Acquisition And Reconstruction Of Video Based On Multi-Dimension Compressive Sensing

Conventional signal processing follows a procedure of sample then compress. Forsampling, the traditional Shannon theory tells us that, to exactly reconstruct the sig-nal, the necessary sampling frequency should be twice of the signal’s bandwidth(theNyquist frequency). For compression, taking into account that the natural signals aresparse, the collected raw data contains a lot of redundancy, the compression can becompleted using some transformation. However, in many real-world application sce-narios, especially for the multimedia signals like images and video, traditional signalprocessing will bring massive data. When the conditions such as time, space, cost andbandwidth are limited, it will be a great challenge to acquire, process, transmit andstore the data.Compressive Sensing is a novel signal processing theory, it utilizes a projectionmatrix which meets the Restricted Isometry Properties(RIP) to project the originalsignal to less non-coherent compressed samples, the original signal can be perfectlyrecovered using the l1convex optimization algorithm. It can be found that the schemeincorporates the sampling and compressing into a single process and makes it possibleto sample the signal in a sub-Nyquist frequency; in addition, the complex recovery isshifted to the’decoder’, this simplifies the’encoder’, these features can save sensorsand improve the sampling efficiency. In view of its good prospects for the application,Compressive Sensing has been widely applied to the field of medical imaging, radarimaging, sensor networks, channel coding and image processing. However, these ap-plications are still stuck in the situation of low-dimensional signals, naturally, moreattentions are paid to the applicability of Compressive Sensing in high-dimensionalsignals. For high dimensional signals like video,3D video and high-spectral image, we must not only consider the structure and data size of higher dimensionality, butalso some special limitations, for example the transience of video frames. Now, to ourbest knowledge, the primary works in this field only involve some specific problems,there are still no universal solutions for high-dimensional Compressive Sensing.The emergence of compressive sensing offers a sub-Nyquist sampling solutionin a reversed complexity shifted from the‘encoder’. However, multidimension-al signals require more consideration on the tradeoff between structured sparsity andlow-complexity sampling.This paper proposes a highly compressed sampling schemefor video acquisition, which involves two major contributions. To optimally utilize thesparsity spanning all dimensions of video, our scheme employs the Kronecker productto generate a synthetic sensing matrix, whose ill-posed factors indicate the compressedsamplings along both spatial and temporal dimensions. Due to the block feature ofKronecker product, the overall sensing matrix enables a distributed sampling mecha-nism which agrees with the progressive fashion of video acquisition. Compared withthe existing Kronecker Compressive Sensing, the proposed scheme preserves a highersampling efficiency by further compressing the temporal components, namely, holo-Kronecker compressive sampling (HKCS). Noticeably, the sampling rate allocationis discussed to find the appropriate spatio-temporal compressive sampling that pro-vides best reconstruction performance. Furthermore, we optimize the sensing matrixin the Kronecker product framework to improve the robustness and efficacy of HKCS.The construction of synthetic sensing matrix implies the divisibility of correspondingmutual coherence within fast low-scale matrix computation. Compared to randomlygenerated matrix, individual optimization of sensing matrix with the sparsifying ba-sis would brings not only more reliable reconstruction, but also faster convergenceto the solution of convex optimization. Besides the proofs of theoretical guarantees,experiments on video datasets show that the proposed scheme substantially improvesthe reconstruction accuracy with less number of necessary samples. The correspond-ing paper “Optimal Spatio-Temporal Projections with Holo-Kronecker CompressiveSensing of Video Acquisition” has been published in IEEE DCC’2012（Data Com-pression Conference，2012）...