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Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations
Template matching via $l_1$ minimization and its application to hyperspectral data
1. | Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095, United States |
2. | Department of Mathematics, University of California, Los Angeles, CA 90095 |
References:
[1] |
, Surface Optics Corporation,, , ().
|
[2] |
, Urban hyperspectral data set,, , ().
|
[3] |
C. Bachmann, T. Donato, G. Lamela, W. Rhea, M. Bettenhausen, R. Fusina, K. Du Bois, J. Porter and B. Truitt, Automatic classification of land cover on Smith Island, VA, using HyMAP imagery, IEEE Transactions on Geoscience and Remote Sensing, 40 (2002), 2313-2330.
doi: 10.1109/TGRS.2002.804834. |
[4] |
C. Bachmann, Improving the performance of classifiers in high-dimensional remote sensing applications: An adaptive resampling strategy for error-prone exemplars (ARESEPE), IEEE Transactions on Geoscience and Remote Sensing, 41 (2003), 2101-2112.
doi: 10.1109/TGRS.2003.817207. |
[5] |
C. Bachmann, T. Ainsworth and R. Fusina, Exploiting manifold geometry in hyperspectral imagery, IEEE Transactions on Geoscience and Remote Sensing, 43 (2005), 441-454.
doi: 10.1109/TGRS.2004.842292. |
[6] |
C. Bachmann, T. Ainsworth and R. Fusina, Improved manifold coordinate representations of large scale hyperspectral imagery, IEEE Transactions on Geoscience and Remote Sensing, 44 (2006), 2786-2803.
doi: 10.1109/TGRS.2006.881801. |
[7] |
J. Bioucas-Dias and M. Figueiredo, Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing, 2nd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing - WHISPERS, Reykjavik, Iceland, (2006). |
[8] |
L. Bregman, The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming, USSR Comput Math and Math. Phys., 7 (1967), 200-217.
doi: 10.1016/0041-5553(67)90040-7. |
[9] |
J. Cai, S. Osher and Z. Shen, Split Bregman methods and frame based image restoration, Multiscale Model. Simul., 8 (2009), 337-369.
doi: 10.1137/090753504. |
[10] |
E. Candes, J. Romberg and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory, 52 (2006), 489-509.
doi: 10.1109/TIT.2005.862083. |
[11] |
E. Conte, M. Lops and G. Ricci, Asymptotically optimum radar detection in compound-Gaussian clutter, IEEE Transactions on Aerospace Electron. Syst., 31 (1995), 617-625.
doi: 10.1109/7.381910. |
[12] |
G. Dimitris, A. Gary and K. Nirmal, Comparative analysis of hyperspectral adaptive matched filter detectors, SPIE., 4049 (2000), 2-17. |
[13] |
D. Donoho, Compressed sensing, IEEE Trans. Inform. Theory, 52 (2006), 1289-1306.
doi: 10.1109/TIT.2006.871582. |
[14] |
T. Goldstein and S. Osher, The split Bregman algorithm for $L_1$ regularized problems, SIAM Journal on Imaging Sciences, 2 (2009), 323-343.
doi: 10.1137/080725891. |
[15] |
T. Goldstein, X. Bresson and S. Osher, "Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction," UCLA CAM Report, 9 (2009). |
[16] |
Z. Guo, T. Wittman and S. Osher, $L_1$ unmixing and its application to hyperspectral image enhancement, in Proc. SPIE Conference on Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery, XV (2009). |
[17] |
J. Harsanyi and C. Chang, Hyperspectral image classification and dimensionality reduction: An orthogonal subspace projection approach, IEEE Transactions on Geoscience and Remote Sensing, 32 (1994), 779-785.
doi: 10.1109/36.298007. |
[18] |
S. Kay, "Fundamentals of Statistical Signal Processing," Englewood Cliffs, NJ: Prentice-Hall, 1993. |
[19] |
S. Kraut and L. Scharf, The CFAR adaptive subspace detector is a scale-invariant GLRT, IEEE Transactions on Signal Processing, 47 (1999), 2538-2541.
doi: 10.1109/78.782198. |
[20] |
S. Kraut, L. Scharf and L. McWhorter, Adaptive subspace detectors, IEEE Transactions on Signal Processing, 49 (2001), 1-16.
doi: 10.1109/78.890324. |
[21] |
F. Kruse, A. Lefkoff, J. Boardman, K. Heidebrecht, A. Shapiro, P. Barloon and A. Goetz, The spectral image processing system (SIPS)-interactive visualization and analysis of imaging spectrometer data, Rem. Sens. Environ, 44 (1993), 145-164.
doi: 10.1016/0034-4257(93)90013-N. |
[22] |
H. Kwon and N. Nasrabadi, Kernel RX-algorithm: A nonlinear anomaly detector for hyperspectral imagery, IEEE Transactions on Geoscience and Remote Sensing, 43 (2005), 388-397.
doi: 10.1109/TGRS.2004.841487. |
[23] |
D. Manolakis and G. Shaw, Detection algorithms for hyperspectral imaging applications, IEEE Signal Processing Magazine, 19 (2002), 29-43.
doi: 10.1109/79.974724. |
[24] |
D. Manolakis, Detection algorithms for hyperspectral imaging applications: A signal processing perspective, IEEE Workshop on Advances in Techniques for Analysis of Remotely Sensed Data, (2003), 378-384.
doi: 10.1109/WARSD.2003.1295218. |
[25] |
S. Osher, M. Burger, D. Goldfarb, J. Xu and W. Yin, An iterative regularization method for total variation based image restoration, Multiscale Model. Simul., 4 (2005), 460-489.
doi: 10.1137/040605412. |
[26] |
S. Osher, Y. Mao, B. Dong and W. Yin, Fast linearized Bregman iteration for compressive sensing and sparse denoising, Commun. Math. Sci., 8 (2010), 93-111. |
[27] |
I. Reed and X. Yu, Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution, IEEE Transactions on Acoustics, Speech and Signal Processing, 38 (1990), 1760-1770.
doi: 10.1109/29.60107. |
[28] |
F. Robey, D. Fuhermann, E. Kelly and R. Nitzberg, A CFAR adaptive matched filter detector, IEEE Transactions on Aerospace and Electronic Systems, 28 (1992), 208-216.
doi: 10.1109/7.135446. |
[29] |
L. Scharf and B. Friedlander, Matched subspace detectors, IEEE Transactions on Signal Processing, 42 (1994), 2146-2157.
doi: 10.1109/78.301849. |
[30] |
D. Snyder, J. Kerekes, I. Fairweather, R. Crabtree, J. Shive and S. Hager, Development of a web-based application to evaluate target finding algorithms, Proceedings of the 2008 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), 2 (2008), 915-918. |
[31] |
D. Stein, S. Beaven, L. Hoff, E. Winter, A. Schaum and A. Stoker, Anomaly detection from hyperspectral imagery, IEEE Signal Processing Magazine, 19 (2002), 58-69.
doi: 10.1109/79.974730. |
[32] |
A. Szlam, Z. Guo and S. Osher, A split Bregman method for non-negative sparsity penalized least squares with applications to hyperspectral demixing, UCLA CAM report, 10-06 (2010). |
[33] |
W. Yin, S. Osher, D. Goldfarb and J. Darbon, Bregman iterative algorithms for $l_1$-minimization with applications to compressed sensing, SIAM J. Imaging Sci., 1 (2008), 143-168.
doi: 10.1137/070703983. |
[34] |
X. Yu, I. Reed and A. Stocker, Comparative performance analysis of adaptive multispectral detectors, IEEE Transactions on Signal Processing, 41 (1993), 2639-2656.
