Denoising with locally estimated kernel

Reset to Original vs Set as Left Image

Richardson-Lucy IID Gaussian AR Gaussian IID Sparse AR Sparse λ=0.01 λ=0.001

These results illustrate the process of denoising on blurred images, allowing for different kernels in different regions. The denoising is performed on overlapping patches (sub-images), and the kernel is estimated separately from each patch using a Fourier domain computation which assumes that image gradients are correlated (according to the AR model described below).

The estimated kernels are cropped to a size of 11 x 11 pixels. Further, for the direct method, entries less than 1% of the maximum are set to 0.

λ is the regularization parameter; larger values give more importance to the prior and less to image fidelity. The AR priors assume that the image gradients are correlated (according to a simple independent 2-D auto-regressive model with correlation parameters 0.3 and 0.6). The IID priors assume that the gradients are independent.

Compare with the results of denoising with a common kernel, where all three images are included.

Images

1. From mathematician and amateur astronomer Sunil Chebolu. The centre and edges of the moon are at significantly different distances from the camera, and thus have different amounts of blur.

2, 3. Frames from the Satyajit Ray film Nayak. The original in the first frame has good focus, but is still visibly improved by denoising. The focus is slighly off in the second frame, which is considerably improved by denoising.