An Optimized Compressed Sensing Recovery Algorithm Based On Support Set Selection And Its Application In Microwave Photonics

With the explosive growth of data in the modern society,limited by the Nyquist Sampling Theorem,values of data acquisition size and sampling rate in the signal processing are often too large,which challenge sampling devices and storage devices a lot.Therefore,compressed sensing(CS)theory came into being.The sampling rate under CS theory no longer depends on the highest frequency of the signal,but the sparsity of the signal and the characteristics of the measurement matrix(MM).Compressed sensing aims at compressing and sampling the signal at the same time,mapping it from high-dimensional space to a low-dimensional space,and obtaining the measured values.With a smaller amount of information,the signal can be reconstructed through recovery algorithms,successfully realizes breaking through the limit of Nyquist sampling rate.This thesis focuses on the theory of compressed sensing,carriying out the following innovative works:(1)A mathematical model is established for a microwave photonics-enabled CS system.We proved that in an ideal CS system,the inner products of the measurements and columns of measurement matrix which corresponding to the signal support set(position indexes of effective information in the sparse domain of signal)are not smaller than the rest of inner products.And the probability of equality is very small,which decreases exponentially with the dimension of the measurements.Based on that,it is further proved that when the CS system is affected by noise,the inner products of measurements and columns of measurement matrix corresponding to the support set is still the maximum under probability of approaching 1.(2)Based on the theoretical analysis,an optimizedz algorithm is come up with,which is called supp-BPDN algorithm.The proposed algorithm executes a step of selecting and recording the support set of original signals before BPDN.In the same words,selecting the position indexes corresponding to the top t values of the inner products and only retaining the recovery information in such position indexes,which can effectively avoid errors from wrong infromation.In the algorithm procedures,it is not necessary to remove the contributions of local optimal values in the measurements during each iteration,which simplifies the process.After comparing the numerical simulations between supp-BPDN and traditional algorithms,recovery errors reconstructed by supp-BPDN is the smallest.(3)Based on the advantages of microwave photonic technologies,a photonicenabled CS system is designed.And a signal with a maximum frequency of 350 MHz can be recovered when digitized at 200 MHz.Even more,a signal with the highest frequency being 1 GHz could be reconstruted when digitized at 500 MHz,achieving a breakthrough in the Nyquist sampling rate.Moreover,we uesed both the supp-BPDN and BPDN algorithms to recover the signals,finding signals recovered by supp-BPDN fit the original signals more closely,verifying the effectiveness and superiority of suppBPDN algorithm.