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This paper proposes a novel fast algorithm for the decomposition and reconstruction of two-dimensional (2-D) signals by box splines. The authors have already proposed an algorithm to calculate the discrete box splines which enables the fast reconstruction of 2-D signals (images) from box spline coefficients. The problem still remains in the decomposition process to derive the box spline coefficients from an input image. This paper first investigates the decomposition algorithm which consists of the truncated geometric series of the inverse filter and the steepest descent method with momentum (SDM). The reconstruction process is also developed to correspond to the enlargement of images. The proposed algorithm is tested for the expansion of several natural images. As a result, the peak signal-to-noise ratio (PSNR) of the reconstructed images became more than 50 dB, which can be considered as enough high level. Moreover, the property of box splines are discussed in comparison with 2-D (the tensor product of) B-splines.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.8 pp.1883-1891

- Publication Date
- 2001/08/01

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Digital Signal Processing)

- Category
- Image/Visual Signal Processing

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Takeshi ASAHI, Koichi ICHIGE, Rokuya ISHII, "An Efficient Algorithm for Decomposition and Reconstruction of Images by Box Splines" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 8, pp. 1883-1891, August 2001, doi: .

Abstract: This paper proposes a novel fast algorithm for the decomposition and reconstruction of two-dimensional (2-D) signals by box splines. The authors have already proposed an algorithm to calculate the discrete box splines which enables the fast reconstruction of 2-D signals (images) from box spline coefficients. The problem still remains in the decomposition process to derive the box spline coefficients from an input image. This paper first investigates the decomposition algorithm which consists of the truncated geometric series of the inverse filter and the steepest descent method with momentum (SDM). The reconstruction process is also developed to correspond to the enlargement of images. The proposed algorithm is tested for the expansion of several natural images. As a result, the peak signal-to-noise ratio (PSNR) of the reconstructed images became more than 50 dB, which can be considered as enough high level. Moreover, the property of box splines are discussed in comparison with 2-D (the tensor product of) B-splines.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_8_1883/_p

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@ARTICLE{e84-a_8_1883,

author={Takeshi ASAHI, Koichi ICHIGE, Rokuya ISHII, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={An Efficient Algorithm for Decomposition and Reconstruction of Images by Box Splines},

year={2001},

volume={E84-A},

number={8},

pages={1883-1891},

abstract={This paper proposes a novel fast algorithm for the decomposition and reconstruction of two-dimensional (2-D) signals by box splines. The authors have already proposed an algorithm to calculate the discrete box splines which enables the fast reconstruction of 2-D signals (images) from box spline coefficients. The problem still remains in the decomposition process to derive the box spline coefficients from an input image. This paper first investigates the decomposition algorithm which consists of the truncated geometric series of the inverse filter and the steepest descent method with momentum (SDM). The reconstruction process is also developed to correspond to the enlargement of images. The proposed algorithm is tested for the expansion of several natural images. As a result, the peak signal-to-noise ratio (PSNR) of the reconstructed images became more than 50 dB, which can be considered as enough high level. Moreover, the property of box splines are discussed in comparison with 2-D (the tensor product of) B-splines.},

keywords={},

doi={},

ISSN={},

month={August},}

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TY - JOUR

TI - An Efficient Algorithm for Decomposition and Reconstruction of Images by Box Splines

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1883

EP - 1891

AU - Takeshi ASAHI

AU - Koichi ICHIGE

AU - Rokuya ISHII

PY - 2001

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E84-A

IS - 8

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - August 2001

AB - This paper proposes a novel fast algorithm for the decomposition and reconstruction of two-dimensional (2-D) signals by box splines. The authors have already proposed an algorithm to calculate the discrete box splines which enables the fast reconstruction of 2-D signals (images) from box spline coefficients. The problem still remains in the decomposition process to derive the box spline coefficients from an input image. This paper first investigates the decomposition algorithm which consists of the truncated geometric series of the inverse filter and the steepest descent method with momentum (SDM). The reconstruction process is also developed to correspond to the enlargement of images. The proposed algorithm is tested for the expansion of several natural images. As a result, the peak signal-to-noise ratio (PSNR) of the reconstructed images became more than 50 dB, which can be considered as enough high level. Moreover, the property of box splines are discussed in comparison with 2-D (the tensor product of) B-splines.

ER -