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CC-CSI
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Cross-Correlated Contrast Source Inversion
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README.md
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CC-CSI
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CC-CSI ====== Introduction ------------ CC-CSI is a MATLAB-based package of the **Cross-Correlated Contrast Source Inversion** algorithm. This package inverts the [Fresnel data](http://www.fresnel.fr/3Ddatabase/) with multiple frequency components. - The error terms - Data error <!--- http://latex.codecogs.com/eqneditor/editor.php --> <!--- \xi_{p,i} = y_{p,i} - \Phi_{p,i}\left(\chi_i e^{\text{inc}}_{p,i} + \chi_i A^{-1}_ij_{p,i}\right) --> <div align=center><img src="http://latex.codecogs.com/gif.latex?%5Crho_%7Bp%2Ci%7D%20%3D%20y_%7Bp%2Ci%7D%20-%20%5CPhi_%7Bp%2Ci%7Dj_%7Bp%2Ci%7D"/></div> - State error <!--- \gamma_{p,i} = \chi_i e^{\text{inc}}_{p,i} + \chi_i A_i^{-1}j_{p,i} - j_{p,i} --> <div align=center><img src="http://latex.codecogs.com/gif.latex?%5Cgamma_%7Bp%2Ci%7D%20%3D%20%5Cchi_i%20e%5E%7B%5Ctext%7Binc%7D%7D_%7Bp%2Ci%7D%20+%20%5Cchi_i%20A_i%5E%7B-1%7Dj_%7Bp%2Ci%7D%20-%20j_%7Bp%2Ci%7D"/></div> - Cross-correlated error <!--- \xi_{p,i} = y_{p,i} - \Phi_{p,i}\left(\chi_i e^{\text{inc}}_{p,i} + \chi_i A^{-1}_ij_{p,i}\right) --> <div align=center><img src="http://latex.codecogs.com/gif.latex?%5Cxi_%7Bp%2Ci%7D%20%3D%20y_%7Bp%2Ci%7D%20-%20%5CPhi_%7Bp%2Ci%7D%5Cleft%28%5Cchi_i%20e%5E%7B%5Ctext%7Binc%7D%7D_%7Bp%2Ci%7D%20+%20%5Cchi_i%20A%5E%7B-1%7D_ij_%7Bp%2Ci%7D%20%5Cright%20%29"/></div> - The cost functional of multi-frequency CC-CSI <!--- \mathcal{C}_{\text{CC-CSI}} = \sum_i\eta^\mathcal{S}_i\sum_p\left\|\rho_{p,i}\right\|^2_\mathcal{S}+\sum_i\eta^\mathcal{D}_i\sum_p\left\|\gamma_{p,i}\right\|^2_\mathcal{D}+\sum_i\eta^\mathcal{S}_i\sum_p\left\|\xi_{p,i}\right\|^2_\mathcal{S} --> <div align=center><img src="http://latex.codecogs.com/gif.latex?%5Cmathcal%7BC%7D_%7B%5Ctext%7BCC-CSI%7D%7D%20%3D%20%5Csum_i%5Ceta%5E%5Cmathcal%7BS%7D_i%5Csum_p%5Cleft%5C%7C%5Crho_%7Bp%2Ci%7D%5Cright%5C%7C%5E2_%5Cmathcal%7BS%7D+%5Csum_i%5Ceta%5E%5Cmathcal%7BD%7D_i%5Csum_p%5Cleft%5C%7C%5Cgamma_%7Bp%2Ci%7D%5Cright%5C%7C%5E2_%5Cmathcal%7BD%7D+%5Csum_i%5Ceta%5E%5Cmathcal%7BS%7D_i%5Csum_p%5Cleft%5C%7C%5Cxi_%7Bp%2Ci%7D%5Cright%5C%7C%5E2_%5Cmathcal%7BS%7D"/></div> This package also contains the MR-CSI (multiplicative-regularized CSI) and CSI algorithms for comparison. - See `INSTALL.md` for installation instruction. - We would be delighted to hear from you if you find CC-CSI useful, or if you have any suggestions, contributions, or bug reports. Please send these to - Shilong Sun (shilongsun@126.com) Citation -------- - [*Cross-Correlated Contrast Source Inversion*](https://arxiv.org/abs/1906.10864), S. Sun, B. J. Kooij, T. Jin, and A. G. Yarovoy, IEEE Transactions on Antennas and Propagation, 65 (5), 2592 - 2603, 2017 - [*Inversion of Multifrequency Data With the Cross‐Correlated Contrast Source Inversion Method*](https://arxiv.org/abs/1906.10814), S. Sun, B. J. Kooij, and A. G. Yarovoy, Radio Science, 53 (6), 710-723, 2018