Mixing space-time derivatives for video compressive sensing

With the increasing use of compressive sensing techniques for better data acquisition and storage, the need for efficient, accurate, and robust reconstruction algorithms continues to be in demand. In this work we present a fast total variation based method for reconstructing video compressive sensing data. Video compressive sensing systems store video sequences by taking a linear combination of consecutive spatially compressed frames. In order to recover the original data, our method regularizes both the spatial and temporal components using a total variation semi-norm that mixes information between dimensions. This mixing provides a more consistent approximation of the connection between neighboring frames with little to no increase in complexity. The algorithm is easy to implement since each iteration contains two shrinkage steps and a few iterations of conjugate gradient. Numerical simulations on real data show large improvements in both the PSNR and visual quality of the reconstructed frame sequences using our method.