Compressive sensing

Handbook of Mathematical Methods in Imaging: Volume 1, Second Edition

Volumn , Issue , 2015, Pages 205-256

  Fornasier, Massimo ^a   Rauhut, Holger ^b  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84944539760     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-1-4939-0790-8_6     Document Type: Chapter

References (160)

1. Achlioptas, D.: Database-friendly random projections. In: Proceedings of the 20th Annual ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Santa Barbara, pp. 274–281 (2001)
2. Affentranger, F., Schneider, R.: Random projections of regular simplices. Discret. Comput. Geom. 7(3), 219–226 (1992)
3. Ailon, N., Liberty, E.: Almost optimal unrestricted fast Johnson-Lindenstrauss transform. In: Symposium on Discrete Algorithms (SODA), San Francisco, (2011)
4. Alexeev, B., Bandeira, A.S., Fickus, M., Mixon, D.G.: Phase retrieval with polarization (2012). arXiv:1210.7752
5. Balan, R., Casazza, P., Edidin, D.: On signal reconstruction without phase. Appl. Comput. Harmon. Anal. 20(3), 345–356 (2006)
6. Baraniuk, R.: Compressive sensing. IEEE Signal Process. Mag. 24(4), 118–121 (2007)
7. Baraniuk, R.G., Davenport, M., DeVore, R.A., Wakin, M.: A simple proof of the restricted isometry property for random matrices. Constr. Approx. 28(3), 253–263 (2008)
8. Bauschke, H.H., Combettes, P.-L., Luke, D.R.: Hybrid projection-reflection method for phase retrieval. J. Opt. Soc. Am. A 20(6), 1025–1034 (2003)
9. Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183–202 (2009)
10. Beck, A., Teboulle, M.: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Process. 18(11), 2419–2434 (2009)
11. Berinde, R., Gilbert, A.C., Indyk, P., Karloff, H., Strauss, M.: Combining geometry and combinatorics: a unified approach to sparse signal recovery. In: Proceedings of the 46th Annual Allerton Conference on Comunication, Control, and Computing 2008, Urbana, IEEE (2008)
12. Blanchard, J.D., Cartis, C., Tanner, J., Thompson, A.: Phase transitions for greedy sparse approximation algorithms. Appl. Comput. Harmon. Anal. 30(2), 188–203 (2011)
13. Blumensath, T., Davies, M.: Iterative hard thresholding for compressed sensing. Appl. Comput. Harmon. Anal. 27(3), 265–274 (2009)
14. Bobin, J., Starck, J.-L., Ottensamer, R.: Compressed sensing in astronomy. IEEE J. Sel. Top. Signal Process. 2(5), 718–726 (2008)
15. Bourgain, J., Dilworth, S., Ford, K., Konyagin, S., Kutzarova, D.: Breaking the k2-barrier for explicit RIP matrices. In: STOC’11, San Jose, pp. 637–644 (2011)
16. Bourgain, J., Dilworth, S., Ford, K., Konyagin, S., Kutzarova, D.: Explicit constructions of RIP matrices and related problems. Duke Math. J. 159(1), 145–185 (2011)
17. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge/New York (2004)
18. Bungartz, H.-J., Griebel, M.: Sparse grids. Acta Numer. 13, 147–269 (2004)
19. Cai, T., Zhang, A.: Sparse representation of a polytope and recovery of sparse signals and low-rank matrices. IEEE Trans. Inf. Theory 60(1), 122–132 (2014)
20. Cai, J.-F., Candès, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956–1982 (2010)
21. Candès, E.J.: Compressive sampling. In: Proceedings of the International Congress of Mathematicians, Madrid (2006)
22. Candès, E.J.: The restricted isometry property and its implications for compressed sensing. C. R. Acad. Sci. Paris Ser. I Math. 346, 589–592 (2008)
23. Candès, E.J., Li, X.: Solving quadratic equations via PhaseLift when there are about as many equations as unknowns. Found. Comput. Math. 14(5), 1017–1026 (2014)
24. Candès, E.J., Plan, Y.: Tight oracle bounds for low-rank matrix recovery from a minimal number of random measurements. IEEE Trans. Inf. Theory 57(4), 2342–2359 (2011)
25. Candès, E.J., Recht, B.: Exact matrix completion via convex optimization. Found. Comput. Math. 9, 717–772 (2009)
