AI for Inverse Sensing Problems


Inverse problems appear e.g. in computer science, engineering and physics and are therefore a core field in data science. In general, the problem is to infer from a set of observations on some unknown quantity of interest. The so called forward model is often known or at least partially known, but the estimation problem itself is ill-posed, i.e., it can not be easily and uniquely inverted. Instead, at least prior structural or distributional assumptions on the unknown quantity are required.

For a well-defined analytical formulation algorithms can be derived, directly or from a Bayesian perspective, and in many cases it even possible to obtain performance bounds. Also, tuning parameters and acceleration techniques can be often computed explicitly. Compressed sensing and its successors are here good examples. However, for many real-world problems it is quite difficult to have such an analytical formulation. Often the forward model is incomplete, explicit prior models do not fit well and algorithms perform poor or need hand-crafted tuning. It is therefore of fundamental importance how data-driven methods can be incorporated.

An important direction is to extend the idea of regularization towards data-driven approach. Several ideas exist already in the literature, like “network Tikhonov regularization” or “regularization by denoising”. For example deep auto-encoders can be trained to represent a certain low-dimensional structure in the data. The corresponding decoder can be used to setup an operational regularization penalty for classical inverse problem algorithms. Another approach is to train a deep generative model to describe the unknown quantity by training data and optimize over latent space variables to solve the inverse problem. In both approaches it is desirable to follow a variational approach since smoothness and regularity in the latent space is crucial for the success of many iterative descent algorithms. Another promising direction is the idea of unfolding or unrolling of classical signal processing algorithms into deep networks and train the computational graph.

In all these approaches, important questions arise about the robustness and uncertainty with respect to changes in the distribution or the domain when going from training to testing. If the new distribution can probed by sampling, changing to the distribution may require retraining and the question is if this can be done efficiently using ideas of transfer learning. Also, the training strategy is important to study. The models, the regularizer or the unfolded algorithm itself can be trained layer-wise, hierarchically or end-to-end with different optimizers. Depending on the loss and its smoothness several difficulties may arise and optimizer may perform differently. Also, it has been intensively discussed recently how important training is versus the structure and the connectivity of the deep networks. Approaches for analytically or directly computing weights and instead learn only parameters of activation functions have been proposed allowing to compute rigorous recovery bounds.

Related Publications

[1] Jakob Gawlikowski, Cedrique Rovile Njieutcheu Tassi, Mohsin Ali, Jongseok Lee, Matthias Humt, Jianxiang Feng, Anna Kruspe, Rudolph Triebel, Peter Jung, Ribana Roscher, Muhammad Shahzad, Wen Yang, Richard Bamler, and Xiao Xiang Zhu. A survey of uncertainty in deep neural networks. Artificial Intelligence Review, jul 2023. [ bib | DOI | arXiv | http ]
[2] Jan Christian Hauffen, Peter Jung, and Nicole Mücke. Algorithm Unfolding for Block-sparse and MMV Problems with Reduced Training Overhead. Frontiers in Applied Mathematics and Statistics, 9, 2023. [ bib | DOI | arXiv | http ]
[3] Jonathan Sauder, Martin Genzel, and Peter Jung. Gradient-Based Learning of Discrete Structured Measurement Operators for Signal Recovery. IEEE Journal on Selected Areas in Information Theory, 3(3):481--492, sep 2022. [ bib | DOI | arXiv | http ]
[4] Jan Christian Hauffen, Linh Kästner, Samim Ahmadi, Peter Jung, Giuseppe Caire, and Mathias Ziegler. Learned Block Iterative Shrinkage Thresholding Algorithm for Photothermal Super Resolution Imaging. Sensors, 22(15):5533, jul 2022. [ bib | DOI | arXiv | http ]
[5] Udaya S. K. P. Miriya Thanthrige, Peter Jung, and Aydin Sezgin. Deep Unfolding of Iteratively Reweighted ADMM for Wireless RF Sensing. Sensors, 22(8), jun 2022. [ bib | DOI | arXiv | http ]
[6] Samim Ahmadi, Linh Kastner, Jan Christian Hauffen, Peter Jung, and Mathias Ziegler. Photothermal-SR-Net: A Customized Deep Unfolding Neural Network for Photothermal Super Resolution Imaging. IEEE Transactions on Instrumentation and Measurement, 71:1--9, apr 2022. [ bib | DOI | arXiv | http ]
[7] Kun Qian, Yuanyuan Wang, Peter Jung, Yilei Shi, and Xiao Xiang Zhu. Basis Pursuit Denoising via Recurrent Neural Network Applied to Super-resolving SAR Tomography. IEEE Transactions on Geoscience and Remote Sensing, pages 1--1, 2022. [ bib | DOI | http ]
[8] Johannes Leonhardt, Lukas Drees, Peter Jung, and Ribana Roscher. Probabilistic Biomass Estimation with Conditional Generative Adversarial Networks. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), volume 13485 LNCS, pages 479--494, 2022. [ bib | DOI | http ]
[9] Kun Qian, Yuanyuan Wang, Peter Jung, Yilei Shi, and Xiao xiang Zhu. Complex-valued Sparse Long Short-term Memory Unit with Application to Super-resolving SAR Tomography. In IGARSS 2022, 2022. [ bib | http ]
[10] Linh Kastner, Samim Ahmadi, Florian Jonietz, Peter Jung, Giuseppe Caire, Mathias Ziegler, and Jens Lambrecht. Classification of Spot-welded Joints in Laser Thermography Data using Convolutional Neural Networks. IEEE Access, pages 1--1, oct 2021. [ bib | DOI | arXiv | http ]
[11] Osman Musa, Peter Jung, and Giuseppe Caire. Plug-And-Play Learned Gaussian-mixture Approximate Message Passing. In ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 4855--4859. IEEE, jun 2021. [ bib | DOI | arXiv | http ]
[12] Jonathan Sauder, Martin Genzel, and Peter Jung. Learning Structured Sparse Matrices for Signal Recovery via Unrolled Optimization. In NeurIPS 2021 Deep Inverse Workshop, 2021. [ bib | http ]
[13] Martin Reiche and Peter Jung. DeepInit Phase Retrieval. jul 2020. [ bib | arXiv | http ]
[14] Anko Börner, Heinz-wilhelm Hübers, Odej Kao, Florian Schmidt, Sören Becker, Joachim Denzlern, Daniel Matolin, David Haber, Sergio Lucia, Wojciech Samek, Rudolph Triebel, Sascha Eichstädt, Felix Biessmann, Anna Kruspe, Peter Jung, Manon Kok, Guillermo Gallego, and Ralf Berger. Sensor Artificial Intelligence and its Application to Space Systems – A White Paper. 2020. [ bib | .pdf ]
[15] Freya Behrens, Jonathan Sauder, and Peter Jung. Towards Neurally Augmented ALISTA. In NeurIPS 2020 Workshop Deep Inverse, page 4, 2020. [ bib | .pdf ]
[16] Peter Jung. AI-Aided Signal Reconstruction for Inverse Problems, 2020. [ bib | .pdf ]
[17] Osman Musa, Peter Jung, and Giuseppe Caire. Plug-And-Play Learned Gaussian-mixture Approximate Message Passing, 2020. [ bib | .pdf ]

This file was generated by bibtex2html 1.99.