Decomposing a signal based upon redundan dictionaries is a new method for data representation on sig- nal processing. It approximates a signal with an overcom- plete system instead of an orthonormal basis to provide a...Decomposing a signal based upon redundan dictionaries is a new method for data representation on sig- nal processing. It approximates a signal with an overcom- plete system instead of an orthonormal basis to provide a sufficient choice for adaptive sparse decompositions. Re- placing the original data with a sparse approximation can result in not only a higher compression ratio, but also greater flexibility in capturing the inherent structure of the natura signals with the redundancy of dictionaries. This paper gives an overview of a series of recent results in this field, and deals with the relationship between sparsity of signal de- composition and incoherence of dictionaries with BP and MP algorithms. The current and future challenges of the dic- tionary construction are discussed.展开更多
It is very slow at present to reconstruct an image from its sparse decomposition results.To overcome this one of the main drawbacks in image sparse decomposition,the property of the energy distribution of atoms is stu...It is very slow at present to reconstruct an image from its sparse decomposition results.To overcome this one of the main drawbacks in image sparse decomposition,the property of the energy distribution of atoms is studied in this paper.Based on the property that energy of most atoms is highly concentrated,an algorithm is proposed to fast reconstruct an image from atoms’parameters by limiting atom reconstruction calculating within the atom energy concentrating area.Moreover,methods for fast calculating atom energy and normalization are also put forward.The fast algorithm presented in this paper improves the speed of the image reconstructing by approximately 32 times without degrading the reconstructed image quality.展开更多
基金This work was supported in part by the National Committee for Nationalities,China Scholarship Council and Education Department of China.
文摘Decomposing a signal based upon redundan dictionaries is a new method for data representation on sig- nal processing. It approximates a signal with an overcom- plete system instead of an orthonormal basis to provide a sufficient choice for adaptive sparse decompositions. Re- placing the original data with a sparse approximation can result in not only a higher compression ratio, but also greater flexibility in capturing the inherent structure of the natura signals with the redundancy of dictionaries. This paper gives an overview of a series of recent results in this field, and deals with the relationship between sparsity of signal de- composition and incoherence of dictionaries with BP and MP algorithms. The current and future challenges of the dic- tionary construction are discussed.
基金supported by the National Natural Science Foundation of China(Grant No.60602043)China Scholarship Council Found(No.2001-3048)Applied Foundational Research of Sichuan Province(No.03JY029-048-2).
文摘It is very slow at present to reconstruct an image from its sparse decomposition results.To overcome this one of the main drawbacks in image sparse decomposition,the property of the energy distribution of atoms is studied in this paper.Based on the property that energy of most atoms is highly concentrated,an algorithm is proposed to fast reconstruct an image from atoms’parameters by limiting atom reconstruction calculating within the atom energy concentrating area.Moreover,methods for fast calculating atom energy and normalization are also put forward.The fast algorithm presented in this paper improves the speed of the image reconstructing by approximately 32 times without degrading the reconstructed image quality.
