高斯噪声对于重构结果的影响最大。

In this paper, we build an imaging model, analyze the influence of noise on the reconstruction results from the view of mathematics, and then simulate the noise in the common imaging model to study the effect of noise on the super-resolution reconstruction results with the mainstream projection onto convex sets approach. According to the different situations, the influence of different degrees of Gaussian noise and multiplicative noise are simulated and analyzed, respectively. The signal-to-noise ratio(SNR)and information entropy serve as evaluation to analyze the impact of image noise on the super-resolution reconstruction results. The results show that the influence on the super-resolution reconstruction results has basically the same trend, regardless of the type of noise. If the noise is small, the impact on the reconstruction results is small. With the increase of noise, the original image is seriously degraded and SNR of the image after reconstruction declined faster and the image quality is worse. On the other hand, in the same SNR conditions, the impact of Gaussian noise on the reconstruction results is greater than that of multiplicative noise.