CLC number: TN919.81

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Received: 2003-12-10

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YANG Zhong-qi, BAI Zhi-can, LI Dong-mei, YANG Chang-sheng. A high fidelity VQ coding algorithm with region adaptive subbanding[J]. Journal of Zhejiang University Science A, 2005, 6(1): 43-48.

@article{title="A high fidelity VQ coding algorithm with region adaptive subbanding",

author="YANG Zhong-qi, BAI Zhi-can, LI Dong-mei, YANG Chang-sheng",

journal="Journal of Zhejiang University Science A",

volume="6",

number="1",

pages="43-48",

year="2005",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.2005.A0043"

}

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%T A high fidelity VQ coding algorithm with region adaptive subbanding

%A YANG Zhong-qi

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%J Journal of Zhejiang University SCIENCE A

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TY - JOUR

T1 - A high fidelity VQ coding algorithm with region adaptive subbanding

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A1 - BAI Zhi-can

A1 - LI Dong-mei

A1 - YANG Chang-sheng

J0 - Journal of Zhejiang University Science A

VL - 6

IS - 1

SP - 43

EP - 48

%@ 1673-565X

Y1 - 2005

PB - Zhejiang University Press & Springer

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DOI - 10.1631/jzus.2005.A0043

**Abstract: **Image subbands can be obtained by using filterbank. Traditional compression method uses direct entropy coding for each subband. After studying the energy distribution in image subbands, we proposed a vector quantization (VQ) coding algorithm to image subband. In the algorithm, vector quantizers were adaptively designed for high-frequency bands in an image. In particular, the edges of the image were examined and fewer bits were assigned to high-energy regions. The experimental result showed that the algorithm had higher SNR and higher compression ratio than possible by traditional subband coding, JPEG and JPEG 2000.

**
**

. INTRODUCTION

This paper proposes a near-lossless compression algorithm which applies a high fidelity vector quantization method to image subbands. The original image was first separated by filterbank into seven subbands. The regions around the edges in each subband were then extracted, and divided by their orientations into several sub-regions. In the third step, different codebook (vector quantizer) was designed for different region, and fewer bits were assigned to regions of higher-energy in the subband. Better compression ratio and fidelity were achieved.

. ENERGY DISTRIBUTION IN IMAGE SUBBANDS

A traditional image compression scheme based on a filterbank splits the signal into

Let

The energy ratio of the

Let the compact energy of the

In the

The proofs of the above properties and Corollaries are given in Kwon and Chellappa (

Since the property of the compact energy ratio is similar to the property of the energy ratio, we can conclude that the compact energy of each subband is almost equally distributed up to

The energy distribution of the image subbands has the following characteristics:

(1) Energy packing property toward the lower frequency subbands: The energy decreases monotonically as

(2) Energy packing property toward the edges: Most of the total HFS energy is concentrated on the edges. The Lena image has been found to contain 84.9% of the total HFS energy in its edge-regions.

(3) Directionality of the energy distribution: Analysis of the compact energy of the subedge-regions showed that the horizontal, vertical, and off-diagonal edge-region has relatively more energy in the horizontal, vertical, and diagonal subbands, respectively, and that the diagonal edge-region has relatively less energy in the diagonal subbands.

. VQ CODING ALGORITHM WITH REGION ADAPTIVE SUBBANDING

(1) Based on the energy packing property toward the edges, for efficient transmission of image, the edge-regions should be emphasized;

(2) Based on the directionality of the energy distribution, different bits should be allocated for different sub-regions;

(3) Based on the energy packing property toward the lower frequency subbands, more bits should be assigned to the lower frequency subbands.

Based on the aforementioned conclusions, we present a high fidelity vector quantization (VQ) coding algorithm with region adaptive subbanding. Our encoder is effective at:

(1) Splitting the original image into seven subbands using two-level Walsh filtering;

(2) Detecting the edges for each subband using Canny detector (Canny,

(3) Partitioning each subband into vectors;

(4) Extracting edge-regions for each subband;

(5) Encoding LFS using VDPCM and encoding HFS using VQ;

(6) Designing entropy coder.

In what follows, we describe in detail each step of our encoder shown in Fig.

Based on the above property, the subband can be downsampled losslessly by two. We have the following conclusion:

The edge-region extraction algorithm of Kwon and Chellappa (

Let the vector-edge-region of the (

A set of well-designed codebooks is crucial for good performance of the reconstruction image. In the frequency domain, the frequency is divided into seven subbands after Walsh transform. Thus, the vectors are classified into seven classes by their subbands in VQ.

A codebook was designed for each sub-region of each subband, with Linde-Buzo-Gray (LBG) algorithm being used to train and obtain the corresponding codebook. For detail of the LBG algorithm, please refer to Linde et al.(

In our approach, dynamic rate allocation was not adequate. Our goal was to use vector quantization coding techniques in the subbands, and to rely on the optimal rate allocation to discriminate between all the possible techniques on each sub-region of each subband. Different number of bits was assigned to each sub-region of each subband by assuming its distributions. Our bit allocation scheme could allocate more bits for the vectors of the LFS and fewer bits for the vectors of the HFS.

Two-dimension VDPCM was selected in this algorithm; Fig.

In the case of the border, one of the coefficients may be absent, then the formula above can be transformed into

In our experiment, the sub-regions of the LFS were directly partitioned into vectors of 4(4 pixels, then the error vectors were trained using the LBG algorithm to obtain the corresponding codebook of the LFS sub-regions.

. EXPERIMENTAL RESULT AND CONCLUSION

Algorithm | Image | RMSE |
PSNR |
CR |

Proposed algorithm | Lena | 2.493 | 40.196 | 9.841 |

Averser8 | 2.716 | 39.451 | 8.854 | |

JPEG (Penne, 1988) |
Lena | 3.3 | 37.7 | 8.4 |

Averser8 | 4.5 | 35.0 | 5.2 | |

JPEG2000 (ISO/IEC JTC1/SC29/WG1 N1577, 2000) |
Lena | 2.6 | 39.7 | 8.68 |

Averser8 | 3.5 | 38.4 | 8.75 |

1. Our algorithm can yield better reconstruction image quality and higher compression ratio than other traditional algorithms such as JPEG.

2. Compared with typical VQ coding, this algorithm has higher

3. Compared with traditional subband coding, this algorithm has higher compression ratio and no ringing effect.

The compression performance of our algorithm shows that it can achieve high fidelity image compression with great improvement in compression ratio. So this algorithm has promising prospect in field of high fidelity image compression, especially the compression field of satellite remote sensing images, medical images, and so on.

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