Study On Signal Reconstrution Of Compressed Sensing And Its Application

The traditional Nyquist sampling theorem requires that the frequency of samplingsignal must be greater than or equal to twice of original signal in order to recover theoriginal signal without distortion, it not only puts forward higher requirements to theability of signal processing, but also brings great challenges to the appropriate hardwaredevices. Compressive sensing theory breaks through the traditional Shannon samplingtheorem, by means of the non-adaptive measurements with a well below the Nyquistsampling frequency and optimization methods, reconstructs signal with high probability.Inthis paper, we deeply research on the shortage of the number of measurements and thequality of reconstruction, and made some improvements as follows.Firstly, Several reconstruction algorithms of compressed sensing, including greedyalgorithms based onl0norm and optimization algorithms based onl1norm, arediscussed and simulated. In many existed algorithms, images are always processed in acolumn-wise manner, for this we put forward a balance scheme. The experimental resultsshow that the proposed scheme improves the quality of reconstruction algorithm.Secondly, because thel1norm optimization problem cannot guarantee an exactreconstruction while the measurements are fewer, we replacel1norm byl pwith thevalues of0p1, and a parameter regularization strategy is introduced into the IRLSalgorithm. Numerical results show that the improved algorithm is useful and helps forbetter recovery. For the problem of more Storage and a long time when a two-dimensionalimage is reconstructed, we introduce the idea of the block into the proposed algorithm,which improves the speed of the algorithm.At last, we proposed compressive sensing applied to wireless sensor networks for itsenergy limitation problem. The experimental results show that it decreases the energyconsumption and extends the survival time of wireless sensor network.