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In this study, we introduce shift-invariant sparse image representations using tree-structured dictionaries. Sparse coding is a generative signal model that approximates signals by the linear combinations of atoms in a dictionary. Since a sparsity penalty is introduced during signal approximation and dictionary learning, the dictionary represents the primal structures of the signals. Under the shift-invariance constraint, the dictionary comprises translated structuring elements (SEs). The computational cost and number of atoms in the dictionary increase along with the increasing number of SEs. In this paper, we propose an algorithm for shift-invariant sparse image representation, in which SEs are learnt with a tree-structured approach. By using a tree-structured dictionary, we can reduce the computational cost of the image decomposition to the logarithmic order of the number of SEs. We also present the results of our experiments on the SE learning and the use of our algorithm in image recovery applications.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.11 pp.2809-2818

- Publication Date
- 2009/11/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E92.A.2809

- Type of Manuscript
- Special Section PAPER (Special Section on Smart Multimedia & Communication Systems)

- Category
- Image Processing

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Makoto NAKASHIZUKA, Hidenari NISHIURA, Youji IIGUNI, "Shift-Invariant Sparse Image Representations Using Tree-Structured Dictionaries" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 11, pp. 2809-2818, November 2009, doi: 10.1587/transfun.E92.A.2809.

Abstract: In this study, we introduce shift-invariant sparse image representations using tree-structured dictionaries. Sparse coding is a generative signal model that approximates signals by the linear combinations of atoms in a dictionary. Since a sparsity penalty is introduced during signal approximation and dictionary learning, the dictionary represents the primal structures of the signals. Under the shift-invariance constraint, the dictionary comprises translated structuring elements (SEs). The computational cost and number of atoms in the dictionary increase along with the increasing number of SEs. In this paper, we propose an algorithm for shift-invariant sparse image representation, in which SEs are learnt with a tree-structured approach. By using a tree-structured dictionary, we can reduce the computational cost of the image decomposition to the logarithmic order of the number of SEs. We also present the results of our experiments on the SE learning and the use of our algorithm in image recovery applications.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.2809/_p

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@ARTICLE{e92-a_11_2809,

author={Makoto NAKASHIZUKA, Hidenari NISHIURA, Youji IIGUNI, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Shift-Invariant Sparse Image Representations Using Tree-Structured Dictionaries},

year={2009},

volume={E92-A},

number={11},

pages={2809-2818},

abstract={In this study, we introduce shift-invariant sparse image representations using tree-structured dictionaries. Sparse coding is a generative signal model that approximates signals by the linear combinations of atoms in a dictionary. Since a sparsity penalty is introduced during signal approximation and dictionary learning, the dictionary represents the primal structures of the signals. Under the shift-invariance constraint, the dictionary comprises translated structuring elements (SEs). The computational cost and number of atoms in the dictionary increase along with the increasing number of SEs. In this paper, we propose an algorithm for shift-invariant sparse image representation, in which SEs are learnt with a tree-structured approach. By using a tree-structured dictionary, we can reduce the computational cost of the image decomposition to the logarithmic order of the number of SEs. We also present the results of our experiments on the SE learning and the use of our algorithm in image recovery applications.},

keywords={},

doi={10.1587/transfun.E92.A.2809},

ISSN={1745-1337},

month={November},}

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TY - JOUR

TI - Shift-Invariant Sparse Image Representations Using Tree-Structured Dictionaries

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2809

EP - 2818

AU - Makoto NAKASHIZUKA

AU - Hidenari NISHIURA

AU - Youji IIGUNI

PY - 2009

DO - 10.1587/transfun.E92.A.2809

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E92-A

IS - 11

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - November 2009

AB - In this study, we introduce shift-invariant sparse image representations using tree-structured dictionaries. Sparse coding is a generative signal model that approximates signals by the linear combinations of atoms in a dictionary. Since a sparsity penalty is introduced during signal approximation and dictionary learning, the dictionary represents the primal structures of the signals. Under the shift-invariance constraint, the dictionary comprises translated structuring elements (SEs). The computational cost and number of atoms in the dictionary increase along with the increasing number of SEs. In this paper, we propose an algorithm for shift-invariant sparse image representation, in which SEs are learnt with a tree-structured approach. By using a tree-structured dictionary, we can reduce the computational cost of the image decomposition to the logarithmic order of the number of SEs. We also present the results of our experiments on the SE learning and the use of our algorithm in image recovery applications.

ER -