In this course we have used several kinds of regularization for the regularization of ill-posed inverse problems in satellite imaging: Tikhonov, Total Variation, sparsity-based and patch-based non-local regularizers.
Convolutional neural networks have recently gained a lot of attention because of their very good performance in several image classification and computer vision tasks. The use of CNNs in image restoration, however, is much less developed, and in most cases based on brute-force training of a neural network for a particular restoration task like denoising [1,2] or depth from defocus [3].
Another approach which is starting to emerge is to use CNNs as a generic way to learn statistical priors on natural images, and then use those priors as a generative model for natural image texture synthesis or as a regularizer of inverse problems in imaging. Two recent examples of this approach are the works by Gatys et al. (2015) on image style transfer, and by Bruna et al. (2016) on super-resolution.
The aim of this exploratory project is to study these two papers, and provide, based on them, a critical view on the potential of CNNs to substitute non-local patch-based methods (like NLMeans, NLBayes, BM3D or EPLL) as a generic regularization method for inverse problems like those encountered in satellite imaging. Numerical simulations are optional. The emphasis of this project should be on identifying and clearly exposing the potential benefits and challenges of this novel approach.
Supervision
Andrés Almansa
Main References
Bruna, J., Sprechmann, P., & LeCun, Y. (2016). Super-Resolution with Deep Convolutional Sufficient Statistics. ICLR, arXiv:1508.06576v2
Gatys, L. A., Ecker, A. S., & Bethge, M. (2015). A Neural Algorithm of Artistic Style, arXiv:1508.06576
Additional References
[1] Burger, H. C., Schuler, C. J., & Harmeling, S. (2012). Image denoising: Can plain neural networks compete with BM3D? (CVPR) EEE Computer Society Conference on Computer Vision and Pattern Recognition, 2392–2399. doi:10.1109/CVPR.2012.6247952
[2] Wang, Y. (2015). Small neural networks can denoise image textures well : a useful complement to BM3D Image denoising neural networks. IPOL, 6, 1–6.
[3] Dumas, T., Trouvé-Peloux, P., & Le-Saux, B. (2015). Réseaux de neurones profonds pour estimer la profondeur grâce au flou de défocalisation. In Gretsi.