Compressed Sensing And Sparse Reconstruction Algrithms

Compressed Sensing (CS) is a new method in signal processing where one seeks to sample sparse signals under far below the Nyquist sampling rate while still retaining the information necessary to reconstruct them. The ideas break through Nyquist bandwidth restriction on the sampling rate and thus received a lot of attention. Recently the theory has a wide range of potential applications in the field of wireless communications, radar imaging, geographic resource exploration and biosensing.Measurement matrix design is closely related to sparse reconstruction algorithms in CS. This paper mainly researches the sparse reconstruction algorithms, particularly the method of measurement matrix design. The first and second chapters introduce the significance and background of CS, including sparse signal representation, measurement matrix design, sparse reconstruction algorithms and applications. The third chapter analyzes the conditions of measurement matrix design, simultaneously gives cumulative coherence level of a random measurement matrix and then dicusses the necessity of training measurement matrix. The fourth chapter studies sparse reconstruction algorithms. Since the OMP algorithm has a low computational complexity and easily implement, the OMP algorithm and its reconstruction conditions is also studied.The fifth chapter primarily gives the probability estimation of cumulative coherence constraint bound and proposes the measurement matrix training algorithm using iteration projection method. The reconstruction ability of the OMP algorithm principal depends on the cumulative coherence level of measurement matrix. This part gives the probability estimation of cumulative coherence constraint bound by using random variable truncated estimation, and the numerical experiments show that the probability estimation are reliable. To low the cumulative coherence level, a measurement matrix training algorithm based on Dictionaries Construction algorithm is proposed using iterative projection method. The experiments indicate that the measurement matrix training algorithm can obviously provide better measurement matrixes to improve the success rate of exactly recovering sparse signals via the OMP algorithm.