Study On Compressive Sensing Reconstruction Based On Manifold Study

Compressive sensing is a new theory of information acquisition, which breaksthrough the traditional sampling theory. It combines data acquisition with datacompression, and then recovers the original signal by reconstruction algorithms.Compressive sensing employs the nonadaptive linear projection to obtain the originalsignal information, and then the signal reconstruction is conducted by using an numericaloptimization problems from projection value. Compressive sensing makes the amount ofdata far less than that the traditional sampling theory needed. Therefore, compressivesensing theory is of much concern in the field of signal and image processing, and it alsohas a wide range of applications.This paper mainly to combines the ideas of manifold learning and methods withcompressive sensing, and put forward a new compressive sensing reconstruction method.It mainly reflects in the following three aspects.Firstly, in this paper, we introduce compressive sensing reconstruction method indetail. At the same time we train dictionary with the method of K-SVD. We makecompressive sensing reconstruction with the idea of the block compressive sensingreconstruction, and analysis and comparison the performance all the methods.Secondly, in this paper, the idea and method of the Locally Linear Embedding in themanifold study is applied to the compressive sensing. It proposes a compressive sensingreconstruction method based on LLE. The experimental results show that thereconstructed images have better visual effect, and it verify the validity of compressivesensing reconstruction method based on LLE we proposed.Finally, according to the image block has the characteristics of low dimensionalmanifolds, the nonlinear manifold can be approximated by linear submanifold. We clusterimage block which we trained, then propose a new method to project image block in themanifold. That is the method of parametric manifold learning. We combine it withcompressive sensing, and propose a compressive sensing reconstruction method based onparametric manifold learning. The experimental results show that reconstruction of natural images has very good results with the method we designed.