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Optimally Sparse Representation in General (non-Orthogonal) Dictionaries via
Sparse Representation Overcomplete Representation
2015/8/21
Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a
linear combination S =
k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for
the sparsest repre...
The Curvelet Representation of Wave Propagators is Optimally Sparse
Curvelet Representation Wave Propagators Optimally Sparse
2015/6/17
This paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations. Curvelets are a recently developed multiscale syst...
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions
Uncertainty principle applications of uncertainty principles random matrices eigenvalues of random matrices sparsity trigonometric expansion convex optimization duality in optimization basis pursuit wavelets linear programming
2015/6/17
In this paper, we develop a robust uncertainty principle for finite signals in CN which states that for nearly all choices T,Ω ⊂ {0, . . . , N − 1} such that |T| + |Ω| (log N...
Optimally Sparse Frames
Computational complexity frame decompositions frame operator frames
2010/12/8
Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions.