基于整数U变换的图像压缩方法

doi:10.12141/j.issn.1000-565X.230784

华南理工大学学报(自然科学版) ›› 2024, Vol. 52 ›› Issue (10): 124-134.doi: 10.12141/j.issn.1000-565X.230784

所属专题： 2024年图像处理

基于整数U变换的图像压缩方法

袁茜茜¹^,²(), 蔡占川³, 石武祯¹(), 尹文楠¹

^1.深圳大学电子与信息工程学院/广东省数字创意技术工程实验室，广东深圳 518060
^2.广东工业大学计算机学院，广东广州 510006
^3.澳门科技大学创新工程学院，澳门 999078

收稿日期:2023-12-24 出版日期:2024-10-25 发布日期:2024-03-22
通信作者: 石武祯 E-mail:xxyuan@gdut.edu.cn;wzhshi@szu.edu.cn
作者简介:袁茜茜（1992—），女，博士，讲师，主要从事计算机图形图像处理研究。E-mail： xxyuan@gdut.edu.cn
基金资助:
国家自然科学基金资助项目(62101346);广东省重点领域研发计划项目(2022B0101010001);广东省基础与应用基础研究基金资助项目(2021A1515011702)

Image Compression Method Based on the Integer U Transform Algorithm

YUAN Xixi¹^,²(), CAI Zhanchuan³, SHI Wuzhen¹(), YIN Wennan¹

^1.College of Electronics and Information Engineering/ Guangdong Provincal Engineering Laboratory for Digital Creative Technology，Shenzhen University，Shenzhen 518060，Guangdong，China
^2.School of Computer Science and Technology，Guangdong University of Technology，Guangzhou 510006，Guangdong，China
^3.Faculty of Innovation Engineering，Macau University of Science and Technology，Macau 999078，China

Received:2023-12-24 Online:2024-10-25 Published:2024-03-22
Contact: SHI Wuzhen E-mail:xxyuan@gdut.edu.cn;wzhshi@szu.edu.cn
Supported by:
the National Natural Science Foundation of China(62101346);the Key-Area R & D Program of Guangdong Province(2022B0101010001);the Basic and Applied Basic Research Foundation of Guangdong Province(2021A1515011702)

摘要/Abstract

摘要：

整数变换方法因其较快的计算速度被国际图像和视频编码标准广泛采纳。现有基于连续正交函数系的整数变换方法不仅难以获得原始变换的准确整数形式，而且无法克服在非连续信号表达时出现的吉布斯震荡现象，降低了重构图像质量。为此，文中提出了基于非连续正交U系统的整数变换算法及其图像压缩方法。首先，采用分段积分法和施密特正交化法计算出U系统的2维正交变换矩阵，提取行向量的缩放因子得到整数矩阵；接着，建立整数U矩阵的可逆正交变换方法，使用整数矩阵将离散图像信息的能量集中到少量数据集，同时将缩放因子与量化步骤合并以减轻计算负担；然后，采用矩阵分解法将整数U矩阵分解为稀疏矩阵的乘积，从而实现图像变换的快速计算；最后，设计基于整数U变换模块和逆变换模块的图像压缩方法，用于减轻图像存储和传输压力。实验结果表明：文中方法与其他相关方法相比，可以降低图像可逆变换的截断误差；在图像和视频压缩实验中，在相同的压缩率下文中方法获得的压缩图像质量更高，而且快速变换方法可以有效地节省运算时间。

关键词: 图像压缩, 整数变换, 非连续正交U系统, 吉布斯现象, 快速计算

Abstract:

The integer transform methods are widely adopted in international image and video coding standards because of its fast calculation speed. The existing integer transform methods based on the continuous orthogonal function system not only struggle to obtain the exact integer form of the original transform, but also fails to overcome the Gibbs oscillation phenomenon in the discontinuous signal representation, thus reduces the reconstructed image quality. This paper proposed a new integer transform algorithm and its image compression method based on discontinuous orthogonal U-system. Firstly, the piecewise integration and the Gram-Schmidt process were used to calculate the two-dimensional orthogonal matrix of the U-system, and the scaling factors of row vectors were extracted to obtain the integer matrix. Secondly, the reversible integer U transform was established and the integer matrix was applied to concentrate the energy of images into a small amount of data sets, while merging scaling factors with quantization to reduce computational burden. Then, the fast integer U transform was achieved by using matrix decomposition and sparse matrices. Finally, the integer U transform module and inverse transform module were designed to alleviate the pressure of image storage and transmission. Experimental results show that the proposed method can reduce truncation errors of reversible image transform compared with related algorithms; the new method obtains higher compression image quality in image and video compression experiments, and the fast transform algorithm effectively saves computational time.

Key words: image compression, integer transform, discontinuous orthogonal U-system, Gibbs phenomenon, fast computation

中图分类号:

TP391.41

袁茜茜, 蔡占川, 石武祯, 尹文楠. 基于整数U变换的图像压缩方法[J]. 华南理工大学学报(自然科学版), 2024, 52(10): 124-134.

