### Abstract

The singular value decomposition (SVD) is an effective tool to reconstruct the image approximately towards the original image. This paper will introduce and explores image reconstruction by applying the SVD on gray-scale image. As quality measurements, we used Compression Ratio (CR) and Root-Mean Squared Error (RMSE). The results indicated that for certain images the value of k is smaller than for other images. The value of k is defined as the rank for the closet matrix and the constant integer k can be chosen expectantly less than diagonal matrix n, and the digital image corresponding to outer product expansion, Q _{k} still have very close to the original image.

Original language | English |
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Title of host publication | AIP Conference Proceedings |

Pages | 269-274 |

Number of pages | 6 |

Volume | 1522 |

DOIs | |

Publication status | Published - 2013 |

Event | 20th National Symposium on Mathematical Sciences - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation, SKSM 2012 - Putrajaya Duration: 18 Dec 2012 → 20 Dec 2012 |

### Other

Other | 20th National Symposium on Mathematical Sciences - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation, SKSM 2012 |
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City | Putrajaya |

Period | 18/12/12 → 20/12/12 |

### Fingerprint

### Keywords

- Gray-scale image
- Image reconstruction
- Singular Value Decomposition (SVD)

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*AIP Conference Proceedings*(Vol. 1522, pp. 269-274) https://doi.org/10.1063/1.4801133

**Image reconstruction using singular value decomposition.** / Abdul Karima, Samsul Ariffin; Mohd Mustafa, Muhammad Izzatullah; Abdul Karim, Bakri; Hasan, Mohammad Khatim; Sulaiman, Jumat; Ismail, Mohd Tahir.

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

*AIP Conference Proceedings.*vol. 1522, pp. 269-274, 20th National Symposium on Mathematical Sciences - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation, SKSM 2012, Putrajaya, 18/12/12. https://doi.org/10.1063/1.4801133

}

TY - GEN

T1 - Image reconstruction using singular value decomposition

AU - Abdul Karima, Samsul Ariffin

AU - Mohd Mustafa, Muhammad Izzatullah

AU - Abdul Karim, Bakri

AU - Hasan, Mohammad Khatim

AU - Sulaiman, Jumat

AU - Ismail, Mohd Tahir

PY - 2013

Y1 - 2013

N2 - The singular value decomposition (SVD) is an effective tool to reconstruct the image approximately towards the original image. This paper will introduce and explores image reconstruction by applying the SVD on gray-scale image. As quality measurements, we used Compression Ratio (CR) and Root-Mean Squared Error (RMSE). The results indicated that for certain images the value of k is smaller than for other images. The value of k is defined as the rank for the closet matrix and the constant integer k can be chosen expectantly less than diagonal matrix n, and the digital image corresponding to outer product expansion, Q k still have very close to the original image.

AB - The singular value decomposition (SVD) is an effective tool to reconstruct the image approximately towards the original image. This paper will introduce and explores image reconstruction by applying the SVD on gray-scale image. As quality measurements, we used Compression Ratio (CR) and Root-Mean Squared Error (RMSE). The results indicated that for certain images the value of k is smaller than for other images. The value of k is defined as the rank for the closet matrix and the constant integer k can be chosen expectantly less than diagonal matrix n, and the digital image corresponding to outer product expansion, Q k still have very close to the original image.

KW - Gray-scale image

KW - Image reconstruction

KW - Singular Value Decomposition (SVD)

UR - http://www.scopus.com/inward/record.url?scp=84876891606&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876891606&partnerID=8YFLogxK

U2 - 10.1063/1.4801133

DO - 10.1063/1.4801133

M3 - Conference contribution

SN - 9780735411500

VL - 1522

SP - 269

EP - 274

BT - AIP Conference Proceedings

ER -