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Integral field spectroscopy of high-redshift galaxies has become a powerfultool for understanding their dynamics and evolutionary states. However, in thecase of gravitationally lensed systems, it has proved difficult to model bothlensing and intrinsic kinematics in a way that takes full advantage of theinformation available in the spectral domain. In this paper, we introduce a newmethod for pixel-based source reconstruction that alters standardregularization schemes for two-dimensional data in a way that leverageskinematic information in a physically motivated but flexible fashion, and thatis better suited to the three-dimensional nature of integral field data. Toevaluate the performance of this method, we compare its results to those of amore traditional two-dimensional non-parametric approach using mock ALMAobservations of a typical high-redshift dusty star-forming galaxy. We find that3D regularization applied to an entire data cube reconstructs a source'sintensity and velocity structure more accurately than 2D regularization appliedto separate velocity channels. Cubes reconstructed with 3D regularization alsohave more uniform noise and resolution properties and are less sensitive to thesignal-to-noise ratio of individual velocity channels than the results of 2Dregularization. Our new approach to modeling integral field observations oflensed systems can be implemented without making restrictive a prioriassumptions about intrinsic kinematics, and opens the door to new observingstrategies that prioritize spectral resolution over spatial resolution (e.g.,for multi-configuration arrays like ALMA).

A New Method for the Reconstruction of Strongly Lensed Galaxies with Resolved Kinematics