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The technique of lossless compression via substring enumeration (CSE) is a kind of enumerative code and uses a probabilistic model built from the circular string of an input source for encoding a one-dimensional (1D) source. CSE is applicable to two-dimensional (2D) sources, such as images, by dealing with a line of pixels of a 2D source as a symbol of an extended alphabet. At the initial step of CSE encoding process, we need to output the number of occurrences of all symbols of the extended alphabet, so that the time complexity increases exponentially when the size of source becomes large. To reduce computational time, we can rearrange pixels of a 2D source into a 1D source string along a space-filling curve like a Hilbert curve. However, information on adjacent cells in a 2D source may be lost in the conversion. To reduce the time complexity and compress a 2D source without converting to a 1D source, we propose a new CSE which can encode a 2D source in a block-by-block fashion instead of in a line-by-line fashion. The proposed algorithm uses the flat torus of an input 2D source as a probabilistic model instead of the circular string of the source. Moreover, we prove the asymptotic optimality of the proposed algorithm for 2D general sources.
Takahiro OTA
Nagano Prefectural Institute of Technology
Hiroyoshi MORITA
The University of Electro-Communications
Akiko MANADA
Shonan Institute of Technology
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Takahiro OTA, Hiroyoshi MORITA, Akiko MANADA, "A Universal Two-Dimensional Source Coding by Means of Subblock Enumeration" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 2, pp. 440-449, February 2019, doi: 10.1587/transfun.E102.A.440.
Abstract: The technique of lossless compression via substring enumeration (CSE) is a kind of enumerative code and uses a probabilistic model built from the circular string of an input source for encoding a one-dimensional (1D) source. CSE is applicable to two-dimensional (2D) sources, such as images, by dealing with a line of pixels of a 2D source as a symbol of an extended alphabet. At the initial step of CSE encoding process, we need to output the number of occurrences of all symbols of the extended alphabet, so that the time complexity increases exponentially when the size of source becomes large. To reduce computational time, we can rearrange pixels of a 2D source into a 1D source string along a space-filling curve like a Hilbert curve. However, information on adjacent cells in a 2D source may be lost in the conversion. To reduce the time complexity and compress a 2D source without converting to a 1D source, we propose a new CSE which can encode a 2D source in a block-by-block fashion instead of in a line-by-line fashion. The proposed algorithm uses the flat torus of an input 2D source as a probabilistic model instead of the circular string of the source. Moreover, we prove the asymptotic optimality of the proposed algorithm for 2D general sources.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.440/_p
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@ARTICLE{e102-a_2_440,
author={Takahiro OTA, Hiroyoshi MORITA, Akiko MANADA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Universal Two-Dimensional Source Coding by Means of Subblock Enumeration},
year={2019},
volume={E102-A},
number={2},
pages={440-449},
abstract={The technique of lossless compression via substring enumeration (CSE) is a kind of enumerative code and uses a probabilistic model built from the circular string of an input source for encoding a one-dimensional (1D) source. CSE is applicable to two-dimensional (2D) sources, such as images, by dealing with a line of pixels of a 2D source as a symbol of an extended alphabet. At the initial step of CSE encoding process, we need to output the number of occurrences of all symbols of the extended alphabet, so that the time complexity increases exponentially when the size of source becomes large. To reduce computational time, we can rearrange pixels of a 2D source into a 1D source string along a space-filling curve like a Hilbert curve. However, information on adjacent cells in a 2D source may be lost in the conversion. To reduce the time complexity and compress a 2D source without converting to a 1D source, we propose a new CSE which can encode a 2D source in a block-by-block fashion instead of in a line-by-line fashion. The proposed algorithm uses the flat torus of an input 2D source as a probabilistic model instead of the circular string of the source. Moreover, we prove the asymptotic optimality of the proposed algorithm for 2D general sources.},
keywords={},
doi={10.1587/transfun.E102.A.440},
ISSN={1745-1337},
month={February},}
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TY - JOUR
TI - A Universal Two-Dimensional Source Coding by Means of Subblock Enumeration
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 440
EP - 449
AU - Takahiro OTA
AU - Hiroyoshi MORITA
AU - Akiko MANADA
PY - 2019
DO - 10.1587/transfun.E102.A.440
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2019
AB - The technique of lossless compression via substring enumeration (CSE) is a kind of enumerative code and uses a probabilistic model built from the circular string of an input source for encoding a one-dimensional (1D) source. CSE is applicable to two-dimensional (2D) sources, such as images, by dealing with a line of pixels of a 2D source as a symbol of an extended alphabet. At the initial step of CSE encoding process, we need to output the number of occurrences of all symbols of the extended alphabet, so that the time complexity increases exponentially when the size of source becomes large. To reduce computational time, we can rearrange pixels of a 2D source into a 1D source string along a space-filling curve like a Hilbert curve. However, information on adjacent cells in a 2D source may be lost in the conversion. To reduce the time complexity and compress a 2D source without converting to a 1D source, we propose a new CSE which can encode a 2D source in a block-by-block fashion instead of in a line-by-line fashion. The proposed algorithm uses the flat torus of an input 2D source as a probabilistic model instead of the circular string of the source. Moreover, we prove the asymptotic optimality of the proposed algorithm for 2D general sources.
ER -