### Abstract

Signal decomposition is a classical problem in signal processing, which aims to separate an observed signal into two or more components, each with its own property. Usually, each component is described by its own subspace or dictionary. Extensive research has been done for the case where the components are additive, but in real-world applications, the components are often non-additive. For example, an image may consist of a foreground object overlaid on a background, where each pixel either belongs to the foreground or the background. In such a situation, to separate signal components, we need to find a binary mask which shows the location of each component. Therefore, it requires solving a binary optimization problem. Since most of the binary optimization problems are intractable, we relax this problem to the approximated continuous problem and solve it by alternating optimization technique. We show the application of the proposed algorithm for three applications: separation of text from a background in images, separation of moving objects from a background undergoing global camera motion in videos, and separation of sinusoidal and spike components in 1-D signals. We demonstrate in each case that considering the non-additive nature of the problem can lead to a significant improvement.

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

Article number | 8625603 |

Pages (from-to) | 3192-3204 |

Number of pages | 13 |

Journal | IEEE Transactions on Image Processing |

Volume | 28 |

Issue number | 7 |

DOIs | |

State | Published - Jul 1 2019 |

### Fingerprint

### Keywords

- ADMM
- alternating optimization
- mixed integer programming
- segmentation
- Signal decomposition

### ASJC Scopus subject areas

- Software
- Computer Graphics and Computer-Aided Design

### Cite this

*IEEE Transactions on Image Processing*,

*28*(7), 3192-3204. [8625603]. https://doi.org/10.1109/TIP.2019.2894966

**An ADMM Approach to Masked Signal Decomposition Using Subspace Representation.** / Minaee, Shervin; Wang, Yao.

Research output: Contribution to journal › Article

*IEEE Transactions on Image Processing*, vol. 28, no. 7, 8625603, pp. 3192-3204. https://doi.org/10.1109/TIP.2019.2894966

}

TY - JOUR

T1 - An ADMM Approach to Masked Signal Decomposition Using Subspace Representation

AU - Minaee, Shervin

AU - Wang, Yao

PY - 2019/7/1

Y1 - 2019/7/1

N2 - Signal decomposition is a classical problem in signal processing, which aims to separate an observed signal into two or more components, each with its own property. Usually, each component is described by its own subspace or dictionary. Extensive research has been done for the case where the components are additive, but in real-world applications, the components are often non-additive. For example, an image may consist of a foreground object overlaid on a background, where each pixel either belongs to the foreground or the background. In such a situation, to separate signal components, we need to find a binary mask which shows the location of each component. Therefore, it requires solving a binary optimization problem. Since most of the binary optimization problems are intractable, we relax this problem to the approximated continuous problem and solve it by alternating optimization technique. We show the application of the proposed algorithm for three applications: separation of text from a background in images, separation of moving objects from a background undergoing global camera motion in videos, and separation of sinusoidal and spike components in 1-D signals. We demonstrate in each case that considering the non-additive nature of the problem can lead to a significant improvement.

AB - Signal decomposition is a classical problem in signal processing, which aims to separate an observed signal into two or more components, each with its own property. Usually, each component is described by its own subspace or dictionary. Extensive research has been done for the case where the components are additive, but in real-world applications, the components are often non-additive. For example, an image may consist of a foreground object overlaid on a background, where each pixel either belongs to the foreground or the background. In such a situation, to separate signal components, we need to find a binary mask which shows the location of each component. Therefore, it requires solving a binary optimization problem. Since most of the binary optimization problems are intractable, we relax this problem to the approximated continuous problem and solve it by alternating optimization technique. We show the application of the proposed algorithm for three applications: separation of text from a background in images, separation of moving objects from a background undergoing global camera motion in videos, and separation of sinusoidal and spike components in 1-D signals. We demonstrate in each case that considering the non-additive nature of the problem can lead to a significant improvement.

KW - ADMM

KW - alternating optimization

KW - mixed integer programming

KW - segmentation

KW - Signal decomposition

UR - http://www.scopus.com/inward/record.url?scp=85065980668&partnerID=8YFLogxK

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U2 - 10.1109/TIP.2019.2894966

DO - 10.1109/TIP.2019.2894966

M3 - Article

C2 - 30703020

AN - SCOPUS:85065980668

VL - 28

SP - 3192

EP - 3204

JO - IEEE Transactions on Image Processing

JF - IEEE Transactions on Image Processing

SN - 1057-7149

IS - 7

M1 - 8625603

ER -