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‎Readme.md

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@@ -20,20 +20,20 @@ Iterative image reconstruction (IIR) methods frequently require regularisation t
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### Single-channel (scalar)
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1. Rudin-Osher-Fatemi (ROF) Total Variation (explicit PDE minimisation scheme) **2D/3D CPU/GPU + CuPy** (Ref. *1*)
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2. Fast-Gradient-Projection (FGP) Total Variation **2D/3D CPU/GPU** (Ref. *2*)
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3. Split-Bregman (SB) Total Variation **2D/3D CPU/GPU** (Ref. *5*)
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4. Primal-Dual (PD) Total Variation **2D/3D CPU/GPU + CuPy** (Ref. *13*)
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5. Total Generalised Variation (TGV) model for higher-order regularisation **2D/3D CPU/GPU** (Ref. *6,13*)
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6. Linear and nonlinear diffusion (explicit PDE minimisation scheme) **2D/3D CPU/GPU** (Ref. *8*)
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7. Anisotropic Fourth-Order Diffusion (explicit PDE minimisation) **2D/3D CPU/GPU** (Ref. *9*)
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8. A joint ROF-LLT (Lysaker-Lundervold-Tai) model for higher-order regularisation **2D/3D CPU/GPU** (Ref. *10,11*)
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9. Nonlocal Total Variation regularisation (GS fixed point iteration) **2D CPU/GPU** (Ref. *12*)
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1. Rudin-Osher-Fatemi (ROF) Total Variation (explicit PDE minimisation scheme) **2D/3D CPU/GPU + CuPy**[^1]
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2. Fast-Gradient-Projection (FGP) Total Variation **2D/3D CPU/GPU**[^2]
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3. Split-Bregman (SB) Total Variation **2D/3D CPU/GPU**[^5]
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4. Primal-Dual (PD) Total Variation **2D/3D CPU/GPU + CuPy**[^13]
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5. Total Generalised Variation (TGV) model for higher-order regularisation **2D/3D CPU/GPU**[^6][^13]
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6. Linear and nonlinear diffusion (explicit PDE minimisation scheme) **2D/3D CPU/GPU**[^8]
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7. Anisotropic Fourth-Order Diffusion (explicit PDE minimisation) **2D/3D CPU/GPU**[^9]
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8. A joint ROF-LLT (Lysaker-Lundervold-Tai) model for higher-order regularisation **2D/3D CPU/GPU**[^10][^11]
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9. Nonlocal Total Variation regularisation (GS fixed point iteration) **2D CPU/GPU**[^12]
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### Multi-channel (vectorial)
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1. Fast-Gradient-Projection (FGP) Directional Total Variation **2D/3D CPU/GPU** (Ref. *3,4,2*)
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2. Total Nuclear Variation (TNV) penalty **2D+channels CPU** (Ref. *7*)
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1. Fast-Gradient-Projection (FGP) Directional Total Variation **2D/3D CPU/GPU**[^3][^4][^2]
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2. Total Nuclear Variation (TNV) penalty **2D+channels CPU**[^7]
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## Installation
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@@ -59,21 +59,19 @@ Once installed please see [Demos](./demos/demo_gpu_regularisers3D_CuPy.py). Plea
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## References
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### Implemented methods
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1. [Rudin, L.I., Osher, S. and Fatemi, E., 1992. Nonlinear total variation based noise removal algorithms. Physica D: nonlinear phenomena, 60(1-4)](https://www.sciencedirect.com/science/article/pii/016727899290242F)
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2. [Beck, A. and Teboulle, M., 2009. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Transactions on Image Processing, 18(11)](https://doi.org/10.1109/TIP.2009.2028250)
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3. [Ehrhardt, M.J. and Betcke, M.M., 2016. Multicontrast MRI reconstruction with structure-guided total variation. SIAM Journal on Imaging Sciences, 9(3)](https://doi.org/10.1137/15M1047325)
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4. [Kazantsev, D., Jørgensen, J.S., Andersen, M., Lionheart, W.R., Lee, P.D. and Withers, P.J., 2018. Joint image reconstruction method with correlative multi-channel prior for X-ray spectral computed tomography. Inverse Problems, 34(6)](https://doi.org/10.1088/1361-6420/aaba86) **Results can be reproduced using the following** [SOFTWARE](https://github.com/dkazanc/multi-channel-X-ray-CT)
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5. [Goldstein, T. and Osher, S., 2009. The split Bregman method for L1-regularized problems. SIAM journal on imaging sciences, 2(2)](https://doi.org/10.1137/080725891)
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6. [Bredies, K., Kunisch, K. and Pock, T., 2010. Total generalized variation. SIAM Journal on Imaging Sciences, 3(3)](https://doi.org/10.1137/090769521)