YUAN Xixi, CAI Zhanchuan, SHI Wuzhen, YIN Wennan. Image Compression Method Based on the Integer U Transform Algorithm[J]. Journal of South China University of Technology(Natural Science Edition), 2024, 52(10): 124-134.

图/表 12

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表5

图像压缩的复杂性和运行时间"

方法	时间复杂度^1）	空间复杂度	压缩和解压缩时间/s
方法	时间复杂度^1）	空间复杂度	Boats	Bus
DCT	$m n a 1 + b 1 / 4$	8mn	1.202	1.522
IntH264	$m n a 2 + b 2 / 4$	4mn	1.176	1.343
IntWMV	$m n a 3 + b 3 / 4$	4mn	1.165	1.380
IntAVS	$m n a 4 + b 4 / 4$	4mn	1.186	1.373
IntHEVC	$m n a 5 + b 5 / 4$	4mn	1.156	1.324
Slant	$m n a 6 + b 6 / 4$	8mn	1.168	1.329
HV	$m n a 7 + b 7 / 4$	8mn	1.026	1.120
UT	$m n a 8 + b 8 / 4$	8mn	1.311	1.515
IntUT	$m n a 9 + b 9 / 4$	4mn	1.172	1.302
FIntUT	$m n a 10 + b 10 / 4$	4mn	0.869	0.934

表5

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采样块编号	PSNR/dB
采样块编号	DCT	IntH264	IntWMV	IntAVS	IntHEVC	UT	IntUT
平均	320.983	327.082	326.929	327.672	75.418	320.799	329.556
1	323.270	323.878	325.550	324.697	72.859	321.302	326.902
2	320.346	327.819	325.498	328.505	73.766	320.859	329.750
3	321.361	329.643	328.611	330.852	75.755	322.428	332.581
4	318.953	326.986	328.055	326.632	79.291	318.607	328.991

方法	PSNR/dB						SSIM
方法	r=0.500	r=0.563	r=0.625	r=0.688	r=0.750	r=0.813	r=0.500	r=0.563	r=0.625	r=0.688	r=0.750	r=0.813
DCT	27.431	27.958	28.627	29.237	30.115	31.153	0.707	0.740	0.772	0.800	0.831	0.857
InTh264	27.375	27.928	28.511	29.214	30.095	31.217	0.707	0.739	0.768	0.801	0.828	0.858
IntWMV	27.470	28.001	28.531	29.162	29.970	31.281	0.709	0.741	0.769	0.798	0.827	0.857
IntAVS	27.452	27.959	28.611	29.259	30.151	31.035	0.709	0.740	0.771	0.801	0.831	0.855
IndHEVC	27.436	27.995	28.625	29.264	29.979	31.165	0.708	0.741	0.771	0.801	0.827	0.858
Slant	27.331	28.118	28.752	29.587	30.380	31.937	0.704	0.745	0.777	0.810	0.839	0.874
HV	27.362	27.874	28.602	29.360	30.219	31.347	0.715	0.747	0.782	0.811	0.841	0.871
UT	27.620	28.374	28.735	30.057	31.031	31.725	0.716	0.749	0.781	0.817	0.845	0.872
IntUT	27.736	28.375	29.034	30.208	31.245	32.793	0.717	0.753	0.783	0.825	0.855	0.887

方法	PSNR/dB					SSIM
方法	Bus	Coastguard	Flower	Waterfafall	Hall	Bus	Coastguard	Flower	Waterfall	Hall
DCT	25.839	31.775	23.831	33.045	38.529	0.809	0.911	0.786	0.906	0.976
InTh264	25.946	31.835	23.770	32.415	38.288	0.813	0.913	0.784	0.893	0.975
IntWMV	26.104	31.908	23.830	32.756	38.487	0.817	0.914	0.785	0.900	0.976
IntAVS	26.203	32.246	23.932	33.500	39.487	0.821	0.917	0.788	0.913	0.979
IndHEVC	25.839	31.986	23.811	33.035	38.505	0.809	0.914	0.786	0.905	0.976
Slant	26.270	31.674	24.001	32.566	37.397	0.837	0.918	0.793	0.898	0.968
HV	26.720	30.851	23.341	32.734	32.096	0.859	0.910	0.774	0.906	0.917
UT	27.228	31.924	23.947	33.606	39.104	0.860	0.913	0.791	0.918	0.971
IntUT	27.787	32.897	24.070	33.902	39.958	0.871	0.930	0.797	0.921	0.982

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基于整数U变换的图像压缩方法

Image Compression Method Based on the Integer U Transform Algorithm

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运算	计算量
运算	DCT	H.264	WMV-9	AVS-China	HEVC	Slant	HV	UT	IntUT	FIntUT
×	64	64	64	64	64	64	40	64	52	22
+/-	56	56	56	56	56	56	35	56	56	41