Reconstruction Algorithms And Optimization Method Of Measurement Matrix In Compressive Sensing Theory

Compressive sensing(CS) is a new sampling theory, which takes advantage of the sparse of original signal. In the theory, random sampling is used to acquire the discrete sample of signal under the circumstances of lower sampling frequency than the Nyquist frequency, and then nonlinear reconstruction algorithm is used to reconstruct the signal.This thesis focuses on signal observation and reconstruction algorithm of compressed sensing. At first, this thesis introduces an optimizing method of measurement matrix based on QR decomposition and gradient descent, and it also simulates the method. Compared to the existed optimizing methods, this method proves to be better in signal reconstruction.Conjugate Gradient algorithm based on Smooth l_o-norm(CGSL0) is also been studied, and simulation experiment proves its feasibility and superiority. Compared to other reconstruction algorithms, CGSL0 performs faster and better during signal reconstruction. When the sampling frequency increases, CGSL0 shows huge advantage over the others.This thesis then introduces the combination of proposed optimizing method and CGSL0. Optimizing of measurement matrix retains the main construction of signal during measurement process, and CGSL0 performs well in signal reconstruction. Simulation experiment proves feasibility of the combination, and the combination shows huge superiority in reconstructive time compared to other reconstruction algorithms.At last, the influence of noise in reconstruction algorithm is introduced. It is known to all, the noise cannot be avoided during signal transmission process. This thesis adds noise in the measured value to observe the reconstruction result of different algorithms. At the meantime, the added noise is harmful, and it should be removed during the signal compressed process.