doi: 10.1109/78.229895. |
[35] |
X. Zhang, M. Burger, X. Bresson and S. Osher, Bregmanized nonlocal regularization for deconvolution and sparse reconstruction, preprint, (1993). |
show all references
References:
[1] |
, Surface Optics Corporation,, , ().
|
[2] |
, Urban hyperspectral data set,, , ().
|
[3] |
C. Bachmann, T. Donato, G. Lamela, W. Rhea, M. Bettenhausen, R. Fusina, K. Du Bois, J. Porter and B. Truitt, Automatic classification of land cover on Smith Island, VA, using HyMAP imagery, IEEE Transactions on Geoscience and Remote Sensing, 40 (2002), 2313-2330.
doi: 10.1109/TGRS.2002.804834. |
[4] |
C. Bachmann, Improving the performance of classifiers in high-dimensional remote sensing applications: An adaptive resampling strategy for error-prone exemplars (ARESEPE), IEEE Transactions on Geoscience and Remote Sensing, 41 (2003), 2101-2112.
doi: 10.1109/TGRS.2003.817207. |
[5] |
C. Bachmann, T. Ainsworth and R. Fusina, Exploiting manifold geometry in hyperspectral imagery, IEEE Transactions on Geoscience and Remote Sensing, 43 (2005), 441-454.
doi: 10.1109/TGRS.2004.842292. |
[6] |
C. Bachmann, T. Ainsworth and R. Fusina, Improved manifold coordinate representations of large scale hyperspectral imagery, IEEE Transactions on Geoscience and Remote Sensing, 44 (2006), 2786-2803.
doi: 10.1109/TGRS.2006.881801. |
[7] |
J. Bioucas-Dias and M. Figueiredo, Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing, 2nd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing - WHISPERS, Reykjavik, Iceland, (2006). |
[8] |
L. Bregman, The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming, USSR Comput Math and Math. Phys., 7 (1967), 200-217.
doi: 10.1016/0041-5553(67)90040-7. |
[9] |
J. Cai, S. Osher and Z. Shen, Split Bregman methods and frame based image restoration, Multiscale Model. Simul., 8 (2009), 337-369.
doi: 10.1137/090753504. |
[10] |
E. Candes, J. Romberg and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory, 52 (2006), 489-509.
doi: 10.1109/TIT.2005.862083. |
[11] |
E. Conte, M. Lops and G. Ricci, Asymptotically optimum radar detection in compound-Gaussian clutter, IEEE Transactions on Aerospace Electron. Syst., 31 (1995), 617-625.
doi: 10.1109/7.381910. |
[12] |
G. Dimitris, A. Gary and K. Nirmal, Comparative analysis of hyperspectral adaptive matched filter detectors, SPIE., 4049 (2000), 2-17. |
[13] |
D. Donoho, Compressed sensing, IEEE Trans. Inform. Theory, 52 (2006), 1289-1306.
doi: 10.1109/TIT.2006.871582. |
[14] |
T. Goldstein and S. Osher, The split Bregman algorithm for $L_1$ regularized problems, SIAM Journal on Imaging Sciences, 2 (2009), 323-343.
doi: 10.1137/080725891. |
[15] |
T. Goldstein, X. Bresson and S. Osher, "Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction," UCLA CAM Report, 9 (2009). |
[16] |
Z. Guo, T. Wittman and S. Osher, $L_1$ unmixing and its application to hyperspectral image enhancement, in Proc. SPIE Conference on Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery, XV (2009). |
[17] |
J. Harsanyi and C. Chang, Hyperspectral image classification and dimensionality reduction: An orthogonal subspace projection approach, IEEE Transactions on Geoscience and Remote Sensing, 32 (1994), 779-785.
doi: 10.1109/36.298007. |
[18] |
S. Kay, "Fundamentals of Statistical Signal Processing," Englewood Cliffs, NJ: Prentice-Hall, 1993. |
[19] |
S. Kraut and L. Scharf, The CFAR adaptive subspace detector is a scale-invariant GLRT, IEEE Transactions on Signal Processing, 47 (1999), 2538-2541.
