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The modeling of phenomenological structure is a crucial aspect in inverse imaging problems.
M. Beckmann, “A continuous model of transportation,” Econometrica: Journal of the Econometric Society , pp. 643–660, 1952
1952
Earlier work this paper cites.
R. E. Kalman, “A new approach to linear filtering and prediction problems,” Journal of Basic Engineering , vol. 82, no. 1, pp. 35–45, Mar. 1960
1960
Earlier work this paper cites.
R. T. Rockafellar, “Monotone operators and the proximal point algorithm,” SIAM journal on control and optimization , vol. 14, no. 5, pp. 877–898, 1976
1976
Earlier work this paper cites.
P.-L. Lions and B. Mercier, “Splitting algorithms for the sum of two nonlinear operators,” SIAM Journal on Numerical Analysis , vol. 16, no. 6, pp. 964–979, 1979
1979
Earlier work this paper cites.
J. Eckstein, “Splitting methods for monotone operators with applications to parallel optimization,” Ph.D. dissertation, Massachusetts Institute of Technology, 1989
1989
Earlier work this paper cites.
W. C. Davidon, “Variable metric method for minimization,” SIAM Journal on Optimization , vol. 1, no. 1, pp. 1–17, 1991
1991
Earlier work this paper cites.
R. Tibshirani, “Regression shrinkage and selection via the Lasso,” Journal of the Royal Statistical Society. Series B (Methodological) , pp. 267–288, 1996
1996
Earlier work this paper cites.
R. Jordan, D. Kinderlehrer, and F. Otto, “The variational formulation of the Fokker–Planck equation,” SIAM journal on mathematical analysis , vol. 29, no. 1, pp. 1–17, 1998
1998
Earlier work this paper cites.
Y. Rubner, C. Tomasi, and L. J. Guibas, “The earth mover’s distance as a metric for image retrieval,” International journal of computer vision , vol. 40, no. 2, pp. 99–121, 2000
2000
Earlier work this paper cites.
C. Villani, Topics in optimal transportation . American Mathematical Soc., 2003, no. 58
2003
Earlier work this paper cites.
D. L. Donoho and J. Tanner, “Sparse nonnegative solution of underdetermined linear equations by linear programming,” Proceedings of the National Academy of Sciences of the United States of America , vol. 102, no. 27, pp. 9446–9451, May 2005
2005
Earlier work this paper cites.
E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on information theory , vol. 52, no. 2, pp. 489–509, 2006
2006
Earlier work this paper cites.
L. V. Kantorovich, “On a problem of Monge,” Journal of Mathematical Sciences , vol. 133, no. 4, pp. 1383–1383, 2006
2006
Earlier work this paper cites.
M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE Journal of Selected Topics in Signal Processing , vol. 1, no. 4, pp. 586–597, Dec. 2007
2007
Earlier work this paper cites.
M. V. Afonso, J. M. Bioucas-Dias, and M. A. Figueiredo, “Fast image recovery using variable splitting and constrained optimization,” IEEE transactions on image processing , vol. 19, no. 9, pp. 2345–2356, 2010
2010
Earlier work this paper cites.
——, “An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems,” IEEE Transactions on Image Processing , vol. 20, no. 3, pp. 681–695, 2010
2010
Earlier work this paper cites.
A. Figalli, “The optimal partial transport problem,” Archive for rational mechanics and analysis , vol. 195, no. 2, pp. 533–560, 2010
2010
Earlier work this paper cites.
L. A. Caffarelli and R. J. McCann, “Free boundaries in optimal transport and Monge-Ampere obstacle problems,” Annals of mathematics , pp. 673–730, 2010
2010
Cited alongside, same era.
M. S. Asif and J. Romberg, “Dynamic updating for ℓ 1 \ell_{1} minimization,” IEEE Journal of Selected Topics in Signal Processing , vol. 4, no. 2, pp. 421–434, Apr. 2010
2010
Cited alongside, same era.
N. Vaswani, “LS-CS-residual (LS-CS): Compressive sensing on least squares residual,” IEEE Transactions on Signal Processing , vol. 58, no. 8, pp. 4108–4120, 2010
2010
Cited alongside, same era.
D. Sejdinović, C. Andrieu, and R. Piechocki, “Bayesian sequential compressed sensing in sparse dynamical systems,” in 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton) . IEEE, 2010, pp. 1730–1736
2010
Cited alongside, same era.
X. Ye, J. Yang, X. Sun, K. Li, C. Hou, and Y. Wang, “Foreground–background separation from video clips via motion-assisted matrix restoration,” IEEE Transactions on Circuits and Systems for Video Technology , vol. 25, no. 11, pp. 1721–1734, Nov. 2015
2015
Later among the works it cites.
