Research On Measurement Matrix And Its Optimization Algorithm For Compressed Sensing

With the information increases continuously, high speed of traditional signal sampling technologies which based on the conditions of signal-compressed and sparseness of the transforming dormin, can easily cause the verbose messages when dealing with the sampling. Candes and others provide that compressed sensing theory which lies on the Functional analysis and Approximation theory, is sampling compressed techniques of low sampling rate. It’s well known for the unique compressed structure and relatively low sampling speed within several years, which solve the issues in traditional methods.This thesis propose the analysis and implementation for three core problems:sparse representation in compressed sensing, measurement matrix and algorithm of image reconstruction. In the representation of the sparse matrix, this thesis use DCT method. This thesis also apply the OMP to construct images. This thesis focus on selection and establishment of measurement matrix. First of all, this thesis provide compressed sensing method based on Beta distribution after considering the features of the beta distribution. Also, this thesis choose three different random ways to set up the measurement matrix. The result shows that Beta distribution based algorithms are no big deal compared with other conventional ways. This thesis also get conclusion of insensitiveness to random changes when use compressed sensing technique.Second, this thesis provides a BA-based scale-free network model to construct the measurement matrix and use the single parameter change method to do the comparative experiment, thus proposing a BA-based scale-free model’s optimization algorithm. The prior image can be reconfigured when compressed sensing rate reached at 0.8 during the experiments. With the comparison result, it concludes that relatively high or low network models are not suitable for compress sensing based sampling compression and reconstruction. To solve this issue, deeply, this thesis apply Orthogonal Transfer method in the measurement matrix of BA-based complex network. By simulating and analyzing, this thesis gives a better algorithm with the result that reconstructing the image can be implemented even when the sampling rate at 0.7.