Research On Compressive Sensing Based On Manifold And Gaussian Mixture Model

Traditional theory of compressive sensing is based on signal sparse model and itbreaks the bondage of traditional Nyquist sampling law, so it realizes low-speed samplingand signal reconstruction process. Based on existing theory and algorithm, this paper usesdifferent models of signal as prior knowledge to represent signals, and researchescompressive sensing method based on different models. Main work is as follows:First of all, this paper researches a multi-scale manifold learning based compressivesensing method. High dimensional data usually show the complex space structure, butgenerally the internal law can take advantage of minority characterization parameters torepresent. The purpose of the manifold learning is excavating smooth low dimensionalmanifold which embedded in high dimensional space by limited sampling points anddescribing high dimensional data. This paper researches a multi-scale manifold learningbased compressive sensing method, combining the data under the way of manifold modelwith compressed sensing theory.Secondly, some classical clustering method is not applicable in high dimensionalspace, this paper proposes an image block clustering method which is based on sparserepresentation. This method characterizes image block data in high dimensional spacevectors and clusters high dimensional data with sparse representation. The method learnsthe characteristics of the EM algorithm and the sparse representation based classificationalgorithm, and it realizes the clustering operation through a series of iterative processfinally. The experimental results show that this algorithm can cluster image block datawell.At last, this paper puts forward the Gaussian mixture model based compressivesensing method, and this method applied a priori knowledge that image signals belong toGaussian mixture model, it processes the signals through model training, the choice ofGaussian distribution and signal reconstruction. At the same time in order to furtherenhance the effect of this method, this paper researches an observation matrixoptimization method based on information theory. This method provides a feedback mechanism to optimize the observation matrix through the link between maximummutual information and minimum mean square error matrix. The experimental resultsshow that Gaussian mixture model based compressive sensing method is able to quicklyreconstruct image well.