sparse image representation via combined transforms - Convex ...
sparse image representation via combined transforms - Convex ... sparse image representation via combined transforms - Convex ...
180 BIBLIOGRAPHY [113] Yurii Nesterov and Arkadii Nemirovskii. Interior-point Polynomial Algorithms in Convex Programming, volume13ofSIAM Studies in Applied Mathematics. SIAM, Philadelphia, PA, 1994. [114] Henry J. Nussbaumer. Fast Fourier Transform and Convolution Algorithms. Springer- Verlag, 1982. [115] Kramer H. P. and Mathews M. V. A linear coding from transmitting a set of correlated signals. IRE Trans. Inform. Theory, 2:41–46, September 1956. [116] C. C. Paige and M. A. Saunders. Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal., 12(4):617–29, 1975. [117] Christopher C. Paige and Michael A. Saunders. LSQR: an algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Software, 8(1):43–71, 1982. [118] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C: The Art of Scientific Computing. Cambridge, second edition, 1995. [119] A. G. Ramm and A. I. Katsevich. Radon Transform and Local Tomography. CRC Press, 1996. [120] B. D. Rao. Signal processing with the sparseness constraint. In Proceedings of ICASSP, pages III–1861–4, 1998. [121] K. R. Rao and P. Yip. Discrete Cosine Transform: Algorithms, Advantages, Applications. Academic Press, 1990. [122] A. H. Reeves. French Patent No. 852,183, October 3 1938. [123] R.T. Rockafellar. Convex Analysis. Princeton University Press, 1970. [124] S. Sardy, A. Bruce, and P. Tseng. Block coordinate relaxation methods for nonparametric signal denoising with wavelet dictionaries. Web page, October 1998. http://www.math.washington.edu/˜tseng/papers.html. [125] S. Sardy, A. G. Bruce, and P. Tseng. Block coordinate relaxation methods for nonparametric signal de-noising. Received from E. Candès, October 1998. [126] K. Sayood. Introduction to Data Compression. Morgan Kaufmann Publishers, 1996.
BIBLIOGRAPHY 181 [127] C. E. Shannon. A mathematical theory of communication. Bell System Technical Journal, 27:379–423, 623–56, October 1948. [128] J. E. Spingarn. Partial inverse of a monotone operator. Applied Mathematics and Optimization, 10:247–65, 1983. [129] Frank Spitzer. Markov random fields and Gibbs ensembles. American Mathematical Monthly, 78:142–54, February 1971. [130] A.S. Stern, D.L Donoho, and Hoch J.C. Iterative thresholding and minimum l 1 -norm reconstruction. based on personal communication, 1996 or later. [131] Mann Steve and Simon Haykin. Adaptive “chirplet” transform: an adaptive generalization of the wavelet transform. Optical Engineering, 31(6):1243–56, June 1992. [132] Gilbert Strang. Wavelets and Filter Banks. Wellesley-Cambridge Press, 1996. [133] Robert Tibshirani. Regression shrinkage and selection via the LASSO. J. the Royal Statistical Society, Series B, 58:267–288, 1996. [134] Richard Tolimieri, Myoung An, and Chao Lu. Algorithms for Discrete Fourier Transform and Convolution. Springer, 2nd edition, 1997. [135] Paul Tseng. Dual coordinate ascent methods for non-strictly convex minimization. Mathematical Programming, 59:231–47, 1993. [136] Charles Van Loan. Computational Frameworks for the Fast Fourier Transform. SIAM, 1992. [137] R. J. Vanderbei. Linear Programming. Kluwer Academic Publishers, 1996. [138] S. Vembu, S. Verdú, and Y. Steinberg. The source-channel separation theorem revisited. IEEE Trans. on Inform. Theory, 41(1):44–54, Jan. 1995. [139] Z. Wang and B.R. Hunt. Comparative performance of two different versions of the discrete cosine transform. IEEE Transactions on Acoustics, Speech and Signal Processing, ASSP-32(2):450–3, 1984. [140] Zhongde Wang. Reconsideration of “a fast computational algorithm for the discrete cosine transform”. IEEE Transactions on Communications, Com-31(1):121–3, Jan. 1983.
