Not yet reviewed by Pith; the record is open.

We present a reconstruction of the line-of-sight motions of the local interstellar medium (ISM) based on the combination of a model of the three-dimensional dust density distribution within 1.25 kpc from the Sun and the HI and CO line emission within Galactic latitudes $|b| < 5^{\circ}$. We used the histogram of oriented gradient (HOG) method, a computer vision technique for evaluating the morphological correlation between images, to match the plane-of-the-sky dust distribution across distances with the atomic and molecular line emission. We identified a significant correlation between the 3D dust model and the line emission. We employed this correlation to assign line-of-sight velocities to the dust across density channels and produce a face-on map of the local ISM radial motions with respect to the local standard of rest (LSR). We find that most of the material in the 3D dust model follows the large-scale pattern of Galactic rotation; however, we also report local departures from the rotation pattern with standard deviations of 10.8 and 6.6 km/s for the HI and CO line emission, respectively. The mean kinetic energy densities corresponding to these streaming motions are around 0.11 and 0.04 eV/cm$^{3}$ from either gas tracer. Assuming homogeneity and isotropy in the velocity field, these values are within a factor of a few of the total kinetic energy density. These kinetic energy values are roughly comparable to other energy densities, thus confirming the near-equipartition in the local ISM. Yet, we identify energy and momentum overdensities of around a factor of ten concentrated in local density structures. Although we do not find evidence of the local spiral arm's impact on these energy overdensities, their distribution suggests the influence of large-scale effects that, in addition to supernova feedback, shape the energy distribution and dynamics in the solar neighborhood.