Research On Recovery Algorithms For Compressed Sensing Of Sparse Signals

Compressed Sensing (CS) is one emerging hotspot in signal processing. This technology employs a special samlping method which can capture and represent compressible signals at a rate significantly below the Nyquist rate, so there are wide application prospects in the areas of radar image, wireless sensor network (WSN), radio frequency communication, medical image processing, image device collecting and so on. One of the important tasks in CS is how to recover the signals more accurately and effectively, which is concerned by many researchers.With the basic theory of CS, the recovery algorithms are discussed in this dissertation. Aimed to improve the recovery probability and reducing the complexity, firstly, this dissertation summarizes several recovery algorithms, especially the matching pursuit (MP) type algorithms in detailed. And then, the recovery algorithms for block-sparse signals are studied. Finally, the dissertation researches the recovery algorithms for analog to information converter (AIC). Simulation results demonstrate the effectiveness of our algorithms. The main contents and research contributions of this dissertation are listed as follows:1.The MP type algorithms especially orthogonal matching pursuit (OMP) are studied. To solve the problem that the support set couldn't be estimated accurately in standard OMP, a modified OMP using correlation coefficient is proposed. The basic idea of the algorithm is that the support set is searched by calculating correlation coefficients between the sensing matrix and the measurement vector instead of inner product. The correlation coefficient can describe the matching level better than inner product, so the proposed algorithm can determine the support set more accurately, which leads to high recovery probability. Simulation results show the proposed algorithm outperforms the standard OMP both on 1-D and 2-D signals.2.Block CS recovery algorithms are studied. Focous on the problems that the most existing block CS recovery algorithms are of low accuracy, high complexity and require some prior, this dissertation proposes three improved algorithms. Firstly, based on the subspace and backtracking idea, a block-sparse subspace matching pursuit algorithm has been proposed. The algorithm determines an estimate of the correct support set during each iteration, and the estimate support set will be refined at next iteration using the backtracking. Compared with the most existing algorithms, our algorithm has high recovery probability and low computational complexity. Subsequently, to solve the problem that the most existing recovery algorithms require block sparsity as prior knowledge, a block sparsity adaptive iteration algorithm has been proposed when the block sparsity is unknown. The proposed algorithm initializes a block sparsity which will increase by steps, until the exact support set and original signal are acquired. The complexity of this algorithm equals to some existing block CS recovery algorithms, but this algorithm doesn't require block sparsity as a prior and has high recovery probability. Finally, for the shortcoming that the most block CS recovery algorithms require the block size and block-sparsity as a prior, this dissertation proposes a block-sparse adaptive matching pursuit algorithm. The most innovation of the proposed algorithm lies in the idea initializing the block size and block sparsity which can alternatively estimate the block size, block sparsity and the target signal. Compared with some existing algorithms, the complexity of this algorithm is a little high, but the proposed algorithm require less prior knowledge, and has high recovery probability, which can be applied in some non-real time problems. Simulation results show that the three presented algorithm is valid in recovery target source.3 . The recovery algorithms for AIC, especially modulated wideband converter (MWC) of multiband signals are studied. Most conventional MWC recovery algorithms employ simultaneous orthogonal matching pursuit (SOMP), which is ineffient and of low recovery probability. To solve the problem, a recovery algorithm which can refine the frequency support occupies is proposed in this dissertation, termed the simultaneous subspace pursuit. The proposed algorithm can estimate the whole frequency support occupy during each iteration, moreover, the frequency support occupies can be refined during next iteration using least mean square criterion. The recovery signal can be determined when the correct support band will be found. Compared with the SOMP, the proposed algorithm has low computational complexity, high recovery probability and good anti-noise performance. Simulation results for the practice multiband signals demonstrate its good performance.