Scherzer, O., Grasmair, M., Grossauer, H., Haltmeier, M., Lenzen, F.: Variational regularization methods for the solution of inverse problems. In: Variational Methods in Imaging (2019)
Ito, K., Jin, B.: Inverse Problems: Tikhonov Theory And Algorithms. Applied Mathematics, World Scientific, Singapore (2014)
Benning, M., Burger, M.: Modern regularization methods for inverse problems. Acta Numer. 27, 1–111 (2018)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60, 259–268 (1992)
Aharon, M., Elad, M., Bruckstein, A.: K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54, 4311–4322 (2006)
Venkatakrishnan, S.V., Bouman, C.A., Wohlberg, B.: Plug-and-play priors for model based reconstruction. In: GlobalSIP, pp. 945–948 (2013)
Meinhardt, T., Moeller, M., Hazirbas, C., Cremers, D.: Learning proximal operators: using denoising networks for regularizing inverse imaging problems. In: ICCV, pp. 1799–1808 (2017)
Romano, Y., Elad, M., Milanfar, P.: The little engine that could: regularization by denoising (red). SIAM J. Imaging Sci. 10, 1804–1844 (2017)
Li, H., Schwab, J., Antholzer, S., Haltmeier, M.: NETT: solving inverse problems with deep neural networks. Inverse Probl. 36, 065005 (2020)
Obmann, D., Nguyen, L., Schwab, J., Haltmeier, M.: Sparse Anett for solving inverse problems with deep learning. In: International Symposium on Biomedical Imaging Workshops, Proceedings (2020)
González, M., Almansa, A., Delbracio, M., Musé, P., Tan, P.: Solving inverse problems by joint posterior maximization with a VAE prior. SIAM J. Imaging Sci. 15, 822–859 (2022)
Lunz, S., Öktem, O., Schönlieb, C.B.: Adversarial regularizers in inverse problems. In: NeurIPS, pp. 8507–8516 (2018)
Arridge, S., Maass, P., Öktem, O., Schönlieb, C.B.: Solving inverse problems using data-driven models. Acta Numer 28, 1–174 (2019)
Bora, A., Jalal, A., Price, E., Dimakis, A.G.: Compressed sensing using generative models. In: ICML, pp. 822–841 (2017)
Dhar, M., Grover, A., Ermon, S.: Modeling sparse deviations for compressed sensing using generative models. In: ICML, vol. 3, pp. 1990–2005 (2018)
Habring, A., Holler, M.: A generative variational model for inverse problems in imaging. SIAM J. Math. Data Sci. 4, 306–335 (2022)
Tripathi, S., Lipton, Z.C., Nguyen, T.Q.: Correction by projection: denoising images with generative adversarial networks. ArXiv Preprint arXiv:1803.04477 (2018)
Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT Press, Cambridge (2016). http://www.deeplearningbook.org
Boink, Y.E., Brune, C.: Learned SVD: solving inverse problems via hybrid autoencoding. ArXiv Preprint arXiv:1912.10840 (2019)
Obmann, D., Schwab, J., Haltmeier, M.: Deep synthesis regularization of inverse problems. ArXiv Preprint arXiv:2002.00155 (2020)
Arjovsky, M., Chintala, S., Bottou, L.: Wasserstein generative adversarial networks. In: ICML, pp. 298–321 (2017)
Gulrajani, I., Ahmed, F., Arjovsky, M., Dumoulin, V., Courville, A.: Improved training of wasserstein GANs. NeurIPS, pp. 5768–5778 (2017)
Goodfellow, I.J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial nets. In: NeurIPS, pp. 2672–2680 (2014)
Kingma, D.P., Welling, M.: Auto-encoding variational bayes. In: ICLR (2014)
