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A direct sampling method for inverse scattering using far-field data
Wavelet frame based color image demosaicing
1. | Department of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China |
2. | Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, 119076, Singapore, Singapore |
3. | Department of Mathematics, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China |
References:
[1] |
B. E. Bayer, Color imaging array, U.S. Patent, 3971065, 1976. |
[2] |
A. Buades, B. Coll, J.-M. Morel and C. Sbert, Self-similarity driven color demosaicking, IEEE Transactions on Image Processing, 18 (2009), 1192-1202.
doi: 10.1109/TIP.2009.2017171. |
[3] |
J. F. Cai, R. Chan, L. Shen and Z. Shen, Simultaneously inpainting in image and transformed domains, Numerische Mathematik, 112 (2009), 509-533.
doi: 10.1007/s00211-009-0222-x. |
[4] |
J. F. Cai, R. H. Chan and Z. Shen, Simultaneous cartoon and texture inpainting, Inverse Problems and Imaging, 4 (2010), 379-395.
doi: 10.3934/ipi.2010.4.379. |
[5] |
J. F. Cai, R. H. Chan and Z. Shen, A framelet-based image inpainting algorithm, Applied and Computational Harmonic Analysis, 24 (2008), 131-149.
doi: 10.1016/j.acha.2007.10.002. |
[6] |
J. F. Cai, H. Ji, F. Shang and Z. Shen, Inpainting for compressed images, Applied and Computational Harmonic Analysis, 29 (2010), 368-381.
doi: 10.1016/j.acha.2010.01.005. |
[7] |
P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., 4 (2005), 1168-1200.
doi: 10.1137/050626090. |
[8] |
I. Daubechies, "Ten Lectures on Wavelets," CBMS-NSF Regional Conference Series in Applied Mathematics, 61. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. xx+357 pp.
doi: 10.1137/1.9781611970104. |
[9] |
I. Daubechies, B. Han, A. Ron and Z. Shen, Framelets: MRA-based constructions of wavelet frames, Applied and Computational Harmonic Analysis, 14 (2003), 1-46.
doi: 10.1016/S1063-5203(02)00511-0. |
[10] |
B. Dong, H. Ji, J. Li, Z. Shen and Y. Xu, Wavelet frame based blind image inpainting, Applied and Computational Harmonic Analysis, 32 (2012), 268-279.
doi: 10.1016/j.acha.2011.06.001. |
[11] |
B. Dong and Z. Shen, MRA based wavelet frames and applications, IAS Lecture Notes Series, Summer Program on "The Mathematics of Image Processing," Park City Mathematics Institute}, 2010. |
[12] |
J. W. Glotzbach, R. W. Schafer, and K. Illgner, A method of color fillter array interpolation with alias cancellation properties, IEEE Int. Conf. Image Processing, 1 (2001), 141-144.
doi: 10.1109/ICIP.2001.958973. |
[13] |
T. Goldstein and S. Osher, The split bregman algorithm for l1 regularized problems, SIAM Journal on Imaging Sciences, 2 (2009), 323-343.
doi: 10.1137/080725891. |
[14] |
B. Gunturk, Y. Altunbasak and R. M. Mersereau, Color plane interpolation using alternating projections, IEEE Transactions on Image Processing, 11 (2002), 997-1013. |
[15] |
A. Haar, Zur theorie der orthogonalen funktionensysteme, Mathematische Annalen, 69 (1910), 331-371.
doi: 10.1007/BF01456326. |
[16] |
J. Hamilton Jr and J. Adams Jr, Adaptive color plan interpolation in single sensor color electronic camera, U.S. Patent, 5 (1997), 629-734. |
[17] |
C. A Laroche and M. A Prescott, Apparatus and method for adaptively interpolating a full color image utilizing chrominance gradients, December 13 1994., US Patent 5, ().
|
[18] |
W. Lu and Y. P. Tan, Color filter array demosaicking: New method and performance measures, IEEE Transactions on Image Processing, 12 (2003), 1194-1210. |
[19] |
H. S Malvar, L.-W. He, and R. Cutler, High-quality linear interpolation for demosaicing of bayer-patterned color images, In "Acoustics, Speech, and Signal Processing," 2004. Proceedings.(ICASSP'04). IEEE International Conference on, 3 (2004), iii-485.
