Illustration of super-resolution. The first two images are from the supplementary website of Efrat et al (2013), Accurate Blur Models vs. Image Priors in Super-Resolution. This website has results for several other methods applied to these images. The third image is a frame from the Buster Keaton film The Electric House, obtained from The Internet Archive. Also used to illustrate denoising.
λ is the regularization parameter; higher values give
more importance to the prior. 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 blur kernel is either
user-supplied (from the Epanechnikov family) with h giving
the bandwidth, or estimated from the input image (using a
Fourier domain computation which assumes the AR model
above) (see the symmetric.blur()
and make.kernel() functions for details). The
estimated kernels are cropped to a size of 15 x
15. Further, for the direct method, entries less than 10%
of the maximum are set to 0.
As seen with test images, the Gaussian priors give better visual results for texture, while the Sparse priors perform better for smooth regions. The IID Sparse prior tends to oversmooth.