A slight modification can be made to the previous example of deconvolving an image with kernel that varies by blocks. Again we take the original image:
Blur it with four different box kernels:
And then combine 256 x 256 blocks from each of the blurred images to create a hybrid image with a block-varying kernel. This time I feather the boundary of each block so that there are no hard boundaries. This is done in the hopes of reducing the ringing effects. We do not only the boundaries in the image but also on the outsides edges of the image with the top/bottom and left/right:
Now we can see the results of the Lucy-Richardson deconvolution (see the previous post) lack so the the artifacts. On the other hand, new ones exist: 
Now I see that the image edges still have crude artifacts. It’s possible that extending the edges in a different way may save the 3rd and 4th image from severe artifacting but it is not clear what to expect.