  Integral field spectroscopy of high-redshift galaxies has become a powerful
tool for understanding their dynamics and evolutionary states. However, in the
case of gravitationally lensed systems, it has proved difficult to model both
lensing and intrinsic kinematics in a way that takes full advantage of the
information available in the spectral domain. In this paper, we introduce a new
method for pixel-based source reconstruction that alters standard
regularization schemes for two-dimensional data in a way that leverages
kinematic information in a physically motivated but flexible fashion, and that
is better suited to the three-dimensional nature of integral field data. To
evaluate the performance of this method, we compare its results to those of a
more traditional two-dimensional non-parametric approach using mock ALMA
observations of a typical high-redshift dusty star-forming galaxy. We find that
3D regularization applied to an entire data cube reconstructs a source's
intensity and velocity structure more accurately than 2D regularization applied
to separate velocity channels. Cubes reconstructed with 3D regularization also
have more uniform noise and resolution properties and are less sensitive to the
signal-to-noise ratio of individual velocity channels than the results of 2D
regularization. Our new approach to modeling integral field observations of
lensed systems can be implemented without making restrictive a priori
assumptions about intrinsic kinematics, and opens the door to new observing
strategies that prioritize spectral resolution over spatial resolution (e.g.,
for multi-configuration arrays like ALMA).