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7. [Duran, J., Moeller, M., Sbert, C. and Cremers, D., 2016. Collaborative total variation: a general framework for vectorial TV models. SIAM Journal on Imaging Sciences, 9(1)](https://doi.org/10.1137/15M102873X)
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8. [Black, M.J., Sapiro, G., Marimont, D.H. and Heeger, D., 1998. Robust anisotropic diffusion. IEEE Transactions on image processing, 7(3)](https://doi.org/10.1109/83.661192)
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9. [Hajiaboli, M.R., 2011. An anisotropic fourth-order diffusion filter for image noise removal. International Journal of Computer Vision, 92(2)](https://doi.org/10.1007/s11263-010-0330-1)
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10. [Lysaker, M., Lundervold, A. and Tai, X.C., 2003. Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Transactions on image processing, 12(12)](https://doi.org/10.1109/TIP.2003.819229)
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11. [Kazantsev, D., Guo, E., Phillion, A.B., Withers, P.J. and Lee, P.D., 2017. Model-based iterative reconstruction using higher-order regularization of dynamic synchrotron data. Measurement Science and Technology, 28(9)](https://doi.org/10.1088/1361-6501/aa7fa8)
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12. [Abderrahim E., Lezoray O. and Bougleux S. 2008. Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing. IEEE Trans. Image Processing 17(7), pp. 1047-1060.](https://ieeexplore.ieee.org/document/4526700)
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13. [Chambolle, A. and Pock, T., 2010. A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of mathematical imaging and vision 40(1)](https://doi.org/10.1007/s10851-010-0251-1)
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[^1]: [Rudin, L.I., Osher, S. and Fatemi, E., 1992. Nonlinear total variation based noise removal algorithms. Physica D: nonlinear phenomena, 60(1-4)](https://www.sciencedirect.com/science/article/pii/016727899290242F)
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[^2]: [Beck, A. and Teboulle, M., 2009. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Transactions on Image Processing, 18(11)](https://doi.org/10.1109/TIP.2009.2028250)
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[^3]: [Ehrhardt, M.J. and Betcke, M.M., 2016. Multicontrast MRI reconstruction with structure-guided total variation. SIAM Journal on Imaging Sciences, 9(3)](https://doi.org/10.1137/15M1047325)
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[^4]: [Kazantsev, D., Jørgensen, J.S., Andersen, M., Lionheart, W.R., Lee, P.D. and Withers, P.J., 2018. Joint image reconstruction method with correlative multi-channel prior for X-ray spectral computed tomography. Inverse Problems, 34(6)](https://doi.org/10.1088/1361-6420/aaba86) **Results can be reproduced using the following** [SOFTWARE](https://github.com/dkazanc/multi-channel-X-ray-CT)
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[^5]: [Goldstein, T. and Osher, S., 2009. The split Bregman method for L1-regularized problems. SIAM journal on imaging sciences, 2(2)](https://doi.org/10.1137/080725891)
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[^6]: [Bredies, K., Kunisch, K. and Pock, T., 2010. Total generalized variation. SIAM Journal on Imaging Sciences, 3(3)](https://doi.org/10.1137/090769521)
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[^7]: [Duran, J., Moeller, M., Sbert, C. and Cremers, D., 2016. Collaborative total variation: a general framework for vectorial TV models. SIAM Journal on Imaging Sciences, 9(1)](https://doi.org/10.1137/15M102873X)
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[^8]: [Black, M.J., Sapiro, G., Marimont, D.H. and Heeger, D., 1998. Robust anisotropic diffusion. IEEE Transactions on image processing, 7(3)](https://doi.org/10.1109/83.661192)
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[^9]: [Hajiaboli, M.R., 2011. An anisotropic fourth-order diffusion filter for image noise removal. International Journal of Computer Vision, 92(2)](https://doi.org/10.1007/s11263-010-0330-1)
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[^10]: [Lysaker, M., Lundervold, A. and Tai, X.C., 2003. Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Transactions on image processing, 12(12)](https://doi.org/10.1109/TIP.2003.819229)
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[^11]: [Kazantsev, D., Guo, E., Phillion, A.B., Withers, P.J. and Lee, P.D., 2017. Model-based iterative reconstruction using higher-order regularization of dynamic synchrotron data. Measurement Science and Technology, 28(9)](https://doi.org/10.1088/1361-6501/aa7fa8)
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[^12]: [Abderrahim E., Lezoray O. and Bougleux S. 2008. Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing. IEEE Trans. Image Processing 17(7), pp. 1047-1060.](https://ieeexplore.ieee.org/document/4526700)
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[^13]: [Chambolle, A. and Pock, T., 2010. A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of mathematical imaging and vision 40(1)](https://doi.org/10.1007/s10851-010-0251-1)
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### Software (please cite if used)
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