  Many astronomical sources produce transient phenomena at radio frequencies,
but the transient sky at low frequencies (<300 MHz) remains relatively
unexplored. Blind surveys with new widefield radio instruments are setting
increasingly stringent limits on the transient surface density on various
timescales. Although many of these instruments are limited by classical
confusion noise from an ensemble of faint, unresolved sources, one can in
principle detect transients below the classical confusion limit to the extent
that the classical confusion noise is independent of time. We develop a
technique for detecting radio transients that is based on temporal matched
filters applied directly to time series of images rather than relying on
source-finding algorithms applied to individual images. This technique has
well-defined statistical properties and is applicable to variable and transient
searches for both confusion-limited and non-confusion-limited instruments.
Using the Murchison Widefield Array as an example, we demonstrate that the
technique works well on real data despite the presence of classical confusion
noise, sidelobe confusion noise, and other systematic errors. We searched for
transients lasting between 2 minutes and 3 months. We found no transients and
set improved upper limits on the transient surface density at 182 MHz for flux
densities between ~20--200 mJy, providing the best limits to date for hour- and
month-long transients.
