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Wu W, Hu D, Cong W, Shan H, Wang S, Niu C, Yan P, Yu H, Vardhanabhuti V, Wang G. Stabilizing deep tomographic reconstruction: Part A. Hybrid framework and experimental results. Patterns (N Y) 2022; 3:100474. [PMID: 35607623 PMCID: PMC9122961 DOI: 10.1016/j.patter.2022.100474] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Revised: 12/24/2021] [Accepted: 03/01/2022] [Indexed: 12/16/2022]
Abstract
A recent PNAS paper reveals that several popular deep reconstruction networks are unstable. Specifically, three kinds of instabilities were reported: (1) strong image artefacts from tiny perturbations, (2) small features missed in a deeply reconstructed image, and (3) decreased imaging performance with increased input data. Here, we propose an analytic compressed iterative deep (ACID) framework to address this challenge. ACID synergizes a deep network trained on big data, kernel awareness from compressed sensing (CS)-inspired processing, and iterative refinement to minimize the data residual relative to real measurement. Our study demonstrates that the ACID reconstruction is accurate, is stable, and sheds light on the converging mechanism of the ACID iteration under a bounded relative error norm assumption. ACID not only stabilizes an unstable deep reconstruction network but also is resilient against adversarial attacks to the whole ACID workflow, being superior to classic sparsity-regularized reconstruction and eliminating the three kinds of instabilities.
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Affiliation(s)
- Weiwen Wu
- Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
- School of Biomedical Engineering, Sun Yat-sen University, Shenzhen, Guangdong, China
- Department of Diagnostic Radiology, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong SAR, China
| | - Dianlin Hu
- The Laboratory of Image Science and Technology, Southeast University, Nanjing, China
| | - Wenxiang Cong
- Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
| | - Hongming Shan
- Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
- Institute of Science and Technology for Brain-inspired Intelligence, Fudan University, Shanghai, China
| | - Shaoyu Wang
- Department of Electrical & Computer Engineering, University of Massachusetts Lowell, Lowell, MA, USA
| | - Chuang Niu
- Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
| | - Pingkun Yan
- Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
| | - Hengyong Yu
- Department of Electrical & Computer Engineering, University of Massachusetts Lowell, Lowell, MA, USA
| | - Varut Vardhanabhuti
- Department of Diagnostic Radiology, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong SAR, China
| | - Ge Wang
- Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
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Wu W, Hu D, Cong W, Shan H, Wang S, Niu C, Yan P, Yu H, Vardhanabhuti V, Wang G. Stabilizing deep tomographic reconstruction: Part B. Convergence analysis and adversarial attacks. Patterns (N Y) 2022; 3:100475. [PMID: 35607615 PMCID: PMC9122974 DOI: 10.1016/j.patter.2022.100475] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Revised: 12/24/2021] [Accepted: 03/01/2022] [Indexed: 11/17/2022]
Abstract
Due to lack of the kernel awareness, some popular deep image reconstruction networks are unstable. To address this problem, here we introduce the bounded relative error norm (BREN) property, which is a special case of the Lipschitz continuity. Then, we perform a convergence study consisting of two parts: (1) a heuristic analysis on the convergence of the analytic compressed iterative deep (ACID) scheme (with the simplification that the CS module achieves a perfect sparsification), and (2) a mathematically denser analysis (with the two approximations: [1] AT is viewed as an inverse A- 1 in the perspective of an iterative reconstruction procedure and [2] a pseudo-inverse is used for a total variation operator H). Also, we present adversarial attack algorithms to perturb the selected reconstruction networks respectively and, more importantly, to attack the ACID workflow as a whole. Finally, we show the numerical convergence of the ACID iteration in terms of the Lipschitz constant and the local stability against noise.
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Affiliation(s)
- Weiwen Wu
- Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
- School of Biomedical Engineering, Sun Yat-sen University, Shenzhen, Guangdong, China
- Department of Diagnostic Radiology, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong SAR, China
| | - Dianlin Hu
- The Laboratory of Image Science and Technology, Southeast University, Nanjing, China
| | - Wenxiang Cong
- Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
| | - Hongming Shan
- Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
- Institute of Science and Technology for Brain-inspired Intelligence, Fudan University, Shanghai, China
| | - Shaoyu Wang
- Department of Electrical & Computer Engineering, University of Massachusetts Lowell, Lowell, MA, USA
| | - Chuang Niu
- Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
| | - Pingkun Yan
- Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
| | - Hengyong Yu
- Department of Electrical & Computer Engineering, University of Massachusetts Lowell, Lowell, MA, USA
- Corresponding author
| | - Varut Vardhanabhuti
- Department of Diagnostic Radiology, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong SAR, China
- Corresponding author
| | - Ge Wang
- Biomedical Imaging Center, Center for Biotechnology and Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
- Corresponding author
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