26. Candès, E.J., Tao, T.: Near optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006)
27. Candès, E.J., Tao, T.: The power of convex relaxation: near-optimal matrix completion. IEEE Trans. Inf. Theory 56(5), 2053–2080 (2010)
28. Candès, E., Wakin, M.: An introduction to compressive sampling. IEEE Signal Process. Mag. 25(2), 21–30 (2008)
29. Candès, E.J., Tao, T., Romberg, J.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006)
30. Candès, E.J., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207–1223 (2006)
31. Candès, E., Li, X., Soltanolkotabi, M.: Phase retrieval from masked Fourier transforms (2013, preprint)
32. Candès, E.J., Strohmer, T., Voroninski, V.: PhaseLift: exact and stable signal recovery from magnitude measurements via convex programming. Commun. Pure Appl.Math. 66(8), 1241–1274 (2013)
33. Capalbo, M., Reingold, O., Vadhan, S., Wigderson, A.: Randomness conductors and constantdegree lossless expanders. In: Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, Montréal, pp. 659–668 (electronic). ACM (2002)
34. Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120–145 (2011)
35. Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20(1), 33–61 (1999)
36. Christensen, O.: An Introduction to Frames and Riesz Bases. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston (2003)
37. Cline, A.K.: Rate of convergence of Lawson’s algorithm. Math. Comput. 26, 167–176 (1972)
38. Cohen, A., Dahmen, W., DeVore, R.A.: Compressed sensing and best k-term approximation. J. Am. Math. Soc. 22(1), 211–231 (2009)
39. Combettes, P., Pesquet, J.-C.: A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery. IEEE J. Sel. Top. Signal Process. 1(4), 564–574 (2007)
40. Combettes, P., Pesquet, J.-C.: Proximal splitting methods in signal processing. In: Bauschke, H., Burachik, R., Combettes, P., Elser, V., Luke, D., Wolkowicz, H. (eds.) Fixed- Point Algorithms for Inverse Problems in Science and Engineering, pp. 185–212. Springer, New York (2011)
41. Combettes, P., Wajs, V.: Signal recovery by proximal forward-backward splitting. Multisc. Model. Simul. 4(4), 1168–1200 (electronic) (2005)
42. Cormode, G., Muthukrishnan, S.: Combinatorial algorithms for compressed sensing. In: CISS, Princeton (2006)
43. Daubechies, I., Defrise, M., De Mol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57(11), 1413–1457 (2004)
44. Daubechies, I., DeVore, R., Fornasier, M., Güntürk, C.: Iteratively re-weighted least squares minimization for sparse recovery. Commun. Pure Appl. Math. 63(1), 1–38 (2010)
45. Davies, M., Gribonval, R.: Restricted isometry constants where p sparse recovery can fail IEEE Trans. Inf. Theory 55(5), 2203–2214 (2009)
46. Do, B., Indyk, P., Price, E., Woodruff, D.: Lower bounds for sparse recovery. In: Proceedings of the SODA, Austin (2010)
47. Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)
48. Donoho, D.L.: For most large underdetermined systems of linear equations the minimal l 1 solution is also the sparsest solution. Commun. Pure Appl. Anal. 59(6), 797–829 (2006)
49. Donoho, D.L.: High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension. Discret. Comput. Geom. 35(4), 617–652 (2006)
50. Donoho, D.L., Elad, M.: Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization. Proc. Natl. Acad. Sci. USA 100(5), 2197–2202 (2003)
51. Donoho, D.L., Huo, X.: Uncertainty principles and ideal atomic decompositions. IEEE Trans. Inf. Theory 47(7), 2845–2862 (2001)
52. Donoho, D., Logan, B.: Signal recovery and the large sieve. SIAM J. Appl. Math. 52(2), 577–591 (1992)
53. Donoho, D.L., Tanner, J.: Neighborliness of randomly projected simplices in high dimensions. Proc. Natl. Acad. Sci. USA 102(27), 9452–9457 (2005)
