ABSTRACT We present the time lag/delay reconstructor (TLDR), an algorithm for reconstructing velocity delay maps in the maximum a posteriori framework for reverberation mapping. Reverberation mapping is a tomographical method for studying the kinematics and geometry of the broad-line region of active galactic nuclei at high spatial resolution. Leveraging modern image reconstruction techniques, including total variation and compressed sensing, TLDR applies multiple regularization schemes to reconstruct velocity delay maps using the alternating direction method of multipliers. Along with the detailed description of the TLDR algorithm we present test reconstructions from TLDR applied to synthetic reverberation mapping spectra as well as a preliminary reconstruction of the Hβ feature of Arp 151 from the 2008 Lick Active Galactic Nuclei Monitoring Project.