# Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion

## Abstract

We develop a sparse image reconstruction method for polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. To obtain a parsimonious measurement model parameterization, we first rewrite the measurement equation using our mass-attenuation parameterization, which has the Laplace integral form. The unknown mass-attenuation spectrum is expanded into basis functions using a B-spline basis of order one. We develop a block coordinate-descent algorithm for constrained minimization of a penalized negative log-likelihood function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and sparsity of the density map image in the wavelet domain. This algorithm alternates between a Nesterov’s proximal-gradient step for estimating the density map image and an active-set step for estimating the incident spectrum parameters. Numerical simulations demonstrate the performance of the proposed scheme.

- Authors:

- Iowa State University, Center for Nondestructive Evaluation, 1915 Scholl Road, Ames, IA 50011 (United States)

- Publication Date:

- OSTI Identifier:
- 22391228

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1650; Journal Issue: 1; Conference: 41. Annual Review of Progress in Quantitative Nondestructive Evaluation, Boise, ID (United States), 20-25 Jul 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ATTENUATION; COMPUTERIZED SIMULATION; COMPUTERIZED TOMOGRAPHY; ENERGY SPECTRA; IMAGE PROCESSING; INTEGRALS; LIMITING VALUES; MATHEMATICAL MODELS; PERFORMANCE; SPLINE FUNCTIONS

### Citation Formats

```
Gu, Renliang, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu, and Dogandžić, Aleksandar, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu.
```*Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion*. United States: N. p., 2015.
Web. doi:10.1063/1.4914792.

```
Gu, Renliang, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu, & Dogandžić, Aleksandar, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu.
```*Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion*. United States. doi:10.1063/1.4914792.

```
Gu, Renliang, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu, and Dogandžić, Aleksandar, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu. Tue .
"Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion". United States.
doi:10.1063/1.4914792.
```

```
@article{osti_22391228,
```

title = {Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion},

author = {Gu, Renliang, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu and Dogandžić, Aleksandar, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu},

abstractNote = {We develop a sparse image reconstruction method for polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. To obtain a parsimonious measurement model parameterization, we first rewrite the measurement equation using our mass-attenuation parameterization, which has the Laplace integral form. The unknown mass-attenuation spectrum is expanded into basis functions using a B-spline basis of order one. We develop a block coordinate-descent algorithm for constrained minimization of a penalized negative log-likelihood function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and sparsity of the density map image in the wavelet domain. This algorithm alternates between a Nesterov’s proximal-gradient step for estimating the density map image and an active-set step for estimating the incident spectrum parameters. Numerical simulations demonstrate the performance of the proposed scheme.},

doi = {10.1063/1.4914792},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1650,

place = {United States},

year = {Tue Mar 31 00:00:00 EDT 2015},

month = {Tue Mar 31 00:00:00 EDT 2015}

}