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In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis.
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A greedoid polynomial which distinguishes rooted arborescences
G. Gordon and E. McMahon · 1989
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Ten lectures on wavelets
I. Daubechies · 1992
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Orthonormal bases of compactly supported wavelets. II. Variations on a theme
I. Daubechies · 1993
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Ideal spatial adaptation by wavelet shrinkage
D. L. Donoho and I. M. Johnstone · 1994
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D. L. Donoho · 1995
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E. Hernández and G. Weiss · 1996
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M. S. Crouse, R. D. Nowak, and R. G. Baraniuk · 1998
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Wavelet-based statistical signal processing using hidden markov models
M. S. Crouse, R. D. Nowak, and R. G. Baraniuk · 1998
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Adaptive wavelet thresholding for image denoising and compression
S. G. Chang, B. Yu, and M. Vetterli · 2000
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Hidden markov tree modeling of complex wavelet transforms
H. Choi, J. Romberg, R. Baraniuk, and N. Kingsbury · 2000
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Hyperspectral Imaging: Techniques for Spectral Detection and Classification
C. I. Chang · 2003
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Image denoising using scale mixtures of Gaussians in the wavelet domain
J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli · 2003
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A review of image denoising algorithms, with a new one
A. Buades, B. Coll, and J. M. Morel · 2005
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Stable signal recovery from incomplete and inaccurate measurements
E. J. Candès, J. K. Romberg, and T. Tao · 2006
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Compressed sensing
D. L. Donoho · 2006
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SPGL1: A solver for large-scale sparse reconstruction, June 2007
E. van den Berg and M. P. Friedlander · 2007
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Enhancing sparsity by reweighted l 1 l_{1} minimization
E. J. Candès, M. B. Wakin, and S. P. Boyd · 2008
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Enhancing sparsity by reweighted minimization
E. J. Candès, M. B. Wakin, and S. P. Boyd · 2008
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Single-pixel imaging via compressive sampling
M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk · 2008
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A general framework for regularized, similarity-based image restoration
A. Kheradmand and P. Milanfar · 2014
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Medical hyperspectral imaging: a review
G. Lu and B. Fei · 2014
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A algorithm for compressed sensing ecg
L. F. Polania and K. E. Barner · 2014
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A fast tree-based algorithm for compressed sensing with sparse-tree prior
H. Bui, C. La, and M. N. Do · 2015
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A. Massa, P. Rocca, and G. Oliveri · 2015
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An Introduction to Frames and Riesz Bases
O. Christensen · 2016
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Wavelet-domain compressive signal reconstruction using a hidden markov tree model
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Compressed sensing mri
M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly · 2008
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Probing the pareto frontier for basis pursuit solutions
E. van den Berg and M. P. Friedlander · 2008
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Exploiting structure in wavelet-based Bayesian compressive sensing
L. He and L. Carin · 2009
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Model-based compressive sensing
R. G. Baraniuk, V. Cevher, M. F. Duarte, and Ch. Hegde · 2010
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Non-Local Means Denoising
A. Buades, B. Coll, and J. Morel · 2011
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H. Rauhut and R. Ward · 2016
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Breaking the coherence barrier: A new theory for compressed sensing
B. Adcock, A. C Hansen, C. Poon, and B. Roman · 2017
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Compressed sensing with local structure: Uniform recovery guarantees for the sparsity in levels class
Ch. Li and B. Adcock · 2017
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Low dimensional manifold model for image processing
S. Osher, Z. Shi, and W. Zhu · 2017
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On oracle-type local recovery guarantees in compressed sensing, 2018
Ben A., C. Boyer, and S. Brugiapaglia · 2018
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Polynomial approximation via compressed sensing of high-dimensional functions on lower sets
A. Chkifa, N. Dexter, H. Tran, and C. G. Webster · 2018
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Analysis of sparse recovery for legendre expansions using envelope bound
H. Tran and C. Webster · 2018
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