Research On Generalized Hadamard Matrix And Matching Pursuit Algorithm In Compressive Sensing

Compressive sensing is different from Nyquist sampling theorem.Compressive sensing theorem makes use of the sparsity of signal,merging the sampling and compressing process into one,which can reduce the requirement for sampling frequency effectively.Thus,compressive sensing is very suitable for the situation of collecting,processing and transmitting signal in resource-limited system.Measurement matrix and reconstruction algorithm are two decisive factors for the performance of compressive sensing.Aimed at resourcelimited systems such as wireless sensor network,this thesis improves the practicality of compressive sensing based on improvement of the Hadamard measurement matrix and matching pursuit algorithm,which is of great significance to the development and application of compressive sensing.Based on the distribution characteristic of sparse coefficient of images obtained by DCT and DWT in the experiment,this thesis makes some modification to the Hadamard matrix.By weighting different parts of Hadamard matrix with different weights,the thesis proposes the generalized Hadamard matrix.Then the weighted construction of Hadamard matrix is extended to the Hadamard matrix with any odd dimension,and constructs the generalized Hadamard matrix with any odd dimension.Under the condition of other condition and methods unchanged,the proposed matrices can obtain better reconstruction performance on images than common matrix,such as Gauss matrix and Hadamard matrix.An improved atom selection strategy is proposed to reduce the calculation of inner product,for the problem that in OMP and g OMP,a big part of calculation is used for the calculation of inner product between residue vector and sensing matrix.The proposed strategy is based on the residue vector relevance.Atoms with high correlation with current residue have high correlation with the previous residue vector or last several residue vectors with overwhelming probability.The proposed strategy can reduce the time consumption of OMP and g OMP effectively with almost same reconstruction effect.To further improve the performance of matching pursuit algorithm,a framework is proposed based on the idea of local optimization and the multiple candidates.By the framework,we get an initial result with a basic matching pursuit algorithm at first,and then minimize the difference between compressed measurement and the least square solution vector based on local optimization to get a local optimal solution.Simulation results show that it can improve the reconstruction performance of OMP and MMP,and the proposed framework can help to reduce the sampling of the systems with resource-limited front-end and resource-unrestricted back-end.