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Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography
| Content Provider | Scilit |
|---|---|
| Author | Antil, Harbir Di, Zichao (Wendy) Khatri, Ratna |
| Copyright Year | 2020 |
| Description | Journal: Inverse Problems In this work we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation regularization. We emphasize that the key advantage of using fractional Laplacian as a regularizer is that it leads to a linear operator, as opposed to the total variation regularization which results in a nonlinear degenerate operator. Inspired by residual neural networks, to learn the optimal strength of regularization and the exponent of fractional Laplacian, we develop a dedicated bilevel optimization neural network with a variable depth for a general regularized inverse problem. We illustrate how to incorporate various regularizer choices into our proposed network. As an example, we consider tomographic reconstruction as a model problem and show an improvement in reconstruction quality, especially for limited data, via fractional Laplacian regularization. We successfully learn the regularization strength and the fractional exponent via our proposed bilevel optimization neural network. We observe that the fractional Laplacian regularization outperforms total variation regularization. This is specially encouraging, and important, in the case of limited and noisy data. |
| Related Links | http://arxiv.org/pdf/1907.09605 https://iopscience.iop.org/article/10.1088/1361-6420/ab80d7/pdf |
| ISSN | 02665611 |
| e-ISSN | 13616420 |
| DOI | 10.1088/1361-6420/ab80d7 |
| Journal | Inverse Problems |
| Issue Number | 6 |
| Volume Number | 36 |
| Language | English |
| Publisher | IOP Publishing |
| Publisher Date | 2020-03-18 |
| Access Restriction | Open |
| Subject Keyword | Journal: Inverse Problems Mathematical and Computational Biology Fractional Laplacian Regularization Total Variation Regularization |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Theoretical Computer Science Signal Processing Mathematical Physics Computer Science Applications |
