  Modern radio interferometers enable observations of spectral lines with
unprecedented spatial resolution and sensitivity. In spite of these technical
advances, many lines of interest are still at best weakly detected and
therefore necessitate detection and analysis techniques specialized for the low
signal-to-noise ratio (SNR) regime. Matched filters can leverage knowledge of
the source structure and kinematics to increase sensitivity of spectral line
observations. Application of the filter in the native Fourier domain improves
SNR while simultaneously avoiding the computational cost and ambiguities
associated with imaging, making matched filtering a fast and robust method for
weak spectral line detection. We demonstrate how an approximate matched filter
can be constructed from a previously observed line or from a model of the
source, and we show how this filter can be used to robustly infer a detection
significance for weak spectral lines. When applied to ALMA Cycle 2 observations
of CH3OH in the protoplanetary disk around TW Hya, the technique yields a ~53%
SNR boost over aperture-based spectral extraction methods, and we show that an
even higher boost will be achieved for observations at higher spatial
resolution. A Python-based open-source implementation of this technique is
available under the MIT license at https://github.com/AstroChem/VISIBLE.