54. Donoho, D.L., Tanner, J.: Counting faces of randomly-projected polytopes when the projection radically lowers dimension. J. Am. Math. Soc. 22(1), 1–53 (2009)
55. Donoho, D.L., Tsaig, Y.: Fast solution of l1-norm minimization problems when the solution may be sparse. IEEE Trans. Inf. Theory 54(11), 4789–4812 (2008)
56. Dorfman, R.: The detection of defective members of large populations. Ann. Stat. 14, 436–440 (1943)
57. Douglas, J., Rachford, H.: On the numerical solution of heat conduction problems in two or three space variables. Trans. Am. Math. Soc. 82, 421–439 (1956)
58. Duarte, M., Davenport, M., Takhar, D., Laska, J., Ting, S., Kelly, K., Baraniuk, R.: Singlepixel imaging via compressive sampling. IEEE Signal Process. Mag. 25(2), 83–91 (2008)
59. Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression. Ann. Stat. 32(2), 407–499 (2004)
60. Ehler, M., Fornasier, M., Sigl, J.: Quasi-linear compressed sensing. MultiscaleModel. Simul. 12(2), 725–754 (2014)
61. Elad, M.: Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. Springer, New York (2010)
62. 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)
63. Eldar, Y., Kutyniok, G. (eds.): Compressed Sensing – Theory and Applications. Cambridge University Press, Cambridge/New York (2012)
64. Eldar, Y., Mendelson, S.: Phase retrieval: stability and recovery guarantees. Appl. Comput. Harmon. Anal. (to appear). Doi:10.1016/j.acha.2013.08.003
65. Ender, J.: On compressive sensing applied to radar. Signal Process. 90(5), 1402–1414 (2010)
66. Fannjiang, A., Yan, P., Strohmer, T.: Compressed remote sensing of sparse objects. SIAM J. Imaging Sci. 3(3), 595–618 (2010)
67. Fazel, M.: Matrix rank minimization with applications. PhD thesis, Stanford University (2002)
68. Fienup, J.R.: Phase retrieval algorithms: a comparison. Appl. Opt. 21(15), 2758–2769 (1982)
69. Fornasier, M.: Numerical methods for sparse recovery. In: Fornasier, M. (ed.) Theoretical Foundations and Numerical Methods for Sparse Recovery. Radon Series on Computational and Applied Mathematics, vol. 9, pp. 93–200. DeGruyter, Berlin (2010). Papers based on the presentations of the summer school “Theoretical Foundations and Numerical Methods for Sparse Recovery”, Vienna, Austria, 31 Aug-4 Sept 2009
70. Fornasier, M., March, R.: Restoration of color images by vector valued BV functions and variational calculus. SIAM J. Appl. Math. 68(2), 437–460 (2007)
71. Fornasier, M., Ramlau, R., Teschke, G.: The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem. Adv. Comput. Math. 31(1–3), 157–184 (2009)
72. Fornasier, M., Langer, A., Schönlieb, C.: A convergent overlapping domain decomposition method for total variation minimization. Numer. Math. 116(4), 645–685 (2010)
73. Fornasier, M., Rauhut, H., Ward, R.: Low-rank matrix recovery via iteratively reweighted least squares minimization. SIAM J. Optim. 21(4), 1614–1640 (2011)
74. Foucart, S.: A note on guaranteed sparse recovery via l1-minimization. Appl. Comput. Harmon. Anal. 29(1), 97–103 (2010)
75. Foucart, S., Lai, M.: Sparsest solutions of underdetermined linear systems via qminimization Appl. Comput. Harmon. Anal. 26(3), 395–407 (2009)
76. Foucart, S., Rauhut, H.: A Mathematical Introduction to Compressive Sensing. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston (2013)
77. Foucart, S., Pajor, A., Rauhut, H., Ullrich, T.: The Gelfand widths of p-balls for 0 < 1. J. Complex. 26(6), 629–640 (2010)
78. Fuchs, J.J.: On sparse representations in arbitrary redundant bases. IEEE Trans. Inf. Theory 50(6), 1341–1344 (2004)
79. Garnaev, A., Gluskin, E.: On widths of the Euclidean ball. Sov. Math. Dokl. 30, 200–204 (1984)
80. Gilbert, A.C., Muthukrishnan, S., Guha, S., Indyk, P., Strauss, M.: Near-optimal sparse Fourier representations via sampling. In: Proceedings of the STOC’02, Montréal, pp. 152–161. Association for Computing Machinery (2002)
