Proceedings Article10.1109/ICASSP.2010.5495207
Structured and incoherent parametric dictionary design
Mehrdad Yaghoobi,Laurent Daudet,Michael Davies +2 more
- 14 Mar 2010
- pp 5486-5489
TL;DR: An extra constraint will be applied on the parametric dictionaries to find a structured dictionary that satisfies a constraint, here the incoherence property, which can help conventional sparse coding methods to find sparser solutions in average.
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Abstract: A new dictionary selection approach for sparse coding, called parametric dictionary design, has recently been introduced. The aim is to choose a dictionary from a class of admissible dictionaries which can be presented parametrically. The designed dictionary satisfies a constraint, here the incoherence property, which can help conventional sparse coding methods to find sparser solutions in average. In this paper, an extra constraint will be applied on the parametric dictionaries to find a structured dictionary. Various structures can be imposed on dictionaries to promote a correlation between the atoms. We intentionally choose a structure to implement the dictionary using a set of filter banks. This indeed helps to implement the dictionary-signal multiplications more efficiently. The price we pay for the extra structure is that the designed dictionary is not as incoherent as unstructured parametric designed dictionaries.
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Citations
•Proceedings Article
2010 ieee international conference on acoustics, speech, and signal processing
Thanasis Tsanas,Max A. Little,Patrick E. McSharry,Lorraine O. Ramig +3 more
- 01 Jan 2010
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•Proceedings Article
Nearest Neighbors Using Compact Sparse Codes
Anoop Cherian
- 21 Jun 2014
TL;DR: This paper proposes a novel dictionary learning formulation with incoherence constraints and an efficient method to solve it, and shows an order of magnitude improvement in retrieval accuracy without sacrificing memory and query time compared to the state-of-the-art methods.
Incoherent Dictionary Learning Method Based on Unit Norm Tight Frame and Manifold Optimization for Sparse Representation
TL;DR: A efficient framework is developed to learn an incoherent dictionary for sparse representation that can approximate an equiangular tight frame and manifold optimization is used to avoid the degeneracy of sparse representation while only reducing the coherence of the learned dictionary.
Fast and incoherent dictionary learning algorithms with application to fMRI
TL;DR: The problem of dictionary learning and its analogy to source separation is addressed and a fast dictionary learning algorithm based on steepest descent method is proposed, which is high speed since both coefficients and dictionary elements are updated simultaneously rather than column-by-column.
References
Matrix analysis: Frontmatter
Roger A. Horn,Charles R. Johnson +1 more
- 01 Jan 1985
TL;DR: This book presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications.
21.4K
$rm K$ -SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
TL;DR: A novel algorithm for adapting dictionaries in order to achieve sparse signal representations, the K-SVD algorithm, an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data.
10K
Uncertainty principles and ideal atomic decomposition
David L. Donoho,Xiaoming Huo +1 more
TL;DR: It is proved that if S is representable as a highly sparse superposition of atoms from this time-frequency dictionary, then there is only one such highly sparse representation of S, and it can be obtained by solving the convex optimization problem of minimizing the l/sup 1/ norm of the coefficients among all decompositions.
Grassmannian frames with applications to coding and communication
Thomas Strohmer,Robert W. Heath +1 more
TL;DR: The application of Grassmannian frames to wireless communication and to multiple description coding is discussed and their connection to unit norm tight frames for frames which are generated by group-like unitary systems is discussed.
1.1K
Computational Methods for Sparse Solution of Linear Inverse Problems
Joel A. Tropp,Stephen J. Wright +1 more
- 29 Apr 2010
TL;DR: This paper surveys the major practical algorithms for sparse approximation with specific attention to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available.
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