1 research outputs found
Monte Carlo non local means: Random sampling for large-scale image filtering
We propose a randomized version of the non-local means (NLM) algorithm for
large-scale image filtering. The new algorithm, called Monte Carlo non-local
means (MCNLM), speeds up the classical NLM by computing a small subset of image
patch distances, which are randomly selected according to a designed sampling
pattern. We make two contributions. First, we analyze the performance of the
MCNLM algorithm and show that, for large images or large external image
databases, the random outcomes of MCNLM are tightly concentrated around the
deterministic full NLM result. In particular, our error probability bounds show
that, at any given sampling ratio, the probability for MCNLM to have a large
deviation from the original NLM solution decays exponentially as the size of
the image or database grows. Second, we derive explicit formulas for optimal
sampling patterns that minimize the error probability bound by exploiting
partial knowledge of the pairwise similarity weights. Numerical experiments
show that MCNLM is competitive with other state-of-the-art fast NLM algorithms
for single-image denoising. When applied to denoising images using an external
database containing ten billion patches, MCNLM returns a randomized solution
that is within 0.2 dB of the full NLM solution while reducing the runtime by
three orders of magnitude.Comment: submitted for publicatio