81. Gilbert, A.C., Muthukrishnan, S., Strauss, M.J.: Approximation of functions over redundant dictionaries using coherence. In: Proceedings of the Fourteenth Annual ACM-SIAM SIAM and Association for Computing Machinery (2003)
82. Gilbert, A.C., Strauss, M., Tropp, J.A., Vershynin, R.: One sketch for all: fast algorithms for compressed sensing. In: Proceedings of the 39th ACM Symposium Theory of Computing (STOC), San Diego (2007)
83. Glowinski, R., Le, T.: Augmented Lagrangian and Operator-Splitting Methods. SIAM, Philadelphia (1989)
84. Gluskin, E.: Norms of random matrices and widths of finite-dimensional sets. Math. USSR-Sb. 48, 173–182 (1984)
85. Goldfarb, D., Ma, S.: Convergence of fixed point continuation algorithms for matrix rank minimization. Found. Comput. Math. 11(2), 183–210 (2011)
86. Gorodnitsky, I., Rao, B.: Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm. IEEE Trans. Signal Process. 45(3), 600–616 (1997)
87. Gribonval, R., Nielsen, M.: Sparse representations in unions of bases. IEEE Trans. Inf. Theory 49(12), 3320–3325 (2003)
88. Gross, D.: Recovering low-rank matrices from few coefficients in any basis. IEEE Trans. Inf. Theory 57(3), 1548–1566 (2011)
89. Gross, D., Liu, Y.-K., Flammia, S.T., Becker, S., Eisert, J.: Quantum state tomography via compressed sensing. Phys. Rev. Lett. 105, 150401 (2010)
90. Gross, D., Krahmer, F., Kueng, R.: Improved recovery guarantees for phase retrieval from coded diffraction patterns (2014, preprint)
91. Gross, D., Krahmer, F., Kueng, R.: A partial derandomization of PhaseLift using spherical designs. J. Fourier Anal. Appl. (to appear)
92. He, B., Yuan, X.: Convergence analysis of primal-dual algorithms for a saddle-point problem: from contraction perspective. SIAM J. Imaging Sci. 5(1), 119–149 (2012)
93. Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge/New York (1990)
94. Hügel, M., Rauhut, H., Strohmer, T.: Remote sensing via l1-minimization. Found. Comput. Math. 14, 115–150 (2014)
95. Johnson, W.B., Lindenstrauss, J. (eds.): Handbook of the Geometry of Banach Spaces, vol. I. North-Holland, Amsterdam (2001)
96. Kashin, B.: Diameters of some finite-dimensional sets and classes of smooth functions. Math. USSR Izv. 11, 317–333 (1977)
97. Keshavan, R.H., Montanari, A., Oh, S.: Matrix completion from a few entries. IEEE Trans. Inf. Theory 56, 2980–2998 (2010)
98. Keshavan, R.H., Montanari, A., Oh, S.: Matrix completion from noisy entries. J. Mach. Learn. Res. 11, 2057–2078 (2010)
99. Krahmer, F., Rauhut, H.: Structured random measurements in signal processing. GAMM Mitteilungen. (to appear)
100. Krahmer, F., Ward, R.: New and improved Johnson-Lindenstrauss embeddings via the restricted isometry property. SIAM J. Math. Anal. 43(3), 1269–1281 (2011)
101. Krahmer, F., Mendelson, S., Rauhut, H.: Suprema of chaos processes and the restricted isometry property. Commun. Pure Appl. Math. (to appear). Doi:10.1002/cpa.21504
102. Lawson, C.: Contributions to the theory of linear least maximum approximation. PhD thesis, University of California, Los Angeles (1961)
103. Ledoux, M., Talagrand, M.: Probability in Banach Spaces. Springer, Berlin/New York (1991)
104. Lee, K., Bresler, Y.: ADMiRA: atomic decomposition for minimum rank approximation. IEEE Trans. Inf. Theory 56(9), 4402–4416 (2010)
105. Li, X., Voroninski, V.: Sparse signal recovery from quadratic measurements via convex programming (2013). arXiv:1209.4785
106. Logan, B.: Properties of high-pass signals. PhD thesis, Columbia University (1965)
107. Lorentz, G.G., von Golitschek, M., Makovoz, Y.: Constructive Approximation: Advanced Problems. Springer, Berlin (1996)
108. Mallat, S.G., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. Signal Process. 41(12), 3397–3415 (1993)
