Bibliographic Notes

Bibliographic Notes¶

Following is a partial list of books and articles which have been referenced heavily in this work. This list is by no means exhaustive.

  • General introduction to optimization can be found in [29].

  • Main references for convex analysis are [7, 31].

  • [10] is a standard textbook for convex optimization theory, applications and algorithms.

  • [27] is a good reference for linear programming.

  • [9] covers alternating direction method of multipliers (ADMM) algorithms.

  • [30] provides good coverage on proximal algorithms.

Bibliography¶

1

Michal Aharon, Michael Elad, and Alfred M Bruckstein. K-svd and its non-negative variant for dictionary design. In Optics & Photonics 2005, 591411–591411. International Society for Optics and Photonics, 2005.

2

Charalambos D Aliprantis and Owen Burkinshaw. Principles of real analysis. Gulf Professional Publishing, 1998.

3

M. Artin. Algebra. Pearson Modern Classics for Advanced Mathematics Series. Pearson, 2017. ISBN 9780134689609. URL: https://books.google.co.in/books?id=ZfIXMQAACAAJ.

4

Afonso S Bandeira, Edgar Dobriban, Dustin G Mixon, and William F Sawin. Certifying the restricted isometry property is hard. IEEE transactions on information theory, 59(6):3448–3450, 2013.

5

Amir Beck. Introduction to nonlinear optimization: Theory, algorithms, and applications with MATLAB. SIAM, 2014.

6

Amir Beck. First-order methods in optimization. SIAM, 2017.

7

Dimitri Bertsekas, Angelia Nedic, and Asuman Ozdaglar. Convex analysis and optimization. Volume 1. Athena Scientific, 2003.

8

Stephen Boyd and Almir Mutapcic. Subgradient methods. 2008.

9

Stephen Boyd, Neal Parikh, and Eric Chu. Distributed optimization and statistical learning via the alternating direction method of multipliers. Now Publishers Inc, 2011.

10

Stephen P Boyd and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004.

11

Emmanuel J Candes and Justin Romberg. Practical signal recovery from random projections. Wavelet Applications in Signal and Image Processing XI Proc. SPIE Conf. 5914., 2004.

12

Emmanuel J Candes and Terence Tao. Decoding by linear programming. Information Theory, IEEE Transactions on, 51(12):4203–4215, 2005.

13

Emmanuel J Candes and Terence Tao. Near-optimal signal recovery from random projections: universal encoding strategies? Information Theory, IEEE Transactions on, 52(12):5406–5425, 2006.

14

Emmanuel J Candès. The restricted isometry property and its implications for compressed sensing. Comptes Rendus Mathematique, 346(9):589–592, 2008.

15

Jie Chen and Xiaoming Huo. Theoretical results on sparse representations of multiple-measurement vectors. Signal Processing, IEEE Transactions on, 54(12):4634–4643, 2006.

16

Scott Shaobing Chen, David L Donoho, and Michael A Saunders. Atomic decomposition by basis pursuit. SIAM journal on scientific computing, 20(1):33–61, 1998.

17

Mark A Davenport and Michael B Wakin. Analysis of orthogonal matching pursuit using the restricted isometry property. Information Theory, IEEE Transactions on, 56(9):4395–4401, 2010.

18

David L Donoho and Michael Elad. Optimally sparse representation in general (nonorthogonal) dictionaries via $l_1$ minimization. Proceedings of the National Academy of Sciences, 100(5):2197–2202, 2003.

19

Michael Elad. Sparse and redundant representations. Springer, 2010.

20

Michael Elad and Alfred M Bruckstein. A generalized uncertainty principle and sparse representation in pairs of bases. Information Theory, IEEE Transactions on, 48(9):2558–2567, 2002.

21

Kjersti Engan, Sven Ole Aase, and J Hakon Husoy. Method of optimal directions for frame design. In Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on, volume 5, 2443–2446. IEEE, 1999.

22

David G Feingold, Richard S Varga, and others. Block diagonally dominant matrices and generalizations of the gerschgorin circle theorem. Pacific J. Math, 12(4):1241–1250, 1962.

23

D. Gopal, A. Deshmukh, A.S. Ranadive, and S. Yadav. An Introduction to Metric Spaces. CRC Press, 2020. ISBN 9781000087994. URL: https://books.google.co.in/books?id=13jtDwAAQBAJ.

24

Rémi Gribonval, Holger Rauhut, Karin Schnass, and Pierre Vandergheynst. Atoms of all channels, unite! average case analysis of multi-channel sparse recovery using greedy algorithms. Journal of Fourier analysis and Applications, 14(5-6):655–687, 2008.

25

Jean-Baptiste Hiriart-Urruty and Claude Lemaréchal. Convex analysis and minimization algorithms I: Fundamentals. Volume 305. Springer science & business media, 2013.

26

Kenneth Hoffman and Ray Kunze. Linear algebra, prentice-hall. Inc., Englewood Cliffs, New Jersey, pages 122–125, 1971.

27

David G Luenberger, Yinyu Ye, and others. Linear and nonlinear programming. Volume 2. Springer, 1984.

28

Deanna Needell and Joel A Tropp. Cosamp: iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis, 26(3):301–321, 2009.

29

Jorge Nocedal and Stephen Wright. Numerical optimization. Springer Science & Business Media, 2006.

30

Neal Parikh and Stephen Boyd. Proximal algorithms. Foundations and Trends in optimization, 1(3):127–239, 2014.

31

Ralph Tyrell Rockafellar. Convex analysis. Princeton university press, 2015.

32

Ron Rubinstein, Alfred M Bruckstein, and Michael Elad. Dictionaries for sparse representation modeling. Proceedings of the IEEE, 98(6):1045–1057, 2010.

33

Ivana Tosic and Pascal Frossard. Dictionary learning. Signal Processing Magazine, IEEE, 28(2):27–38, 2011.

34

W.F. Trench. Introduction to Real Analysis. Open Textbook Library. Prentice Hall/Pearson Education, 2003. ISBN 9780130457868. URL: https://books.google.co.in/books?id=NkFkQgAACAAJ.

35

Joel A Tropp. Greed is good: algorithmic results for sparse approximation. Information Theory, IEEE Transactions on, 50(10):2231–2242, 2004.

36

Joel A Tropp. Just relax: convex programming methods for subset selection and sparse approximation. ICES report, 2004.

37

Joel A Tropp. Just relax: convex programming methods for identifying sparse signals in noise. Information Theory, IEEE Transactions on, 52(3):1030–1051, 2006.

38

Joel A Tropp and Anna C Gilbert. Signal recovery from random measurements via orthogonal matching pursuit. Information Theory, IEEE Transactions on, 53(12):4655–4666, 2007.

39

Wikipedia contributors. Ordered pair — Wikipedia, the free encyclopedia. URL: https://en.wikipedia.org/wiki/Ordered_pair.

40

Wikipedia contributors. Relation (mathematics) — Wikipedia, the free encyclopedia. URL: https://en.wikipedia.org/wiki/Relation_(mathematics).

41

Wikipedia contributors. Tuple — Wikipedia, the free encyclopedia. URL: https://en.wikipedia.org/wiki/Tuple.