Examples illustrating the use of a robust (Huber) loss function as a post-processing step. All examples use the AR sparse prior with α = 0.6, with the robustness of the loss function controlled by the parameter k, and regularization parameter λ set to either 0.01 or 0.001. In general, λ = 0.001 is too small to have any effect, but λ = 0.01 leads to visible improvement.
In our implementation, the Huber loss function sets its scale parameter to k multiplied by a robust estimate of the standard deviation of the residuals in each IRLS step, namely MAD / 0.6745. Thus, k = 1 is equivalent to a shift to absolute error loss at a distance of one standard error, and k = 10 is essentially equivalent to squared error loss.
Image details
1. The result of Richardson-Lucy deconvolution on the first image here. The input image has numerous "spots" that are effectively removed by denoising with a robust loss function.
2. The result of denoising and super-resolution using the AR Gaussian prior and an estimated kernel with λ = 0.001, shown here. The input image has prominent artifacts that are substantially improved.
3. A noisy photo of Satyen Bose and Paul Dirac, from social media.