### Abstract

Original language | English (US) |
---|---|

Title of host publication | 2018 25th IEEE International Conference on Image Processing (ICIP) |

Publisher | IEEE |

ISBN (Electronic) | 978-1479970612 |

DOIs | |

State | Published - 2018 |

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### Cite this

*2018 25th IEEE International Conference on Image Processing (ICIP)*IEEE. https://doi.org/10.1109/ICIP.2018.8451710

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*2018 25th IEEE International Conference on Image Processing (ICIP).*IEEE. https://doi.org/10.1109/ICIP.2018.8451710

**An Interior Point Method for Nonnegative Sparse Signal Reconstruction.** / Huang, Xiang; He, Kuan; Yoo, Seunghwan; Cossairt, Oliver Strides; Katsaggelos, Aggelos K; Ferrier, Nicola; Hereld, Mark.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - An Interior Point Method for Nonnegative Sparse Signal Reconstruction

AU - Huang, Xiang

AU - He, Kuan

AU - Yoo, Seunghwan

AU - Cossairt, Oliver Strides

AU - Katsaggelos, Aggelos K

AU - Ferrier, Nicola

AU - Hereld, Mark

PY - 2018

Y1 - 2018

N2 - We present a primal-dual interior point method (IPM) with a novel preconditioner to solve the ℓ 1 -norm regularized least square problem for nonnegative sparse signal reconstruction. IPM is a second-order method that uses both gradient and Hessian information to compute effective search directions and achieve super-linear convergence rates. It therefore requires many fewer iterations than first-order methods such as iterative shrinkage/thresholding algorithms (ISTA) that only achieve sub-linear convergence rates. However, each iteration of IPM is more expensive than in ISTA because it needs to evaluate an inverse of a Hessian matrix to compute the Newton direction. We propose to approximate each Hessian matrix by a diagonal matrix plus a rank-one matrix. This approximation matrix is easily invertible using the Sherman-Morrison formula, and is used as a novel preconditioner in a preconditioned conjugate gradient method to compute a truncated Newton direction. We demonstrate the efficiency of our algorithm in compressive 3D volumetric image reconstruction. Numerical experiments show favorable results of our method in comparison with previous interior point based and iterative shrinkage/thresholding based algorithms.

AB - We present a primal-dual interior point method (IPM) with a novel preconditioner to solve the ℓ 1 -norm regularized least square problem for nonnegative sparse signal reconstruction. IPM is a second-order method that uses both gradient and Hessian information to compute effective search directions and achieve super-linear convergence rates. It therefore requires many fewer iterations than first-order methods such as iterative shrinkage/thresholding algorithms (ISTA) that only achieve sub-linear convergence rates. However, each iteration of IPM is more expensive than in ISTA because it needs to evaluate an inverse of a Hessian matrix to compute the Newton direction. We propose to approximate each Hessian matrix by a diagonal matrix plus a rank-one matrix. This approximation matrix is easily invertible using the Sherman-Morrison formula, and is used as a novel preconditioner in a preconditioned conjugate gradient method to compute a truncated Newton direction. We demonstrate the efficiency of our algorithm in compressive 3D volumetric image reconstruction. Numerical experiments show favorable results of our method in comparison with previous interior point based and iterative shrinkage/thresholding based algorithms.

U2 - 10.1109/ICIP.2018.8451710

DO - 10.1109/ICIP.2018.8451710

M3 - Conference contribution

BT - 2018 25th IEEE International Conference on Image Processing (ICIP)

PB - IEEE

ER -