2016
Later among the works it cites.
A. S. Charles, A. Balavoine, and C. J. Rozell, “Dynamic filtering of time-varying sparse signals via ℓ 1 \ell_{1} minimization,” IEEE Transactions on Signal Processing , vol. 64, no. 21, pp. 5644–5656, Nov. 2016
2016
Later among the works it cites.
T. Bouwmans, N. S. Aybat, E.-h. Zahzah, N. S. Aybat, and E.-h. Zahzah, Handbook of Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing . Chapman and Hall/CRC, Jul. 2016
2016
Later among the works it cites.
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Z. Zhou, X. Li, J. Wright, E. Candès, and Y. Ma, “Stable principal component pursuit,” in 2010 IEEE International Symposium on Information Theory , Jun. 2010, pp. 1518–1522
2010
Cited alongside, same era.
A. Chambolle and T. Pock, “A first-order primal-dual algorithm for convex problems with applications to imaging,” Journal of mathematical imaging and vision , vol. 40, no. 1, pp. 120–145, 2011
2011
Cited alongside, same era.
E. J. Candès, X. Li, Y. Ma, and J. Wright, “Robust principal component analysis?” Journal of the ACM (JACM) , vol. 58, no. 3, p. 11, 2011
2011
Cited alongside, same era.
S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein et al. , “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Foundations and Trends® in Machine learning , vol. 3, no. 1, pp. 1–122, 2011
2011
Cited alongside, same era.
S. Farahmand, G. B. Giannakis, and D. Angelosante, “Doubly robust smoothing of dynamical processes via outlier sparsity constraints,” IEEE Transactions on Signal Processing , vol. 59, no. 10, pp. 4529–4543, 2011
2011
Cited alongside, same era.
A. E. Waters, A. C. Sankaranarayanan, and R. Baraniuk, “SpaRCS: Recovering low-rank and sparse matrices from compressive measurements,” in Advances in Neural Information Processing Systems 24 , J. Shawe-Taylor, R. S. Zemel, P. L. Bartlett, F. Pereira, and K. Q. Weinberger, Eds. Curran Associates, Inc., 2011, pp. 1089–1097
2011
Cited alongside, same era.
E. Mainini, “A description of transport cost for signed measures,” Journal of Mathematical Sciences , vol. 181, no. 6, pp. 837–855, 2012
2012
Cited alongside, same era.
M. Cuturi, “Sinkhorn distances: Lightspeed computation of optimal transport,” in Advances in neural information processing systems , 2013, pp. 2292–2300
2013
Cited alongside, same era.
A. S. Charles, N. P. Bertrand, J. Lee, and C. J. Rozell, “Earth-mover’s distance as a tracking regularizer,” in 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) , Dec 2017, pp. 1–5
2017
Later among the works it cites.
J. Karlsson and A. Ringh, “Generalized Sinkhorn iterations for regularizing inverse problems using optimal mass transport,” SIAM Journal on Imaging Sciences , vol. 10, no. 4, pp. 1935–1962, 2017
2017
Later among the works it cites.
E. K. Ryu, W. Li, P. Yin, and S. Osher, “Unbalanced and partial L 1 L_{1} Monge-Kantorovich problem: a scalable parallel first-order method,” Journal of Scientific Computing , pp. 1–18, Nov. 2017
2017
Later among the works it cites.
I. Abraham, R. Abraham, M. Bergounioux, and G. Carlier, “Tomographic reconstruction from a few views: a multi-marginal optimal transport approach,” Applied Mathematics & Optimization , vol. 75, no. 1, pp. 55–73, 2017
2017
Later among the works it cites.
2018
Later among the works it cites.
W. Li, E. K. Ryu, S. Osher, W. Yin, and W. Gangbo, “A parallel method for earth mover’s distance,” Journal of Scientific Computing , vol. 75, no. 1, pp. 182–197, 2018
2018
Later among the works it cites.
M. Liero, A. Mielke, and G. Savaré, “Optimal entropy-transport problems and a new Hellinger–Kantorovich distance between positive measures,” Inventiones mathematicae , vol. 211, no. 3, pp. 969–1117, 2018
2018
Later among the works it cites.
N. P. Bertrand, J. Lee, A. S. Charles, P. Dunn, and C. J. Rozell, “Sparse dynamic filtering via earth mover’s distance regularization,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Calgary, Alberta, Canada , Apr 2018
2018
Later among the works it cites.
2018
Later among the works it cites.
2018
Later among the works it cites.
G. Peyré, M. Cuturi et al. , “Computational optimal transport,” Foundations and Trends® in Machine Learning , vol. 11, no. 5-6, pp. 355–607, 2019
2019
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