## A Plug-and-Play Priors Approach for Solving Nonlinear Imaging Inverse Problems

## Abstract

In the past two decades, nonlinear image reconstruction methods have led to substantial improvements in the capabilities of numerous imaging systems. Such methods are traditionally formulated as optimization problems that are solved iteratively by simultaneously enforcing data consistency and incorporating prior models. Recently, the Plug-and-Play Priors (PPP) framework suggested that by using more sophisticated denoisers, not necessarily corresponding to an optimization objective, it is possible to improve the quality of reconstructed images. Here in this letter, we show that the PPP approach is applicable beyond linear inverse problems. In particular, we develop the fast iterative shrinkage/thresholding algorithm variant of PPP for model-based nonlinear inverse scattering. The key advantage of the proposed formulation over the original ADMM-based one is that it does not need to perform an inversion on the forward model. We show that the proposed method produces high quality images using both simulated and experimentally measured data.

- Authors:

- Mitsubishi Electric Research Lab. (MERL), Cambridge, MA (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1469540

- Report Number(s):
- LA-UR-17-26597

Journal ID: ISSN 1070-9908

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- IEEE Signal Processing Letters

- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 12; Journal ID: ISSN 1070-9908

- Publisher:
- IEEE Signal Processing Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Information Science; Mathematics; Fast iterative shrinkage/thresholding algorithm (FISTA); image reconstruction; inverse scattering; nonlinear inverse problems; plug-and-play priors (PPP)

### Citation Formats

```
Kamilov, Ulugbek S., Mansour, Hassan, and Wohlberg, Brendt. A Plug-and-Play Priors Approach for Solving Nonlinear Imaging Inverse Problems. United States: N. p., 2017.
Web. doi:10.1109/LSP.2017.2763583.
```

```
Kamilov, Ulugbek S., Mansour, Hassan, & Wohlberg, Brendt. A Plug-and-Play Priors Approach for Solving Nonlinear Imaging Inverse Problems. United States. doi:10.1109/LSP.2017.2763583.
```

```
Kamilov, Ulugbek S., Mansour, Hassan, and Wohlberg, Brendt. Fri .
"A Plug-and-Play Priors Approach for Solving Nonlinear Imaging Inverse Problems". United States. doi:10.1109/LSP.2017.2763583. https://www.osti.gov/servlets/purl/1469540.
```

```
@article{osti_1469540,
```

title = {A Plug-and-Play Priors Approach for Solving Nonlinear Imaging Inverse Problems},

author = {Kamilov, Ulugbek S. and Mansour, Hassan and Wohlberg, Brendt},

abstractNote = {In the past two decades, nonlinear image reconstruction methods have led to substantial improvements in the capabilities of numerous imaging systems. Such methods are traditionally formulated as optimization problems that are solved iteratively by simultaneously enforcing data consistency and incorporating prior models. Recently, the Plug-and-Play Priors (PPP) framework suggested that by using more sophisticated denoisers, not necessarily corresponding to an optimization objective, it is possible to improve the quality of reconstructed images. Here in this letter, we show that the PPP approach is applicable beyond linear inverse problems. In particular, we develop the fast iterative shrinkage/thresholding algorithm variant of PPP for model-based nonlinear inverse scattering. The key advantage of the proposed formulation over the original ADMM-based one is that it does not need to perform an inversion on the forward model. We show that the proposed method produces high quality images using both simulated and experimentally measured data.},

doi = {10.1109/LSP.2017.2763583},

journal = {IEEE Signal Processing Letters},

number = 12,

volume = 24,

place = {United States},

year = {2017},

month = {12}

}

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