doi: 10.1109/ICASSP.2004.1326587. |
[20] |
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. |
[21] |
D. Paliy, V. Katkovnik, R. Bilcu, S. Alenius and K. Egiazarian, Spatially adaptive color filter array interpolation for noiseless and noisy data, International Journal of Imaging Systems and Technology, 17 (2007), 105-122.
doi: 10.1002/ima.20109. |
[22] |
A. Ron and Z. Shen, Affine systems in $ l_2(\mathbbR^d)$: The analysis of the analysis operator, Journal of Functional Analysis, 148 (1997), 408-447.
doi: 10.1006/jfan.1996.3079. |
[23] |
Z. Shen, Wavelet frames and image restorations, Proceedings of the International Congress of Mathematicians, IV (2010), 2834-2863, Hindustan Book Agency, New Delhi. |
[24] |
X. Wu and N. Zhang, Primary-consistent soft-decision color demosaicking for digital cameras (patent pending), Image Processing, IEEE Transactions on, 13 (2004), 1263-1274.
doi: 10.1109/TIP.2004.832920. |
[25] |
L. Zhang and X. Wu, Color demosaicking via directional linear minimum mean square-error estimation, IEEE Transactions on Image Processing, 14 (2005), 2167-2178. |
[26] |
L. Zhang, X. Wu, A. Buades and X. Li, Color demosaicking by local directional interpolation and non-local adaptive thresholding, Journal of Electronic Imaging, 20 (2011), 023016. |
[27] |
X. Zhang, M. Burger, X. Bresson and S. Osher, Bregmanized nonlocal regularization for deconvolution and sparse reconstruction, SIAM Journal on Imaging Sciences, 3 (2010), 253-276.
doi: 10.1137/090746379. |
[28] |
X. Zhang, M. Burger and S. Osher, A unified primal-dual algorithm framework based on bregman iteration, Journal of Scientific Computing, 46 (2010), 20-46.
doi: 10.1007/s10915-010-9408-8. |
show all references
References:
[1] |
B. E. Bayer, Color imaging array, U.S. Patent, 3971065, 1976. |
[2] |
A. Buades, B. Coll, J.-M. Morel and C. Sbert, Self-similarity driven color demosaicking, IEEE Transactions on Image Processing, 18 (2009), 1192-1202.
doi: 10.1109/TIP.2009.2017171. |
[3] |
J. F. Cai, R. Chan, L. Shen and Z. Shen, Simultaneously inpainting in image and transformed domains, Numerische Mathematik, 112 (2009), 509-533.
doi: 10.1007/s00211-009-0222-x. |
[4] |
J. F. Cai, R. H. Chan and Z. Shen, Simultaneous cartoon and texture inpainting, Inverse Problems and Imaging, 4 (2010), 379-395.
doi: 10.3934/ipi.2010.4.379. |
[5] |
J. F. Cai, R. H. Chan and Z. Shen, A framelet-based image inpainting algorithm, Applied and Computational Harmonic Analysis, 24 (2008), 131-149.
doi: 10.1016/j.acha.2007.10.002. |
[6] |
J. F. Cai, H. Ji, F. Shang and Z. Shen, Inpainting for compressed images, Applied and Computational Harmonic Analysis, 29 (2010), 368-381.
doi: 10.1016/j.acha.2010.01.005. |
[7] |
P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., 4 (2005), 1168-1200.
doi: 10.1137/050626090. |
[8] |
I. Daubechies, "Ten Lectures on Wavelets," CBMS-NSF Regional Conference Series in Applied Mathematics, 61. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. xx+357 pp.
doi: 10.1137/1.9781611970104. |
[9] |
I. Daubechies, B. Han, A. Ron and Z. Shen, Framelets: MRA-based constructions of wavelet frames, Applied and Computational Harmonic Analysis, 14 (2003), 1-46.
