Enhancing Sparsity by Reweighted ℓ 1 Minimization
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Taylor, H.L., Banks, S.C., McCoy, J.F.: Deconvolution with the ℓ 1 norm. Geophysics 44(1), 39–52 (1979)
Santosa, F., Symes, W.W.: Linear inversion of band-limited reflection seismograms. SIAM J. Sci. Stat. Comput. 7(4), 1307–1330 (1986)
Donoho, D.L., Stark, P.B.: Uncertainty principles and signal recovery. SIAM J. Appl. Math. 49(3), 906–931 (1989)
Donoho, D.L., Logan, B.F.: Signal recovery and the large sieve. SIAM J. Appl. Math. 52(2), 577–591 (1992)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. B 58(1), 267–288 (1996)
Chen, S., Donoho, D., Saunders, M.: Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20(1), 33–61 (1998)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(1–4), 259–268 (1992)
Blomgren, P., Chan, T.F.: Color TV: total variation methods for restoration of vector-valued images. IEEE Trans. Image Process. 7, 304–309 (1998)
Vandenberghe, L., Boyd, S., El Gamal, A.: Optimal wire and transistor sizing for circuits with non-tree topology. In: Proceedings of the 1997 IEEE/ACM International Conference on Computer Aided Design, pp. 252–259 (1997)
Vandenberghe, L., Boyd, S., El Gamal, A.: Optimizing dominant time constant in RC circuits. IEEE Trans. Comput.-Aided Des. 2(2), 110–125 (1998)
Hassibi, A., How, J., Boyd, S.: Low-authority controller design via convex optimization. AIAA J. Guid. Control Dyn. 22(6), 862–872 (1999)
Dahleh, M., Diaz-Bobillo, I.: Control of Uncertain Systems: A Linear Programming Approach. Prentice-Hall, Englewood Cliffs (1995)
Lobo, M., Fazel, M., Boyd, S.: Portfolio optimization with linear and fixed transaction costs. Ann. Oper. Res. 152(1), 341–365 (2006)
Ghosh, A., Boyd, S.: Growing well-connected graphs. In: Proceedings of the 45th IEEE Conference on Decision and Control, December 2006, pp. 6605–6611
Sun, J., Boyd, S., Xiao, L., Diaconis, P.: The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem. SIAM Rev. 48(4), 681–699 (2006)
Kim, S.-J., Koh, K., Boyd, S., Gorinevsky, D.: ℓ 1 trend filtering. SIAM Rev. (2008, to appear); available at www.stanford.edu/~boyd/l1_trend_filter.html
Donoho, D.L., Huo, X.: Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inf. Theory 47(7), 2845–2862 (2001)
Elad, M., Bruckstein, A.M.: A generalized uncertainty principle and sparse representation in pairs of bases. IEEE Trans. Inf. Theory 48(9), 2558–2567 (2002)
Gribonval, R., Nielsen, M.: Sparse representations in unions of bases. IEEE Trans. Inf. Theory 49(12), 3320–3325 (2003)
Tropp, J.A.: Just relax: convex programming methods for identifying sparse signals in noise. IEEE Trans. Inf. Theory 52, 1030–1051 (2006)
Candès, E.J., Romberg, J., Tao, T.: Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006)
Candès, E.J., Tao, T.: Near optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006)
Donoho, D.L., Tanner, J.: Counting faces of randomly-projected polytopes when the projection radically lowers dimension. J. Am. Math. Soc. 22, 1–53 (2009)
Candès, E.J., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207–1223 (2006)
Takhar, D., Bansal, V., Wakin, M., Duarte, M., Baron, D., Kelly, K.F., Baraniuk, R.G.: A compressed sensing camera: New theory and an implementation using digital micromirrors. In: Proceedings of Comp. Imaging IV at SPIE Electronic Imaging, San Jose, California, January 2006
Lustig, M., Donoho, D., Pauly, J.M.: Sparse MRI: The application of compressed sensing for rapid MR imaging. Preprint (2007)
Candès, E.J., Tao, T.: Decoding by linear programming. IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005)
Candès, E.J., Randall, P.A.: Highly robust error correction by convex programming. Available on the ArXiV preprint server ( cs/0612124 ) (2006)
Healy, D.L.: Analog-to-information (A-to-I). DARPA/MTO Broad Agency Announcement BAA 05-35 (July 2005)