Kingma, D.P., Welling, M.: An introduction to variational autoencoders. Found. Trends Mach. Learn. 12, 307–392 (2019)
Dave, A., Vadathya, A.K., Subramanyam, R., Baburajan, R., Mitra, K.: Solving inverse computational imaging problems using deep pixel-level prior. IEEE Trans. Comput. Imaging 5, 37–51 (2018)
Jacobsen, J.H., Smeulders, A., Oyallon, E.: i-RevNet: deep invertible networks. In: ICLR (2018)
Kingma, D.P., Dhariwal, P.: Glow: generative flow with invertible 1×1 convolutions. In: NeurIPS, pp. 10215–10224 (2018)
Oberlin, T., Verm, M.: Regularization via deep generative models: an analysis point of view. In: ICIP, pp. 404–408 (2021)
Song, Y., Ermon, S.: Improved techniques for training score-based generative models. In: NeurIPS (2020)
Ramzi, Z., Remy, B., Lanusse, F., Starck, J.-L., Ciuciu, P.: Denoising score-matching for uncertainty quantification in inverse problems. In: NeurIPS (2020)
Jalal, A., Arvinte, M., Daras, G., Price, E., Dimakis, A.G., Tamir, J.I.: Robust compressed sensing mri with deep generative priors. In: NeurIPS (2021)
Behrmann, J., Vicol, P., Wang, K.-C., Grosse, R., Jacobsen, J.-H.: Understanding and mitigating exploding inverses in invertible neural networks. In: AISTATS, PMLR, vol. 130, pp. 1792–1800 (2021)
Gu, J., Shen, Y., Zhou, B.: Image processing using multi-code GAN prior. In: CVPR, pp. 3009–3018 (2020)
Mosser, L., Dubrule, O., Blunt, M.J.: Stochastic seismic waveform inversion using generative adversarial networks as a geological prior. Math. Geosci. 52, 53–79 (2020)
Chandramouli, P., Gandikota, K.V., Goerlitz, A., Kolb, A., Moeller, M.: Generative models for generic light field reconstruction. In: TPAMI (2020)
Asim, M., Shamshad, F., Ahmed, A.: Blind image deconvolution using deep generative priors. IEEE Trans. Comput. Imaging 6, 1493–1506 (2020)
Hand, P., Leong, O., Voroninski, V.: Phase retrieval under a generative prior. In: NeurIPS, pp. 9136–9146 (2018)
Hand, P., Voroninski, V.: Global guarantees for enforcing deep generative priors by empirical risk. IEEE Trans. Inf. Theory 66, 401–418 (2020)
Lei, Q., Jalal, A., Dhillon, I.S., Dimakis, A.G.: Inverting deep generative models, one layer at a time. In: NeurIPS, vol. 32 (2019)
Daskalakis, C., Rohatgi, D., Zampetakis, M.: Constant-expansion suffices for compressed sensing with generative priors. In: NeurIPS (2020)
Shah, V., Hegde, C.: Solving linear inverse problems using GAN priors: an algorithm with provable guarantees. In: ICASSP, pp. 4609–4613 (2018)
Jagatap, G., Hegde, C.: Algorithmic guarantees for inverse imaging with untrained network priors. In: NeurIPS, vol. 32 (2019)
Candes, E.J., Tao, T.: Decoding by linear programming. IEEE Trans. Inf. Theory 51, 4203–4215 (2005)
Peng, P., Jalali, S., Yuan, X.: Auto-encoders for compressed sensing. In: NeurIPS (2019)
Hegde, C.: Algorithmic aspects of inverse problems using generative models. In: 56th Annual Allerton Conference on Communication, Control, and Computing, pp. 166–172 (2019)
Menon, S., Damian, A., Hu, S., Ravi, N., Rudin, C.: Pulse: self-supervised photo upsampling via latent space exploration of generative models. In: CVPR, pp. 2437–2445 (2020)
Daras, G., Dean, J., Jalal, A., Dimakis, A.G.: Intermediate layer optimization for inverse problems using deep generative models. In: ICML (2021)