- Page 157 and 158: Chapter 7 Future Work In the future
- Page 159 and 160: 7.2. MODIFYING EDGELET DICTIONARY 1
- Page 161 and 162: 7.3. ACCELERATING THE ITERATIVE ALG
- Page 163 and 164: Appendix A Direct Edgelet Transform
- Page 165 and 166: A.2. EXAMPLES 137 edgelet transform
- Page 167 and 168: A.3. DETAILS 139 (a) Stick image (b
- Page 169 and 170: A.3. DETAILS 141 (a) Lenna image (b
- Page 171 and 172: A.3. DETAILS 143 Ordering of Dyadic
- Page 173 and 174: A.3. DETAILS 145 (1,K +1), (1,K +2)
- Page 175 and 176: A.3. DETAILS 147 x 1 , y 1 x 2 , y
- Page 177 and 178: Appendix B Fast Edgelet-like Transf
- Page 179 and 180: B.1. TRANSFORMS FOR 2-D CONTINUOUS
- Page 181 and 182: B.2. DISCRETE ALGORITHM 153 B.2.1 S
- Page 183 and 184: B.2. DISCRETE ALGORITHM 155 extensi
- Page 185 and 186: B.2. DISCRETE ALGORITHM 157 For the
- Page 187 and 188: B.3. ADJOINT OF THE FAST TRANSFORM
- Page 189 and 190: B.4. ANALYSIS 161 above matrix, whi
- Page 191 and 192: B.5. EXAMPLES 163 B.5 Examples B.5.
- Page 193 and 194: B.5. EXAMPLES 165 And so on. Note f
- Page 195 and 196: B.6. MISCELLANEOUS 167 It takes abo
- Page 197 and 198: B.6. MISCELLANEOUS 169 The function
- Page 199 and 200: Bibliography [1] Sensor Data Manage
- Page 201 and 202: BIBLIOGRAPHY 173 [24] C. Victor Che
- Page 203 and 204: BIBLIOGRAPHY 175 [50] David L. Dono
- Page 205 and 206: BIBLIOGRAPHY 177 [75] Vivek K. Goya
- Page 207: BIBLIOGRAPHY 179 [100] Stéphane Ma
BIBLIOGRAPHY 181<br />
[127] C. E. Shannon. A mathematical theory of communication. Bell System Technical<br />
Journal, 27:379–423, 623–56, October 1948.<br />
[128] J. E. Spingarn. Partial inverse of a monotone operator. Applied Mathematics and<br />
Optimization, 10:247–65, 1983.<br />
[129] Frank Spitzer. Markov random fields and Gibbs ensembles. American Mathematical<br />
Monthly, 78:142–54, February 1971.<br />
[130] A.S. Stern, D.L Donoho, and Hoch J.C. Iterative thresholding and minimum l 1 -norm<br />
reconstruction. based on personal communication, 1996 or later.<br />
[131] Mann Steve and Simon Haykin. Adaptive “chirplet” transform: an adaptive generalization<br />
of the wavelet transform. Optical Engineering, 31(6):1243–56, June 1992.<br />
[132] Gilbert Strang. Wavelets and Filter Banks. Wellesley-Cambridge Press, 1996.<br />
[133] Robert Tibshirani. Regression shrinkage and selection <strong>via</strong> the LASSO. J. the Royal<br />
Statistical Society, Series B, 58:267–288, 1996.<br />
[134] Richard Tolimieri, Myoung An, and Chao Lu. Algorithms for Discrete Fourier Transform<br />
and Convolution. Springer, 2nd edition, 1997.<br />
[135] Paul Tseng. Dual coordinate ascent methods for non-strictly convex minimization.<br />
Mathematical Programming, 59:231–47, 1993.<br />
[136] Charles Van Loan. Computational Frameworks for the Fast Fourier Transform. SIAM,<br />
1992.<br />
[137] R. J. Vanderbei. Linear Programming. Kluwer Academic Publishers, 1996.<br />
[138] S. Vembu, S. Verdú, and Y. Steinberg. The source-channel separation theorem revisited.<br />
IEEE Trans. on Inform. Theory, 41(1):44–54, Jan. 1995.<br />
[139] Z. Wang and B.R. Hunt. Comparative performance of two different versions of the<br />
discrete cosine transform. IEEE Transactions on Acoustics, Speech and Signal Processing,<br />
ASSP-32(2):450–3, 1984.<br />
[140] Zhongde Wang. Reconsideration of “a fast computational algorithm for the discrete<br />
cosine transform”. IEEE Transactions on Communications, Com-31(1):121–3, Jan.<br />
1983.
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