Study On Compressed Sensing Based Video Reconstruction

Compressed sensing(CS) has attracted a lot of research interests in the signal processing community. It provides a new way to collect data incorporating both acquisition and compression in the sense of "information sampling". The CS technique enables to directly and efficiently capture compressed signals via randomly projecting at a rate that is far below the Nyquist rate, and thus has special experimental and creative value in military and civil fields, due to the great reduction of sampling rate, power consumption, and computational complexity.In image/video acquisition, CS can help reduce the number of measurements to be collected and transcend hardwared limitations at the front end. It can also combine data sampling and compression into a single step without exploring data redundancy at the encoder, and then substantially reduce the computational complexity. However, if the CS theory is directly applied to video signals, it is possible to result in poor reconstruction performance, since the traditional orthogonal basis cannot provide sparse enough coefficients. Furthermore, only sparsity but no other signal structure characters is considered in conventional CS recovery algorithms, which could also seriously affect the reconstruction quality. In this way, the remaining challenge is how to utilize the correlation to develop the efficient CS-based video sampling and reconstruction methods, since there exists significant spatiotemporal reduncancy in video.Based on the CS theory, this dissertation tries to improve the compressed video sensing(CVS) reconstruction performance while retaining the signficant low-complexity in signal acquisition equipments. We mainly focus on the design of efficient CVS reconstruction techniques, in order to achieve an adaptive framework by incorporating the video spatiotemproal characteristic. Then, the required number of sampling rate can be reduced, and the recovery quality could also be improved. The relevant work is supported by the National Natural Science Foundation of China, the Research Fund for the Doctoral Program of Higher Education of China, and etc.The main content of this dissertation is summarized as follows.1) In the first part, we study the weighted l1 minimization problem for CS reconstruction when partial support information is available. Especially, we focus on the coherence-based performance guarantees and show that if an estimated support can be obtained with its accuracy and relative size satisfying certain coherence-related conditions, the weighted l1 minimization is then stable and robust under weaker sufficient conditions than that of the analogous standard l1 optimization. Meanwhile, better upper bounds on the reconstruction error could also be obtained. 2) Second, we propose a novel rate allocation scheme in the CVS framework to achieve adaptive video sampling, and thus improving the reconstruction performance. As the raw pixel data could not be accessed at the fornt end, it is a great challenge to develop the rate allocation scheme when signals are compressively sampled. Therefore, we firstly present a new distortion model, and then propose an adaptive CVS scheme with joint sampling rate SR and quantization bit-depth B optimization. In this way, we are able to compute rate-distortion(RD) optimal values for SR and B by solving an rate-distortion-optimization problem. Experimental results show our method offers improved RD performance in comparison to the existing methods. 3) Third, we focus on the design of efficient sparse reconstruction methods for CVS by exploring the video spatiotemporal sparsity characteristic, since sparsity alone is essentially not suffuicient for video reconstruction with good visual quality. Specially, i) by leveraging more prior information extracted from the temporal redundancy, a regularized reweighted basis pursuit denoising method with estimated support and signal value is proposed for CVS, and an ADMM based algorithm is presented to solve the optimization problem. ii) A novel optimal-correlation-based method is proposed for CVS reconstruction from multiple measurement vectors, and a two-phase Bregman iterative based algorithm is outlined for solving the optimization problem. Simulation results show that our proposal achieves an improved reconstruction performance when compared with the conventional approaches. 4) Lastly, we study the key techniques of sparse reconstruction in distributed compressed video sensing(DCVS). To be specific, i) we propose a novel―undersampled‖ correlation noise model to describe the correlation between the current frame and its side information in compressively sampled video signals; ii) we present a maximum-likelihood dictionary learning based reconstruction algorithm for DCVS; and furthermore, iii) we propose a novel spatiotemporal dictionary learning(DL) based reconstruction method for DCVS, wherein both the DL model and the l1-analysis based recovery with correlation constraints are included in the minimization problem to achieve the joint optimization of sparse representation and signal reconstruction. Besides, an ADMM based numerical algorithm is outlined for solving the underlying optimization problem. Simulation results show that our proposal compares favorably with other existing methods in the CS reconstruction performance.