Bajwa, W., Haupt, J., Sayeed, A., Nowak, R.: Compressive wireless sensing. In: Proceedings of Fifth Int. Conf. on Information Processing in Sensor Networks, pp. 134–142 (2006)
Baron, D., Wakin, M.B., Duarte, M.F., Sarvotham, S., Baraniuk, R.G.: Distributed compressed sensing. Preprint (2005)
Fazel, M.: Matrix rank minimization with applications. Ph.D. thesis, Electrical Engineering Department, Stanford University (2002)
Lobo, M.S., Fazel, M., Boyd, S.: Portfolio optimization with linear and fixed transaction costs. Ann. Oper. Res. 152(1), 341–365 (2007)
Fazel, M., Hindi, H., Boyd, S.: Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices. In: Proceedings of Am. Control Conf., June 2003
Figueiredo, M.A.T., Nowak, R.D.: A bound optimization approach to wavelet-based image deconvolution. In: Proceedings of IEEE Int. Conf. on Image Processing (ICIP), vol. 2 (2005)
Figueiredo, M., Bioucas-Dias, J.M., Nowak, R.D.: Majorization–minimization algorithms for wavelet-based image restoration. IEEE Trans. Image Process. 16(12), 2980–2991 (2007)
Wipf, D.P., Nagarajan, S.: A new view of automatic relevance determination. In: Proceedings on Neural Information Processing Systems (NIPS), vol. 20 (2008)
Zou, H.: The adaptive Lasso and its oracle properties. J. Am. Stat. Assoc. 101(476), 1418–1429 (2006)
Zou, H., Li, R.: One-step sparse estimates in nonconcave penalized likelihood models. Ann. Stat. 36(4), 1509–1533 (2008)
Schlossmacher, E.J.: An iterative technique for absolute deviations curve fitting. J. Am. Stat. Assoc. 68(344), 857–859 (1973)
Holland, P., Welsch, R.: Robust regression using iteratively reweighted least-squares. Commun. Stat. Theor. Methods A6, 813–827 (1977)
Yarlagadda, R., Bednar, J.B., Watt, T.L.: Fast algorithms for ℓ p deconvolution. IEEE Trans. Acoust. Speech Signal Process. 33(1), 174–182 (1985)
Yin, W., Osher, S., Goldfarb, D., Darbon, J.: Bregman iterative algorithms for ℓ 1-minimization with applications to compressed sensing. SIAM J. Imaging Sci. 1(1), 143–168 (2008)
Candès, E.J., Tao, T.: The Dantzig selector: Statistical estimation when p is much larger than n. Ann. Stat. 35(6), 2313–2351 (2007)
Goldfarb, D., Yin, W.: Second-order cone programming methods for total variation-based image restoration. SIAM J. Sci. Comput. 27(2), 622–645 (2005)
Chartrand, R.: Exact reconstruction of sparse signals via nonconvex minimization. Signal Process. Lett. 14(10), 707–710 (2007)
Starck, J.-L., Elad, M., Donoho, D.L.: Redundant multiscale transforms and their application for morphological component analysis. Adv. Imaging Electron. Phys. 132, 288–348 (2004)
Elad, M., Milanfar, P., Rubinstein, R.: Analysis versus synthesis in signal priors. Inverse Probl. 23(3), 947–968 (2007)
Gorodnitsky, I.F., Rao, B.D.: Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm. IEEE Trans. Signal Process. 45(3), 600–616 (1997)
Chartrand, R., Yin, W.: Iteratively reweighted algorithms for compressive sensing. In: Proceedings of Int. Conf. on Acoustics, Speech, Signal Processing (ICASSP), pp. 3869–3872 (2008)
Wipf, D.P.: Personal communication (January 2008)
Harikumar, G., Bresler, Y.: A new algorithm for computing sparse solutions to linear inverse problems. In: Proceedings of Int. Conf. on Acoustics, Speech, Signal Processing (ICASSP). IEEE, New York (1996)
Delaney, A.H., Bresler, Y.: Globally convergent edge-preserving regularized reconstruction: An application to limited-angle tomography. IEEE Trans. Image Process. 7(2), 204–221 (1998)
Saab, R., Chartrand, R., Yilmaz, O.: Stable sparse approximations via nonconvex optimization. In: 33rd International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2008
Black, M.J., Sapiro, G., Marimont, D.H., Heeger, D.: Robust anisotropic diffusion. IEEE Trans. Image Process. 7(3), 421–432 (1998)
Boyd, S.: Lecture notes for EE364B: convex optimization II. Available at www.stanford.edu/class/ee364b/ (2007)