Research On Construction And Optimization Of Measurement Matrix For Compressed Sensing

Compressed sensing(CS) is a novel sampling paradigm. CS has recently gained a lot of attention in many fields. Conventional approaches to sampling signals follow Shannon’s celebrated theorem: the sampling rate must be at least twice the maximum frequency present in the signal. CS builds upon the fundamental fact that we can present many signals using only a few non-zero coefficients in a suitable basis or dictionary. Nonlinear optimization can then enable recovery of such signals from very few measurements. This thesis introduces the theory, and researches on the construction and optimization of measurement matrix for CS. The main work is as follows:(1). This thesis focuses on structured matrix for its good performance and easy to implement after studying the common measurement matrix. Drawing on the advantages of circulant matrix and generalized rotation matrix, the thesis proposes a new method to design a measurement matrix based on random circulant. The simulation results suggest the new matrix has better performance in signal’s reconstruction;(2). Learning from the fact that minimizing the coherence of measurement matrix can get better performance in the signal’s reconstruction. The thesis proposes a method to increase the independence of the measurement matrix column vector by imposed the Gram-Schmidt orthogonalization on the matrix. The new method could result a better restored signals when it combined with OMP;(3). Analyzing the feasibility of reducing the cross-correlation of the sensing matrix could optimize the measurement matrix, the thesis proposes a method to optimize the measurement matrix based on Grassmannian frames. The new method spends less time and have better capability to reconstruct the origin signals.