A linearly convergent algorithm for solving a class of nonconvex/affine feasibility problems

Springer Optimization and Its Applications

Volumn 49, Issue , 2011, Pages 33-48

  Beck, Amir ^a   Teboulle, Marc ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Affine rank minimization; Compressive sensing; Gradient projection algorithm; Inverse problems; Linear rate of convergence; Mutual coherence of a matrix; Nonconvex affine feasibility; Scalable restricted isometry; Sparse signal recovery

Indexed keywords

EID: 84976509864     PISSN: 19316828     EISSN: 19316836     Source Type: Book Series    
DOI: 10.1007/978-1-4419-9569-8_3     Document Type: Chapter

References (23)

1. Bauschke, H.H., Borwein, J.M.: On projection algorithms for solving convex feasibility problems. SIAM Review 38, 367-426 (1996)
2. Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sciences 2, 183-202 (2009)
3. Beck, A., Teboulle, M.: Gradient-based algorithms with applications to signal recovery problems. In: D. Palomar, Y. Eldar (eds.) Convex Optimization in Signal Processing and Communications, 42-88. Cambridge University Press (2010)
4. Bertsekas, D.: Non-Linear Programming, 2nd ed. Athena Scientific, Belmont, MA (1999)
5. Blumensath, T., Davies, M.E.: Iterative hard thresholding for Sparse Approximations. The Journal of Fourier Analysis and Applications 14, 629-654 (2008)
6. Bruckstein, A. M., Donoho, D. L., Elad, M.: From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Review 51, 34-81 (2009)
7. Cadzow, J.A.: Signal enhancement - a composite property mapping algorithm. IEEE Trans. Acoustics, Speech, Signal Process. 36, 49-62 (1988)
8. Candès, E.J., Romberg, J., Tao, T.: Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52:489-509 (2006)
9. Candés, E.J.: The restricted isometry property and its implications for compressed sensing. Compte Rendus de l’Academie des Sciences, Paris, Serie I 346, 589-592 (2008)
10. Chartrand, R.: Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Process. Letters 14, 707-710 (2007)
11. Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Review 43, 129-159 (2001)
12. Combettes, P.L.: The foundations of set theoeretic estimation. Proc. IEEE 81, 182-208 (1993)
13. Combettes, P.L., Trussell, H.J.: Method of successive projections for finding a common point of sets in metric spaces. J. Optim. Theory Appl. 67, 487-507 (1990)
14. Donoho, D.L.: Compressed sensing. IEEE Transactions on Information Theory 52, 1289-1306 (2006)
15. Donoho, D.L., Huo, X.: Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inform. Theory 47, 2845-2862 (2001)
16. Elad, M., Bruckstein, A.M.: A generalized uncertainty principle and sparse representation in pairs of bases. IEEE Trans. Inform. Theory 48, 2558-2567 (2002)
17. Engl, H.W., Hanke, M., Neubauer, A.: Regularization of inverse problems, volume 375 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht (1996)
18. Fazel, M., Hindi, H., Boyd, S.: Rank minimization and applications in system theory. In: American Control Conference, 3272-3278 (2004)
19. Golub, G., Loan, C.V.: Matrix computations, 3rd edn. Johns Hopkins University Press (1996)
20. Natarajan, B.K.: Sparse approximation solutions to linear systems. SIAM J. Computing 24, 227-234 (1995)
21. Recht, B., Fazel, M., Parrilo, P.: Guaranteed minimum rank solutions of matrix equations via nuclear norm minimization. SIAM Review 52, 471-501 (2010)
22. Santosa, F., Symes, W.W.: Linear inversion of band-limited reflection seismograms. SIAM J. Sci. Statist. Comput. 7, 1307-1330 (1986)
23. Taylor, H.L., Banks, S.C., McCoy, J.F.: Deconvolution with the l1 norm. Geophysics 44, 39-52 (1979)