1.6 Noise analysis

Noise Analysis

Normally, all element values of an image matrix fall within the interval $[0,1]$ . However, the introduced noise reduces the deblurring quality, resulting in some elements having values above 1 orbelow 0 in the deblurred image matrix. This effect has been compensated in the previous part. We then compute the $\text{PSNR}$ of the deblurred images with respect to the original/ground-truth and plot thePSNR values against different levels of noise, characterized by the variances of the independent and identically distributed zero-meanGaussian random variables. The formula of $\text{PSNR}$ is $PSNR=10·\text{lo}{g}_{10}\left(\frac{\text{MA}{X_I}^2}{\text{MSE}}\right)=20·\text{lo}{g}_{10}\left(\frac{\text{MA}{X}_I}{\text{MS}{E}^{0.5}}\right)$ where $\text{MA}{X}_I$ is the maximum possible pixel value of the image and $\text{MSE}$ is the mean squared error between the deblurred image and the ground-truth image.