doi: 10.1109/78.782198. |
[20] |
S. Kraut, L. Scharf and L. McWhorter, Adaptive subspace detectors, IEEE Transactions on Signal Processing, 49 (2001), 1-16.
doi: 10.1109/78.890324. |
[21] |
F. Kruse, A. Lefkoff, J. Boardman, K. Heidebrecht, A. Shapiro, P. Barloon and A. Goetz, The spectral image processing system (SIPS)-interactive visualization and analysis of imaging spectrometer data, Rem. Sens. Environ, 44 (1993), 145-164.
doi: 10.1016/0034-4257(93)90013-N. |
[22] |
H. Kwon and N. Nasrabadi, Kernel RX-algorithm: A nonlinear anomaly detector for hyperspectral imagery, IEEE Transactions on Geoscience and Remote Sensing, 43 (2005), 388-397.
doi: 10.1109/TGRS.2004.841487. |
[23] |
D. Manolakis and G. Shaw, Detection algorithms for hyperspectral imaging applications, IEEE Signal Processing Magazine, 19 (2002), 29-43.
doi: 10.1109/79.974724. |
[24] |
D. Manolakis, Detection algorithms for hyperspectral imaging applications: A signal processing perspective, IEEE Workshop on Advances in Techniques for Analysis of Remotely Sensed Data, (2003), 378-384.
doi: 10.1109/WARSD.2003.1295218. |
[25] |
S. Osher, M. Burger, D. Goldfarb, J. Xu and W. Yin, An iterative regularization method for total variation based image restoration, Multiscale Model. Simul., 4 (2005), 460-489.
doi: 10.1137/040605412. |
[26] |
S. Osher, Y. Mao, B. Dong and W. Yin, Fast linearized Bregman iteration for compressive sensing and sparse denoising, Commun. Math. Sci., 8 (2010), 93-111. |
[27] |
I. Reed and X. Yu, Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution, IEEE Transactions on Acoustics, Speech and Signal Processing, 38 (1990), 1760-1770.
doi: 10.1109/29.60107. |
[28] |
F. Robey, D. Fuhermann, E. Kelly and R. Nitzberg, A CFAR adaptive matched filter detector, IEEE Transactions on Aerospace and Electronic Systems, 28 (1992), 208-216.
doi: 10.1109/7.135446. |
[29] |
L. Scharf and B. Friedlander, Matched subspace detectors, IEEE Transactions on Signal Processing, 42 (1994), 2146-2157.
doi: 10.1109/78.301849. |
[30] |
D. Snyder, J. Kerekes, I. Fairweather, R. Crabtree, J. Shive and S. Hager, Development of a web-based application to evaluate target finding algorithms, Proceedings of the 2008 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), 2 (2008), 915-918. |
[31] |
D. Stein, S. Beaven, L. Hoff, E. Winter, A. Schaum and A. Stoker, Anomaly detection from hyperspectral imagery, IEEE Signal Processing Magazine, 19 (2002), 58-69.
doi: 10.1109/79.974730. |
[32] |
A. Szlam, Z. Guo and S. Osher, A split Bregman method for non-negative sparsity penalized least squares with applications to hyperspectral demixing, UCLA CAM report, 10-06 (2010). |
[33] |
W. Yin, S. Osher, D. Goldfarb and J. Darbon, Bregman iterative algorithms for $l_1$-minimization with applications to compressed sensing, SIAM J. Imaging Sci., 1 (2008), 143-168.
doi: 10.1137/070703983. |
[34] |
X. Yu, I. Reed and A. Stocker, Comparative performance analysis of adaptive multispectral detectors, IEEE Transactions on Signal Processing, 41 (1993), 2639-2656.
doi: 10.1109/78.229895. |
[35] |
X. Zhang, M. Burger, X. Bresson and S. Osher, Bregmanized nonlocal regularization for deconvolution and sparse reconstruction, preprint, (1993). |
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