On The Sparse Representation And Compressive Sensing Based Efficient Signal Processing Techniques And Its Applications

With the advent of the Internet of things and cloud computing, many areas have more st ringent requirements on the increasingly huge amounts of data, such as video data, real-time video, astronomical data and so on, the storage and transmission of the data have become a problem that need the solution urgently. In wide applications of signal processing, we focus on the challenging problem: the sparse representation of data.According to t he characteristics of the signal, the appropriate over-complete dictionary is selected to decompose the signal, in order to obtain the simple expression of signal, name-ly, the sparse representation of signal. Since the sparse representation can be close to the features of signal, the research of sparse decomposition can provide important theoretical significance and wide application. The sparse representation instead of the original data can reduce the cost of signal processing and improve the compression efficiency. Com-pressed Sensing ?CS? has been shown that since the signal is sparse or approximately sparse in the transformation domain, it is possible to merge the acquisition and com-pression processes by performing a reduced number of measurements and recovering the most important features by utilizing an incoherent sampling mechanism. As long as the original signal is sparse, CS can greatly reduce the sampling rate of the signal, the signal processing time, complexity, costs and other expenses.Based on this, this paper studies the sparse signal reconstruction algorithm, that is to say, how to reconstruct the original high-dimensional signal from the limited number of measurements. By the fact that s-parse representation can describe the signal more sparse in transform domain, we studies image super-resolution reconstruction and watermarking method. Using CS can compress the data, the MIMO and OFDM communication system based on CS are proposed.Firstly, the reconstruction algorithm of sparse signal is presented. The l₁- and l₂-norm joint regularization based reconstruction framework is proposed to approach the original l₀-norm based sparseness-inducing constrained sparse signal reconstruction prob-lcm. It is shown that, the new formulation provides an effective framework to deduce the solution as the original sparse signal reconstruction problem with the l₀-norm regular-ization item and the upper reconstruction error limit is analyzed. The simulation results validate the availability of proposed sparse signal reconstruction approach.Sparse representation and CS theory has been widely applied in various fields of signal processing and image processing, such as image compression, denoising, blind signal separation, image super-resolution ?SR.? reconstruction and so on, however, there are bottlenecks for the existing technologies. For SR scheme, to ensure alignment of the dictionary pair, both dictionaries should have the same number of atoms which usually are very large. Our approach can avoid the problems, a new sparse doniain approach is proposed to realize the single image SR reconstruction based upon one single hybrid dictionary, which is deduced from the mixture of both the high resolution ?HR? image patch samples and the low resolution ?LR? ones. Moreover, a linear model is proposed to characterize the relationship between the sparse representations of both the HR image patches and the corresponding LR ones over the same hybrid dictionary. It is shown that,the requirement on the identical sparse represoncation of both HR and LR image patches over the corresponding HR dictionary and the LR dictionary can be relaxed. Moreover,the proposed linear model between the sparse representations of both the HR patch and the corresponding LR patch over the same hybrid dictionary offers us a new method to interpret the image degeneration characteristics in sparse domain. The simulation results are presented to test and verify the proposed SR approach. According to the adaptivity of the over-complete training dictionary, a novel sparse domain based information hiding framework is proposed to attach the watermarking signal to the most significant sparse components of the host signal. Sincce the sparse domain can be customized from the given samples, but also the sparse transform coefficients of the original watermarking signal can be embedded, which provides inherent privacy the adaptive sparse domain can provide better security and robustness. Experimental results demonstrate the superiority of the proposed sparse domain digital watermarking technique over the traditional frequency domain or spatial domain schemes.We propose a novel CS-based signal multiplexing and detection approach. At the transmitter, the signal is compressed and multiplexed by choosing the measurement ma-trix as the multiplex matrix, at the receiver, the exhaustive over-complete dictionary which consider all possible combinations of signal is used to guarantee the sparsity of the signal which equals to 1. The original signal can be detected by the sparsity over redun-dant dictionary and the reconstruction algorithms. Inspired by the idea of CS, we can not only transform the signal detection problem into the signal reconstruction issue which has the same form with CS, so the resulting optimization is to find sparse solution to the underdetermined linear system of equations, but also fewer receiving antennas are de-manded to detect the all original signal. We also demonstrate the feasibility of combining CS into communication system. In order to avoid the excessive complexity, the sub-block based dictionary and the sub-block based CS restoration is proposed. We apply CS into MIMO system and analyze the bit error rate under corresponding scenarios. Analytical and simulation results show that the proposed multiplexing algorithm can multiplex more data stream to the receiver, getting larger multiplexing gain and transmission capacity than the original system, while guarantee the bit error rate. At last, a novel CS based enhanced MIMO-OFDM?Orthogonal Frequency Division Multiplexing? signal multiplex-ing scheme is proposed to further improve the multiplexing gain. A Gaussia.n random measurement matrix in CS is employed in order to carry more data streams. At the receiver, it is proposed to reformulate the detection of the MIMO-OFDM multiplexing signal into two steps. In the first step, the sparse signal can be restored by reconstruction and the original signal can be reconstructed by multiplying the over-complete dictionary.The simulation results are presented to show the feasibility of the proposed CS based enhanced MIMO-OFDM multiplexing scheme. Compared with the existing orthogonal access technology, CS based MIMO-OFDM can hold more users under the same number of resources; or transmit more data under the same number of transmitting and receiving antenna by combining measurement matrix and over-complete dictionary. The research shows CS-OFDM can improve the system of multiplexing gain and the number of the service users at the same time effectively, helping the next generation wireless network to realize the demand of large capacity and super massive connection.