Research On Sparse Representation And Low-rank Model And Applications On Image Processing

With the rapid development of information technology,the era of big data is coming.A huge amounts of visual data,such as images and video sequences,are produced every day.These data are with not only big volume,but also high dimension.As is well-known,the high dimension will lead to the curse of dimensionality,which will make it intractable to process these data.Fortunately,leveraging its structural property,we can effectively process these data and obtain useful information from them.Recent development of the theory of sparse representation and compressed sensing shows that it is effective to model and analyze the big volume and high dimensional data by adapting the sparsity.In general,L0 norm is used to describe the sparsity for a vector.For a matrix,rank is used as the measurement of sparsity,which results in the low-rank model.This thesis studies the applications of sparse representation and low-rank model in image processing,including sparse representation-based classification,image restoration based on sparse representation and background modeling from static v ideo based on low-rank model and so on.Additional,the batch image alignment by sparse and low-rank model is further studied in this thesis.Since there usually exist many similar images with a same class in the high dimensional image data set,they can be modelled by low-rank and sparsity constraint and derive some optimization problems.To obtain the solution,convex relaxation is exploited to convert the NP-hard problems to convex optimization problems which can be solve by existing algorithms.Moreover,in image processing,the influence of illumination and partial occlusions and corruptions can be get rid of by treating them as sparse errors.Hence,it will be more robust in real-world applications.This thesis introduces the model of a union of subspaces into the problem of batch image alignment.The key of this problem is to seek a group of transformations to align images.In this thesis,a new method to solve this problem is proposed.The proposed method holds the point of view that a batch images are drawn from a union of subspaces and the transformation parameters can be obtained by iterative linearization and alternative sparsity pursuit.Experiments on various kind of images,such as faces,video sequences and handwritten digits,demonstrate the effectiveness and robustness of the proposed method.In addition,evaluation based on Peak Signal to Noise Ratio and structural similarity index,it demonstrates that the proposed method has better performance compared with the existing method.