doi: 10.1016/S1063-5203(02)00511-0. |
[10] |
B. Dong, H. Ji, J. Li, Z. Shen and Y. Xu, Wavelet frame based blind image inpainting, Applied and Computational Harmonic Analysis, 32 (2012), 268-279.
doi: 10.1016/j.acha.2011.06.001. |
[11] |
B. Dong and Z. Shen, MRA based wavelet frames and applications, IAS Lecture Notes Series, Summer Program on "The Mathematics of Image Processing," Park City Mathematics Institute}, 2010. |
[12] |
J. W. Glotzbach, R. W. Schafer, and K. Illgner, A method of color fillter array interpolation with alias cancellation properties, IEEE Int. Conf. Image Processing, 1 (2001), 141-144.
doi: 10.1109/ICIP.2001.958973. |
[13] |
T. Goldstein and S. Osher, The split bregman algorithm for l1 regularized problems, SIAM Journal on Imaging Sciences, 2 (2009), 323-343.
doi: 10.1137/080725891. |
[14] |
B. Gunturk, Y. Altunbasak and R. M. Mersereau, Color plane interpolation using alternating projections, IEEE Transactions on Image Processing, 11 (2002), 997-1013. |
[15] |
A. Haar, Zur theorie der orthogonalen funktionensysteme, Mathematische Annalen, 69 (1910), 331-371.
doi: 10.1007/BF01456326. |
[16] |
J. Hamilton Jr and J. Adams Jr, Adaptive color plan interpolation in single sensor color electronic camera, U.S. Patent, 5 (1997), 629-734. |
[17] |
C. A Laroche and M. A Prescott, Apparatus and method for adaptively interpolating a full color image utilizing chrominance gradients, December 13 1994., US Patent 5, ().
|
[18] |
W. Lu and Y. P. Tan, Color filter array demosaicking: New method and performance measures, IEEE Transactions on Image Processing, 12 (2003), 1194-1210. |
[19] |
H. S Malvar, L.-W. He, and R. Cutler, High-quality linear interpolation for demosaicing of bayer-patterned color images, In "Acoustics, Speech, and Signal Processing," 2004. Proceedings.(ICASSP'04). IEEE International Conference on, 3 (2004), iii-485.
doi: 10.1109/ICASSP.2004.1326587. |
[20] |
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. |
[21] |
D. Paliy, V. Katkovnik, R. Bilcu, S. Alenius and K. Egiazarian, Spatially adaptive color filter array interpolation for noiseless and noisy data, International Journal of Imaging Systems and Technology, 17 (2007), 105-122.
doi: 10.1002/ima.20109. |
[22] |
A. Ron and Z. Shen, Affine systems in $ l_2(\mathbbR^d)$: The analysis of the analysis operator, Journal of Functional Analysis, 148 (1997), 408-447.
doi: 10.1006/jfan.1996.3079. |
[23] |
Z. Shen, Wavelet frames and image restorations, Proceedings of the International Congress of Mathematicians, IV (2010), 2834-2863, Hindustan Book Agency, New Delhi. |
[24] |
X. Wu and N. Zhang, Primary-consistent soft-decision color demosaicking for digital cameras (patent pending), Image Processing, IEEE Transactions on, 13 (2004), 1263-1274.
doi: 10.1109/TIP.2004.832920. |
[25] |
L. Zhang and X. Wu, Color demosaicking via directional linear minimum mean square-error estimation, IEEE Transactions on Image Processing, 14 (2005), 2167-2178. |
[26] |
L. Zhang, X. Wu, A. Buades and X. Li, Color demosaicking by local directional interpolation and non-local adaptive thresholding, Journal of Electronic Imaging, 20 (2011), 023016. |
[27] |
X. Zhang, M. Burger, X. Bresson and S. Osher, Bregmanized nonlocal regularization for deconvolution and sparse reconstruction, SIAM Journal on Imaging Sciences, 3 (2010), 253-276.
doi: 10.1137/090746379. |
[28] |
X. Zhang, M. Burger and S. Osher, A unified primal-dual algorithm framework based on bregman iteration, Journal of Scientific Computing, 46 (2010), 20-46.
doi: 10.1007/s10915-010-9408-8. |
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