109. Marple, S.: Digital Spectral Analysis with Applications. Prentice-Hall, Englewood Cliffs (1987)
110. Mendelson, S., Pajor, A., Tomczak Jaegermann, N.: Uniform uncertainty principle for Bernoulli and subgaussian ensembles. Constr. Approx. 28(3), 277–289 (2009)
111. Millane, R.: Phase retrieval in crystallography and optics. J. Opt. Soc. Am. A 7(3), 394–411 (1990)
112. Mixon, D.: Short, fat matrices. Blog (2013)
113. Mohan, K., Fazel, M.: Reweighted nuclear norm minimization with application to system identification. In: Proceedings of the American Control Conference, Baltimore, pp. 2953–2959 (2010)
114. Natarajan, B.K.: Sparse approximate solutions to linear systems. SIAM J. Comput. 24, 227–234 (1995)
115. Nesterov, Y., Nemirovskii, A.: Interior-Point Polynomial Algorithms in Convex Programming. Volume 13 of SIAM Studies in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1994)
116. Netrapalli, P., Jain, P., Sanghavi, S.: Phase retrieval using alternating minimization (2013). arXiv:1306.0160
117. Novak, E.: Optimal recovery and n-widths for convex classes of functions. J. Approx. Theory 80(3), 390–408 (1995)
118. Ohlsson, H., Yang, A.Y., Dong, R., Sastry, S.S.: Nonlinear basis pursuit. In: 47th Asilomar Conference on Signals, Systems and Computers, Pacific Grove (2013)
119. Osborne, M., Presnell, B., Turlach, B.: A new approach to variable selection in least squares problems. IMA J. Numer. Anal. 20(3), 389–403 (2000)
120. Osborne, M., Presnell, B., Turlach, B.: On the LASSO and its dual. J. Comput. Graph. Stat. 9(2), 319–337 (2000)
121. Oymak, S., Mohan, K., Fazel, M., Hassibi, B.: A simplified approach to recovery conditions for low-rank matrices. In: Proceedings of the IEEE International Symposium on Information Theory (ISIT), St. Petersburg (2011)
122. Pfander, G.E., Rauhut, H.: Sparsity in time-frequency representations. J. Fourier Anal. Appl. 16(2), 233–260 (2010)
123. Pfander, G.E., Rauhut, H., Tanner, J.: Identification of matrices having a sparse representation. IEEE Trans. Signal Process. 56(11), 5376–5388 (2008)
124. Pfander, G.E., Rauhut, H., Tropp, J.A.: The restricted isometry property for time-frequency structured random matrices. Probab. Theory Relat. Fields 156, 707–737 (2013)
125. Pock, T., Chambolle, A.: Diagonal preconditioning for first order primal-dual algorithms in convex optimization. In: IEEE International Conference Computer Vision (ICCV), Barcelona, pp. 1762–1769 (2011)
126. Pock, T., Cremers, D., Bischof, H., Chambolle, A.: An algorithm for minimizing the Mumford-Shah functional. In: ICCV Proceedings, Kyoto. Springer (2009)
127. Prony, R.: Essai expérimental et analytique sur les lois de la Dilatabilité des uides élastique et sur celles de la Force expansive de la vapeur de lÃoeau et de la vapeur de l’alkool, à différentes températures. J. École Polytechnique 1, 24–76 (1795)
128. Rauhut, H.: Random sampling of sparse trigonometric polynomials. Appl. Comput. Harmon. Anal. 22(1), 16–42 (2007)
129. Rauhut, H.: Stability results for random sampling of sparse trigonometric polynomials. IEEE Trans. Inf Theory 54(12), 5661–5670 (2008)
130. Rauhut, H.: Circulant and Toeplitz matrices in compressed sensing. In: Proceedings of the SPARS’09 (2009)
131. Rauhut, H.: Compressive sensing and structured random matrices. In: Fornasier, M. (ed.) Theoretical Foundations and Numerical Methods for Sparse Recovery. Radon Series on Computational and Applied Mathematics, vol. 9, pp. 1–92. DeGruyter, Berlin (2010). Papers based on the presentations of the summer school “Theoretical Foundations and Numerical Methods for Sparse Recovery”, Vienna, Austria, 31 Aug-4 Sept 2009
132. Rauhut, H., Ward, R.: Interpolation via weighted l1 minimization (2013). ArXiv:1308.0759
