Super-resolution at factors 3x, 2x, and 1x. The 1x case is just denoising or decovolution, not super-resolution, but is included here for comparison.
λ is the regularization parameter; higher values give
more importance to the prior. The AR prior assumes 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 blur kernel is either
estimated from the input image (using a Fourier domain
computation which assumes the AR model above), or fixed
(from the Epanechnikov family) with h giving the bandwidth
(see the symmetric.blur()
and make.kernel() functions for details).
The estimated kernels are cropped to a size of 5 x 5 pixels. Further, for the direct method, entries less than 1% of the maximum are set to 0. These seem to work well for all the images except the fourth one, for which the strong striping patterns in the image confuses the estimator. For fixed kernels, h = 1.4 works well for the first four images (which are slighly blurred), and 0.7 works well for the last four.
A fair idea of the trade-off between Gaussian and Sparse priors can be had by comparing the results for λ = 0.001. In particular, for the first four images, set λ = 0.001, h = 1.4 and compare IID Gaussian and AR Sparse. Generally speaking, the Gaussian prior gives better visual results for texture, while the Sparse prior performs better for smooth regions. The IID Sparse prior tends to oversmooth.
The first four test images are from Levin et al (2009), Understanding and evaluating blind deconvolution algorithms. The other four test images are from the personal collection of the authors.