Image Restoration

Here we shall explore image restoration (eg, deblurring) using Weiner and Lucy Richardson filtering.

First consider this pair of images:

In MATLAB, we have the functions deconvwnr and deconvlucy that performs Weiner and Lucy-Richardson filtering respectively. However we must also specify the filter that was used in the blurring process. Looking at the images above it seems that a gaussian blurring might be the reason for the transformation. However, we do not know the appropriate kernel size and variance of the gaussian filter

First we keep sigma constant at 5 and plot the PSNRs for the 2 methods. The graphs below show that a window size of 11 is appropriate for sigma = 5

Next we vary both sigma and window size to find the optimal filter. We observe that for sigma=5, we get best performance.

Thus choosing filter size = 11 and sigma = 5, we get the following restorations. Lucy-Richardson's output looks sharper, but has more ringing artifacts at the edge.

Now we consider this image, whose ground truth is unknown

We try 3 types of filters all of window size = 11: average, gaussian (sigma = 5) and motion blur kernel (angle = 45 degree). The results are shown below:

The results look sharper than the input image. In general Lucy-Richardson's output looks more sharper.