  I present a family of algorithms to reduce noise in astrophysical im- ages
and image sequences, preserving more information from the original data than is
retained by conventional techniques. The family uses locally adaptive filters
("noise gates") in the Fourier domain, to separate coherent image structure
from background noise based on the statistics of local neighborhoods in the
image. Processing of solar data limited by simple shot noise or by additive
noise reveals image structure not easily visible in the originals, preserves
photometry of observable features, and reduces shot noise by a factor of 10 or
more with little to no apparent loss of resolution, revealing faint features
that were either not directly discernible or not sufficiently strongly detected
for quantitative analysis. The method works best on image sequences containing
related subjects, for example movies of solar evolution, but is also applicable
to single images provided that there are enough pixels. The adaptive filter
uses the statistical properties of noise and of local neighborhoods in the
data, to discriminate between coherent features and incoherent noise without
reference to the specific shape or evolution of the those features. The
technique can potentially be modified in a straightforward way to exploit
additional a priori knowledge about the functional form of the noise.
