  We propose a method to reduce non-uniform sample variance to a predetermined
target level. The proposed space-variant filter can equalize variance of the
non-stationary signal, or vary filtering strength based on image features, such
as edges, etc., as shown by applications in this work. This approach computes
variance reduction ratio at each point of the image, based on the given target
variance. Then, a space-variant filter with matching variance reduction power
is applied. A mathematical framework of atomic kernels is developed to
facilitate stable and fast computation of the filter bank kernels. Recursive
formulation allows using small kernel size, which makes the space-variant
filter more suitable for fast parallel implementation. Despite the small kernel
size, the recursive filter possesses strong variance reduction power. Filter
accuracy is measured by the variance reduction against the target variance;
testing demonstrated high accuracy of variance reduction of the recursive
filter compared to the fixed-size filter. The proposed filter was applied to
adaptive filtering in image reconstruction and edge-preserving denoising.
