Many algorithms have been proposed to find sparse representations over redundant dictionaries or transforms. This paper gives an overview of these algorithms by classifying them into three categories： greedy pursuit ...Many algorithms have been proposed to find sparse representations over redundant dictionaries or transforms. This paper gives an overview of these algorithms by classifying them into three categories： greedy pursuit algorithms, lp norm regularization based algorithms, and iterative shrinkage algorithms. We summarize their pros and cons as well as their connections. Based on recent evidence, we conclude that the algorithms of the three categories share the same root： lp norm regularized inverse problem. Finally, several topics that deserve further investigation are also discussed.展开更多
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
基金Supported by the Joint Research Fund for Overseas Chinese Young Scholars of the National Natural Science Foundation of China (Grant No.60528004)the Key Project of the National Natural Science Foundation of China (Grant No. 60528004)
文摘Many algorithms have been proposed to find sparse representations over redundant dictionaries or transforms. This paper gives an overview of these algorithms by classifying them into three categories： greedy pursuit algorithms, lp norm regularization based algorithms, and iterative shrinkage algorithms. We summarize their pros and cons as well as their connections. Based on recent evidence, we conclude that the algorithms of the three categories share the same root： lp norm regularized inverse problem. Finally, several topics that deserve further investigation are also discussed.
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.
