This paper addresses the problem of 3D motion reconstruction from a series of 2D projections under low reconstructibility. Reconstructibility defines the accuracy of a 3D reconstruction from 2D projections given a particular trajectory basis, 3D point trajectory, and 3D camera center trajectory. Reconstructibility accuracy is inherently related to the correlation between point and camera trajectories. Poor correlation leads to good reconstruction, high correlation leads to poor reconstruction. Unfortunately, in most real-world situations involving non-rigid objects (e.g. bodies), camera and point motions are highly correlated (i.e., slow and smooth) resulting in poor reconstructibility. In this paper, we propose a novel approach for 3D motion reconstruction of non-rigid body motion in the presence of real-world camera motion. Specifically we: (i) propose the inclusion of a small number of keyframes in the video sequence from which 3D coordinates are inferred/estimated to circumvent ambiguities between point and camera motion, and (ii) employ a L 1 penalty term to enforce a spar-sity constraint on the trajectory basis coefficients so as to ensure our reconstructions are consistent with the natural compressibility of human motion. We demonstrate impressive 3D motion reconstruction for 2D projection sequences with hitherto low reconstructibility.