  This paper focuses on the dataset-free Blind Image Super-Resolution (BISR).
Unlike existing dataset-free BISR methods that focus on obtaining a degradation
kernel for the entire image, we are the first to explicitly design a
spatially-variant degradation model for each pixel. Our method also benefits
from having a significantly smaller number of learnable parameters compared to
data-driven spatially-variant BISR methods. Concretely, each pixel's
degradation kernel is expressed as a linear combination of a learnable
dictionary composed of a small number of spatially-variant atom kernels. The
coefficient matrices of the atom degradation kernels are derived using
membership functions of fuzzy set theory. We construct a novel Probabilistic
BISR model with tailored likelihood function and prior terms. Subsequently, we
employ the Monte Carlo EM algorithm to infer the degradation kernels for each
pixel. Our method achieves a significant improvement over other
state-of-the-art BISR methods, with an average improvement of 1 dB (2x).Code
will be released at https://github.com/shaojieguoECNU/SVDSR.
