# TV-based conjugate gradient method and discrete L-curve for few-view CT reconstruction of X-ray *in vivo* data

## Abstract

High-resolution, three-dimensional (3D) imaging of soft tissues requires the solution of two inverse problems: phase retrieval and the reconstruction of the 3D image from a tomographic stack of two-dimensional (2D) projections. The number of projections per stack should be small to accommodate fast tomography of rapid processes and to constrain X-ray radiation dose to optimal levels to either increase the duration o f *in vivo* time-lapse series at a given goal for spatial resolution and/or the conservation of structure under X-ray irradiation. In pursuing the 3D reconstruction problem in the sense of compressive sampling theory, we propose to reduce the number of projections by applying an advanced algebraic technique subject to the minimisation of the total variation (TV) in the reconstructed slice. This problem is formulated in a Lagrangian multiplier fashion with the parameter value determined by appealing to a discrete L-curve in conjunction with a conjugate gradient method. The usefulness of this reconstruction modality is demonstrated for simulated and *in vivo* data, the latter acquired in parallel-beam imaging experiments using synchrotron radiation.

- Authors:

- Karlsruhe Inst. of Technology (KIT), Karlsruhe (Germany)
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1190778

- Grant/Contract Number:
- AC02-06CH11357

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Optics Express

- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 5; Journal ID: ISSN 1094-4087

- Publisher:
- Optical Society of America (OSA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 62 RADIOLOGY AND NUCLEAR MEDICINE

### Citation Formats

```
Yang, Xiaoli, Hofmann, Ralf, Dapp, Robin, van de Kamp, Thomas, Rolo, Tomy dos Santos, Xiao, Xianghui, Moosmann, Julian, Kashef, Jubin, and Stotzka, Rainer.
```*TV-based conjugate gradient method and discrete L-curve for few-view CT reconstruction of X-ray in vivo data*. United States: N. p., 2015.
Web. doi:10.1364/OE.23.005368.

```
Yang, Xiaoli, Hofmann, Ralf, Dapp, Robin, van de Kamp, Thomas, Rolo, Tomy dos Santos, Xiao, Xianghui, Moosmann, Julian, Kashef, Jubin, & Stotzka, Rainer.
```*TV-based conjugate gradient method and discrete L-curve for few-view CT reconstruction of X-ray in vivo data*. United States. doi:10.1364/OE.23.005368.

```
Yang, Xiaoli, Hofmann, Ralf, Dapp, Robin, van de Kamp, Thomas, Rolo, Tomy dos Santos, Xiao, Xianghui, Moosmann, Julian, Kashef, Jubin, and Stotzka, Rainer. Thu .
"TV-based conjugate gradient method and discrete L-curve for few-view CT reconstruction of X-ray in vivo data". United States.
doi:10.1364/OE.23.005368. https://www.osti.gov/servlets/purl/1190778.
```

```
@article{osti_1190778,
```

title = {TV-based conjugate gradient method and discrete L-curve for few-view CT reconstruction of X-ray in vivo data},

author = {Yang, Xiaoli and Hofmann, Ralf and Dapp, Robin and van de Kamp, Thomas and Rolo, Tomy dos Santos and Xiao, Xianghui and Moosmann, Julian and Kashef, Jubin and Stotzka, Rainer},

abstractNote = {High-resolution, three-dimensional (3D) imaging of soft tissues requires the solution of two inverse problems: phase retrieval and the reconstruction of the 3D image from a tomographic stack of two-dimensional (2D) projections. The number of projections per stack should be small to accommodate fast tomography of rapid processes and to constrain X-ray radiation dose to optimal levels to either increase the duration o fin vivo time-lapse series at a given goal for spatial resolution and/or the conservation of structure under X-ray irradiation. In pursuing the 3D reconstruction problem in the sense of compressive sampling theory, we propose to reduce the number of projections by applying an advanced algebraic technique subject to the minimisation of the total variation (TV) in the reconstructed slice. This problem is formulated in a Lagrangian multiplier fashion with the parameter value determined by appealing to a discrete L-curve in conjunction with a conjugate gradient method. The usefulness of this reconstruction modality is demonstrated for simulated and in vivo data, the latter acquired in parallel-beam imaging experiments using synchrotron radiation.},

doi = {10.1364/OE.23.005368},

journal = {Optics Express},

number = 5,

volume = 23,

place = {United States},

year = {Thu Jan 01 00:00:00 EST 2015},

month = {Thu Jan 01 00:00:00 EST 2015}

}

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