Gunn, S., Cocola, J., Hand, P.: Regularized training of intermediate layers for generative models for inverse problems. arXiv preprint arXiv:2203.04382 (2022)
Narnhofer, D., Hammernik, K., Knoll, F., Pock, T.: Inverse GANs for accelerated MRI reconstruction. In: SPIE—The International Society for Optical Engineering, p. 45 (2019)
Hussein, S.A., Tirer, T., Giryes, R.: Image-adaptive GAN based reconstruction. In: AAAI, pp. 3121–3129 (2019)
White, T.: Sampling generative networks. arXiv:1609.04468 (2016)
Dai, B., Wipf, D.: Diagnosing and enhancing VAE models. In: ICLR (2019)
Bauer, M., Mnih, A.: Resampled priors for variational autoencoders. In: PMLR, pp. 66–75 (2020)
Veen, D.V., Jalal, A., Soltanolkotabi, M., Price, E., Vishwanath, S., Dimakis, A.G.: Compressed sensing with deep image prior and learned regularization. ArXiv Preprint (2018)
Yeh, R.A., Chen, C., Lim, T.Y., Schwing, A.G., Hasegawa-Johnson, M., Do, M.N.: Semantic image inpainting with deep generative models. In: CVPR, pp. 6882–6890 (2017)
Lahiri, A., Jain, A.K., Nadendla, D., Biswas, P.K.: Faster unsupervised semantic inpainting: a GAN based approach. In: ICIP, pp. 2706–2710 (2019)
Anirudh, R., Thiagarajan, J.J., Kailkhura, B., Bremer, T.: MimicGAN: robust projection onto image manifolds with corruption mimicking. In: IJCV (2020)
Adler, J., Öktem, O.: Deep Bayesian inversion. ArXiv Preprint (2018)
Park, H.S., Baek, J., You, S.K., Choi, J.K., Seo, J.K.: Unpaired image denoising using a generative adversarial network in X-ray CT. IEEE Access 7, 110414–110425 (2019)
Yang, G., Yu, S., Dong, H., Slabaugh, G., Dragotti, P.L., Ye, X., Liu, F., Arridge, S., Keegan, J., Guo, Y., Firmin, D.: Dagan: deep de-aliasing generative adversarial networks for fast compressed sensing MRI reconstruction. IEEE Trans. Med. Imaging 37, 1310–1321 (2018)
Lv, J., Zhu, J., Yang, G.: Which GAN? a comparative study of generative adversarial network-based fast MRI reconstruction. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 379, 20200203 (2021)
Zhu, J.Y., Park, T., Isola, P., Efros, A.A.: Unpaired image-to-image translation using cycle-consistent adversarial networks. In: ICCV, pp. 2242–2251 (2017)
Oh, G., Sim, B., Chung, H.J., Sunwoo, L., Ye, J.C.: Unpaired deep learning for accelerated MRI using optimal transport driven CycleGAN. IEEE Trans. Comput. Imaging 6, 1285–1296 (2020)
Sim, B., Oh, G., Ye, J.C.: Optimal transport structure of CycleGAN for unsupervised learning for inverse problems. In: ICASSP, pp. 8644–8647 (2020)
Kabkab, M., Samangouei, P., Chellappa, R.: Task-aware compressed sensing with generative adversarial networks. In: AAAI, pp. 2297–2304 (2018)
Gupta, H., McCann, M.T., Donati, L., Unser, M.: CryoGAN: a new reconstruction paradigm for single-particle cryo-EM via deep adversarial learning. IEEE Trans. Comput. Imaging 7, 759–774 (2021)
Ulyanov, D., Vedaldi, A., Lempitsky, V.: Deep image prior. Int. J. Comput. Vis. 128, 1867–1888 (2020)
Dittmer, S., Kluth, T., Maass, P., Baguer, D.O.: Regularization by architecture: a deep prior approach for inverse problems. J. Math. Imaging Vis. 62, 456–470 (2020)
Borji, A.: Pros and cons of GAN evaluation measures. Comput. Vis. Image Underst. 179, 41–65 (2019)
