Optimal Spatio-Temporal Projections with Holo-Kronecker Compressive Sensing of Video Acquisition

In this paper, we proposes a highly compressed video sampling scheme that optimally utilizes the redundancy spanning all the dimensions of the signal. Considering that we further compress the redundant measurements of the existing Kronecker compressive sensing (KCS), the proposed scheme will significantly improve the sampling efficiency. The contribution of our work is two fold. First, a holo-compressive sampling spanning both temporal and spatial dimensions is proposed to overcome the drawback of KCS, and named HKCS. This new scheme keeps on employing Kronecker product to design the sensing matrix. However, it is worth emphasizing that the original identity matrix, a factor of the conventional Kronecker product sensing matrix, is replaced by an ill-posed matrix which enables compressive samplings along the temporal dimension. The advantages of HKCS include: samplings of video along the temporal and spatial dimensions are simultaneously compressed and the necessary measurements for exact recovery are signihcantly reduced; moreover, the Kronecker product sensing matrix retains the block structure, which ensures a feasible distributed sampling scheme for practical application. We prove that, with the same sampling rate, matrices of HKCS have relatively smaller mutual coherence.