Research On Compressive Sensing Theory And Its Application

Nyquist sampling theorem require sampling frequency should be not less than twice the highest frequency of the signal, which leads to huge amounts of sample data and brings great challenges to the signal processing. Then the compressive sensing theory emerged. The compressive sensing theory can extract concise infrmation from the comp licated signal, thereby reducing large amount of data to process.First of all, the thesis introduces basic principle of compressive sensing and describes the processing procedure of signals under compressive sensing framework. Compressive sensing mainly consists three parts which are sparse representation, observation matrix and signal reconstruction. The main methods for sparse representation are summarized. The observation matrix should have restricted isometric property and the feasibility of signal recovery is explained. Finally, a comparison is made between l0 and l1, optimization problem and the advantages and disadvantages of different reconstruction algorithm are also discussed. Then the thesis makes in-depth research on Greedy reconstruction algorithm of compressive sensing theory. Finally, the theory is applied to image denoising and video coding.The main work of the thesis is as follows:1. The greedy reconstruction algorithms which are often used in compressive sensing are analyzed. The thesis describes the advantages and disadvantages each algorithm. The simulate experiments are carried out to comparing the effect and running time of different reconstruction algorithms and the experimental results are analyzed. Since the StOMP algorithm requires parameter configuration artificially, so the set of parameter values are often vary from person to person, which leads to the reconstruction effects are uneven and the experience value often cannot make the algorithm to achieve optimal performance. Aiming at this problem, the particle swarm optimization algorithm is used to guidance parameters configuration, experiments show that after parameter configuration, this algorithm can achieve better reconstruction results.2. The compressive sensing is used in image denoising. At first, the denoising model based on compressive sensing is established. Then the de-noising algorithm over K-SVD is used to solve the model. The experiments show that the algorithm can effectively eliminate the noise of image. However, the algorithm should running a long time and can’t meet real-time requirement. So the fast sparse decomposition algorithm Batch-OMP is used to replace OMP algorithm to improve the algorithm. The developed algorithm can greatly shorten the running time without reducing the performance.3. The compressed sensing is applied to video coding. As the classical video coding scheme requires complicated motion estimation at the encoder side, so it’s not suitable for some scene with limited computing capacity. To solve the problem, the thesis combined with compressive sensing and distributed video coding theory, designing a distributed video coding scheme based on compressive sensing. The scheme is able to transfer the complexity of encoder to the decoder, which could make up for the shortage of classic video encoding.