Sparse coding with invariance constraints
ICANN/ICONIP'03 Proceedings of the 2003 joint international conference on Artificial neural networks and neural information processing
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Sparse and shift-Invariant representations of music
IEEE Transactions on Audio, Speech, and Language Processing
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
Dictionary learning for image prediction
Journal of Visual Communication and Image Representation
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In this paper, we introduce shift-invariant sparse image representations using tree-structured dictionaries. Sparse coding is a generative signal model that approximates signals by the linear combinations of atoms in a dictionary. Since a sparsity penalty is introduced during signal approximation and dictionary learning, the dictionary represents the primal structures of the signals. Under the shift-invariance constraint, the dictionary comprises translated structuring elements (SEs). The computational cost and number of atoms in the dictionary increase along with the increasing number of SEs. In this paper, we propose an algorithm for shift-invariant sparse image representation, in which SEs are learnt with a tree-structured approach. By using a tree-structured dictionary, we can reduce the computational cost of the image decomposition to the logarithmic order of the number of SEs. We also present the results of our experiments on SE learning and the use of our algorithm in an image recovery application.