Stabilization and optimization of PLUS factorization and its application in image coding

Lei Yang; Pengwei Hao; Dapeng Wu

doi:10.1016/j.jvcir.2010.09.006

Stabilization and optimization of PLUS factorization and its application in image coding

Lei Yang^*, Pengwei Hao, Dapeng Wu

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

1 Citation (Scopus)

Abstract

A recently developed PLUS factorization holds great promise in image coding due to its simplicity and integer reversibility. However, existing PLUS factorizations did not consider stability and optimality. To address these problems, we propose methodologies to design stable and optimal PLUS factorization algorithms. Firstly, we propose three stable PLUS factorization algorithms, prove the stability theorem under no perturbation and analyze stability under perturbation. Furthermore, we obtain a closed-form formula for transform error, and use the formula to design an algorithm for optimal PLUS factorization. Then, we apply the PLUS factorization to image coding. The integer DCTs implemented with the optimal PLUS factorizations found by our algorithms outperform the integer DCT with expansion factors in terms of entropy. The optimal PLUS factorizations are superior to the lifting factorization in JPEG-XR. The experimental results agree with analytical results of PLUS factorization, and show superior performance of our algorithms in image coding. © 2010 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	9-22
Journal	Journal of Visual Communication and Image Representation
Volume	22
Issue number	1
DOIs	https://doi.org/10.1016/j.jvcir.2010.09.006
Publication status	Published - Jan 2011
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Discrete cosine transform
Image compression
Integer reversible transform
Lapped Transform
Lifting factorization
Optimization
PLUS factorization
Stable algorithm
Transform coding

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title = "Stabilization and optimization of PLUS factorization and its application in image coding",

abstract = "A recently developed PLUS factorization holds great promise in image coding due to its simplicity and integer reversibility. However, existing PLUS factorizations did not consider stability and optimality. To address these problems, we propose methodologies to design stable and optimal PLUS factorization algorithms. Firstly, we propose three stable PLUS factorization algorithms, prove the stability theorem under no perturbation and analyze stability under perturbation. Furthermore, we obtain a closed-form formula for transform error, and use the formula to design an algorithm for optimal PLUS factorization. Then, we apply the PLUS factorization to image coding. The integer DCTs implemented with the optimal PLUS factorizations found by our algorithms outperform the integer DCT with expansion factors in terms of entropy. The optimal PLUS factorizations are superior to the lifting factorization in JPEG-XR. The experimental results agree with analytical results of PLUS factorization, and show superior performance of our algorithms in image coding. {\textcopyright} 2010 Elsevier Inc. All rights reserved.",

keywords = "Discrete cosine transform, Image compression, Integer reversible transform, Lapped Transform, Lifting factorization, Optimization, PLUS factorization, Stable algorithm, Transform coding",

author = "Lei Yang and Pengwei Hao and Dapeng Wu",

note = "Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].",

year = "2011",

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doi = "10.1016/j.jvcir.2010.09.006",

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AU - Yang, Lei

AU - Hao, Pengwei

AU - Wu, Dapeng

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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N2 - A recently developed PLUS factorization holds great promise in image coding due to its simplicity and integer reversibility. However, existing PLUS factorizations did not consider stability and optimality. To address these problems, we propose methodologies to design stable and optimal PLUS factorization algorithms. Firstly, we propose three stable PLUS factorization algorithms, prove the stability theorem under no perturbation and analyze stability under perturbation. Furthermore, we obtain a closed-form formula for transform error, and use the formula to design an algorithm for optimal PLUS factorization. Then, we apply the PLUS factorization to image coding. The integer DCTs implemented with the optimal PLUS factorizations found by our algorithms outperform the integer DCT with expansion factors in terms of entropy. The optimal PLUS factorizations are superior to the lifting factorization in JPEG-XR. The experimental results agree with analytical results of PLUS factorization, and show superior performance of our algorithms in image coding. © 2010 Elsevier Inc. All rights reserved.

AB - A recently developed PLUS factorization holds great promise in image coding due to its simplicity and integer reversibility. However, existing PLUS factorizations did not consider stability and optimality. To address these problems, we propose methodologies to design stable and optimal PLUS factorization algorithms. Firstly, we propose three stable PLUS factorization algorithms, prove the stability theorem under no perturbation and analyze stability under perturbation. Furthermore, we obtain a closed-form formula for transform error, and use the formula to design an algorithm for optimal PLUS factorization. Then, we apply the PLUS factorization to image coding. The integer DCTs implemented with the optimal PLUS factorizations found by our algorithms outperform the integer DCT with expansion factors in terms of entropy. The optimal PLUS factorizations are superior to the lifting factorization in JPEG-XR. The experimental results agree with analytical results of PLUS factorization, and show superior performance of our algorithms in image coding. © 2010 Elsevier Inc. All rights reserved.

KW - Discrete cosine transform

KW - Image compression

KW - Integer reversible transform

KW - Lapped Transform

KW - Lifting factorization

KW - Optimization

KW - PLUS factorization

KW - Stable algorithm

KW - Transform coding

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U2 - 10.1016/j.jvcir.2010.09.006

DO - 10.1016/j.jvcir.2010.09.006

M3 - RGC 21 - Publication in refereed journal

SN - 1047-3203

VL - 22

SP - 9

EP - 22

JO - Journal of Visual Communication and Image Representation

JF - Journal of Visual Communication and Image Representation

IS - 1

ER -

Stabilization and optimization of PLUS factorization and its application in image coding

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Research Keywords

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