133. Rauhut, H., Romberg, J.K., Tropp, J.A.: Restricted isometries for partial random circulant matrices. Appl. Comput. Harmon. Anal. 32(2), 242–254 (2012)
134. Recht, B.: A simpler approach to matrix completion. J. Mach. Learn. Res. 12, 3413–3430 (2012)
135. Recht, B., Fazel, M., Parrilo, P.: Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev. 52(3), 471–501 (2010)
136. Romberg, J.: Imaging via compressive sampling. IEEE Signal Process. Mag. 25(2), 14–20 (2008)
137. Romberg, J.K.: Compressive sensing by random convolution. SIAM J. Imaging Sci. 2(4), 1098–1128 (2009)
138. Rudelson, M., Vershynin, R.: On sparse reconstruction from Fourier and Gaussian measurements. Commun. Pure Appl. Math. 61, 1025–1045 (2008)
139. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(1–4), 259–268 (1992)
140. Santosa, F., Symes, W.: Linear inversion of band-limited reflection seismograms. SIAM J. Sci. Stat. Comput. 7(4), 1307–1330 (1986)
141. Schnass, K., Vandergheynst, P.: Dictionary preconditioning for greedy algorithms. IEEE Trans. Signal Process. 56(5), 1994–2002 (2008)
142. Starck, J.-L., Murtagh, F., Fadili, J.: Sparse Image and Signal Processing Wavelets, Curvelets, Cambridge University Press, Cambridge (2010)
143. Strohmer, T., Heath, R.W., Jr.: Grassmannian frames with applications to coding and communication. Appl. Comput. Harmon. Anal. 14(3), 257–275 (2003)
144. Strohmer, T., Hermann, M.: Compressed sensing radar. In: IEEE Proceedings of the International Conference on Acoustic, Speech, and Signal Processing, Las Vegas, pp. 1509–1512 (2008)
145. Tadmor, E.: Numerical methods for nonlinear partial differential equations. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science. Springer, New York/London (2009)
146. Talagrand, M.: Selecting a proportion of characters. Isr. J. Math. 108, 173–191 (1998)
147. Tauböck, G., Hlawatsch, F., Eiwen, D., Rauhut, H.: Compressive estimation of doubly selective channels in multicarrier systems: leakage effects and sparsity-enhancing processing. IEEE J. Sel. Top. Signal Process. 4(2), 255–271 (2010)
148. Taylor, H., Banks, S., McCoy, J.: Deconvolution with the l1-norm. Geophys. J. Int. 44(1), 39–52 (1979)
149. Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B 58(1), 267–288 (1996)
150. Traub, J., Wasilkowski, G., Wo’zniakowski, H.: Information-Based Complexity. Computer Science and Scientific Computing. Academic, Boston (1988)
151. Tropp, J.A.: Greed is good: algorithmic results for sparse approximation. IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004)
152. Tropp, J.A.: Just relax: convex programming methods for identifying sparse signals in noise. IEEE Trans. Inf. Theory 51(3), 1030–1051 (2006)
153. Tropp, J., Needell, D.: CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009)
154. Tropp, J.A., Laska, J.N., Duarte, M.F., Romberg, J.K., Baraniuk, R.G.: Beyond nyquist: efficient sampling of sparse bandlimited signals. IEEE Trans. Inf. Theory 56(1), 520–544 (2010)
155. Unser, M.: Sampling—50 years after Shannon. Proc. IEEE 88(4), 569–587 (2000)
156. van den Berg, E., Friedlander, M.: Probing the Pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 31(2), 890–912 (2008)
157. Vybiral, J.: Widths of embeddings in function spaces. J. Complex. 24(4), 545–570 (2008)
158. Wagner, G., Schmieder, P., Stern, A., Hoch, J.: Application of non-linear sampling schemes to cosy-type spectra. J. Biomol. NMR 3(5), 569 (1993)
159. Willett, R., Marcia, R., Nichols, J.: Compressed sensing for practical optical imaging systems: a tutorial. Opt. Eng. 50(7), 072601–072601–13 (2011)
160. Willett, R., Duarte, M., Davenport, M., Baraniuk, R.: Sparsity and structure in hyperspectral imaging: sensing, reconstruction, and target detection. IEEE Signal Proc. Mag. 31(1), 116–126 (2014)