Theis, L., Oord, A.V.D., Bethge, M.: A note on the evaluation of generative models. In: ICLR (2016)
Rubner, Y., Tomasi, C., Guibas, L.J.: Metric for distributions with applications to image databases. In: ICCV, pp. 59–66 (1998)
Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., Hochreiter, S.: GANs trained by a two time-scale update rule converge to a local nash equilibrium. In: NeurIPS, pp. 6627–6638 (2017)
Gretton, A., Borgwardt, K.M., Rasch, M.J., Smola, A., Schölkopf, B., Gretton, A.S.: A kernel two-sample test. JMLR 13, 723–773 (2012)
Lopez-Paz, D., Oquab, M.: Revisiting classifier two-sample tests. In: ICLR (2017)
Arora, S., Risteski, A., Zhang, Y.: Do GANs learn the distribution? Some theory and empirics. In: ICLR, pp. 1–16 (2018)
LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86, 2278–2323 (1998)
Salimans, T., Goodfellow, I., Zaremba, W., Cheung, V., Radford, A., Chen, X.: Improved techniques for training GANs. In: NeurIPS, pp. 2234–2242 (2016)
GoogleResearch: TensorFlow: large-scale machine learning on heterogeneous systems. Software available from tensorflow.org
Bredies, K., Lorenz, D.: Mathematical Image Processing, pp. 1–469. Springer, Berlin (2018)
Flamary, R., Courty, N.: POT python optimal transport library. J. Mach Learn. Res. 22, 3571–3578 (2021)
Censor, Y.: The Mathematics of Computerized Tomography, vol. 18, p. 283. SIAM, New Delhi (2002)
Davenport, M.A., Duarte, M.F., Eldar, Y.C., Kutyniok, G.: Introduction to Compressed Sensing
Adler, J., Kohr, H., Öktem, O.: Operator Discretization Library (ODL)
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., Duchesnay, É.: Scikit-learn: machine learning in python. JMLR 12, 2825–2830 (2011)
Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120–145 (2011)
Bolte, J., Sabach, S., Teboulle, M.: Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Program. 146, 459–494 (2014)
Tikhonov, A.N., Goncharsky, A.V., Stepanov, V.V., Yagola, A.G.: Numerical Methods for the Solution of Ill-Posed Problems. Kluwer Academic, Netherlands (1995)
Knoll, F., Zbontar, J., Sriram, A., Muckley, M.J., Bruno, M., Defazio, A., Parente, M., Geras, K.J., Katsnelson, J., Chandarana, H., Zhang, Z., Drozdzalv, M., Romero, A., Rabbat, M., Vincent, P., Pinkerton, J., Wang, D., Yakubova, N., Owens, E., Zitnick, C.L., Recht, M.P., Sodickson, D.K., Lui, Y.W.: fastMRI: a publicly available raw k-space and DICOM dataset of knee images for accelerated MR image reconstruction using machine learning. Radiol. Artif. Intell. 2, 190007 (2020)
Zbontar, J., Knoll, F., Sriram, A., Murrell, T., Huang, Z., Muckley, M.J., Defazio, A., Stern, R., Johnson, P., Bruno, M., Parente, M., Geras, K.J., Katsnelson, J., Chandarana, H., Zhang, Z., Drozdzal, M., Romero, A., Rabbat, M., Vincent, P., Yakubova, N., Pinkerton, J., Wang, D., Owens, E., Zitnick, C.L., Recht, M.P., Sodickson, D.K., Lui, Y.W.: fastMRI: an open dataset and benchmarks for accelerated MRI. ArXiv Preprint (2018)
![Testing learning-enabled cyber-physical systems with Large-Language Models: A Formal Approach. (arXiv:2311.07377v2 [cs.SE] UPDATED)](https://aigumbo.com/wp-content/themes/sociallyviral/images/nothumb-sociallyviral_related.png)
