Researches Of Signal Reconstruction Based On Compressive Sensing

The Nyquist sampling theorem which was an important traditional sampling method should be followed by signals, namely the sampling rate must not be less than twice of the highest frequency of the signals, only by this way, the original signals could be guaranteed to completely reconstruct. However, with the development of society, the signals of people require were became varied, and the amount of the data was increased, so if it was continued to get the signal sampling theorem that would bring some challenges on the devices and computing, So a new signal acquisition mode which broken through the Nyquist sampling theorem was resulted, namely compressed sensing. In this theory, sampling and compression were combined together simultaneously, the process reduced the computation time and the amount of the obtained valid data.this differed from the traditional Nyquist sampling theorem about signals acquisition mode, so this theory had become an important change in recent years in the field of information.Compressed sensing mainly included three parts, namely sparse representation, linear measurement and rebuilding algorithm. Reconstruction algorithm was an important part of compressed sensing, it ensured that low dimensional measurements accurately and quickly restored to full high-dimensional original signal. Therefore, this paper around the compressed sensing reconstruction algorithms and compressed sensing theory study the work as follows:(1) The classic greedy algorithm OMP, ROMP, SAMP, COSAMP of compressed sensing reconstruction algorithm were analyzed and the specific process were detail introduced, different dimensional signal were experimented with these algorithms, and compared the peak signal to noise ratio of each algorithm reconstruction effect, rebuild time and the accuracy of the reconstruction.(2) ROMP of the compressed sensing reconstruction greedy algorithm was improved:the conjugate symmetry properties of Fourier transform was applied to ROMP. The characteristic of sparse base was introduced into the selection process of the atom to change the characteristics of the greedy algorithm only using the correlation to select atom. The atoms were only selected in the first half of the correlation coefficient, and then these points corresponding with the target atoms would be founded in the latter half correlation using conjugate symmetric properties. By reducing the selection range of atomic reduce the blindness of atomic filter, the accuracy of the selection of the atoms were improved, at the same time, the speed of the selection of atoms were improved too.(3) In this thesis, on basis of MS-BCS-SPL, multi-scale block compressed sensing adaptive sampling is realized by distributing total sampling rate into all sub-block of each sub-band, which uses the difference of edge information and directivity of image blocks. First, the edge features are used for image block to adaptive sampling; second, the total sampling rate is distributed adaptively into every block of each sub-band by the characteristics of the Wavelet transform and the direction of blocks. By introducing the idea of these two adaptive sampling, it is shown by experiments that with different sampling rate especially lower, not only high quality images are reconstructed, also less samples is used and reasonable resources distribution is achieved.