Image Compression Method Based on the Integer U Transform Algorithm

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

Abstract

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

CLC Number:

TP391.41

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.

Figures/Tables 12

Fig.1

Table 1

Fig.2

Fig.3

Table 2

Fig.4

Table 3

Fig.5

Fig.6

Table 4

Fig.7

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

References 29

1	杨春玲，梁梓文．特征域近端高维梯度下降图像压缩感知重构网络［J］．华南理工大学学报（自然科学版），2024，52（3）：119-130.
	YANG Chunling， LIANG Ziwen ．Feature-domain proximal high-dimensional gradient descent network for image compressed sensing［J］．Journal of South China University of Technology （Natural Science Edition），2024，52（3）：119-130.
2	TELLEZ D， LITJENS G， LAAK J V D，et al ．Neural image compression for gigapixel histopathology image analysis［J］．IEEE Transactions on Pattern Analysis and Machine Intelligence，2021，43（2）：567-578.
3	YAN N， GAO C， LIU D，et al ．SSSIC：semantics-to-signal scalable image coding with learned structural representations［J］．IEEE Transactions on Image Processing，2021，30：8939-8954.
4	QIU H， ZHENG Q， MEMMI G，et al ．Deep residual learning-based enhanced JPEG compression in the internet of things［J］．IEEE Transactions on Industrial Informatics，2021，17（3）：2124-2133.
5	SULLIVAN G J， TOPIWALA P N， LUTHRA A ． The H.264/AVC advanced video coding standard：overview and introduction to the fidelity range extensions［C］∥ Proceedings of the SPIE 49th Annual Meeting on Optical Science and Technology．Denver：SPIE，2004：454-474.
6	WANG Yong， HUANG Jiwu ．Robust AVS audio watermarking［J］．Science China：Information Sciences，2010，53（3）：607-618.
7	SRINIVASAN S， HSU P J， HOLCOMB T，et al ．Windows media video 9：overview and applications［J］．Signal Processing：Image Communication，2004，19（9）：851-875.
8	CHEN Z， PAN X ．An optimized rate control for low-delay H.265/HEVC［J］．IEEE Transactions on Image Processing，2019，28（9）：4541-4552.
9	ZHU B， LIU J Z， CAULEY S F，et al ．Image reconstruction by domain-transform manifold learning［J］．Nature，2018，555（7697）：487-492.
10	CINTRA R J， BAYER F M， TABLADA C ．Low-complexity 8-point DCT approximations based on integer functions［J］．Signal Processing，2014，99：201-214.
11	TERRY-JACK M， O’KEEFE S ．Fourier transform bounded Kolmogorov complexity［J］．Physica D：Nonlinear Phenomena，2023，453：133824/1-7.
12	PARFIENIUK M ．Lifting-based algorithms for computing the 4-point Walsh-Hadamard transform［C］∥ Proceedings of 2019 Signal Processing Symposium．Krakow：IEEE，2019：221-226.
13	SHAIK A， THANIKAISELVAN V ．Comparative analysis of integer wavelet transforms in reversible data hiding using threshold based histogram modification ［J］．Journal of King Saud University：Computer and Information Sciences，2021，33（7）：878-889.
14	LI Q， ELIE B Z， WILLIAM A ．The impact and treatment of the Gibbs phenomenon in immersed boundary method simulations of momentum and scalar transport ［J］．Journal of Computational Physics，2016，310：237-251.
15	齐东旭，冯玉瑜．关于Fourier—U级数的收敛性［J］．中国科学技术大学学报，1983，13（）：7-17.
	QI Dong-xu， FENG Yu-yu ．On the convergence of Fourier-U series［J］．Journal of China University of Science and Technology，1983，13（S1）：7-17.
16	FENG Y， QI D ．A sequence of piecewise orthogonal polynomials［J］．SIAM Journal Mathematical Analysis，1984，15（4）：834-844.
17	SONG R， MA H， WANG T，et al ．The complete orthogonal V-system and its applications［J］．Communications on Pure & Applied Analysis，2007，6（3）：853-871.
18	WALSH J L ．A closed set of normal orthogonal functions［J］．American Journal of Mathematics，1923，45（1）：5-24.
19	ALFRED H ．Zur Theorie der orthogonalen Funktionensysteme［J］．Mathematische Annalen，1910，69：331-371.
20	齐东旭，陶尘钧，宋瑞霞，等．基于正交完备U-系统的参数曲线图组表达［J］．计算机学报，2006，29（5）：778-785.
	QI Dong-xu， TAO Chen-jun， SONG Rui-xia，et al ．Representation for a group of parametric curves based on the orthogonal complete U-system［J］．Chinese Journal of Computers，2006，29（5）：778-785.
21	YUAN X， CAI Z ．A generalized Walsh system and its fast algorithm［J］．IEEE Transactions on Signal Processing，2021，69：5222-5233.
22	齐东旭，宋瑞霞，李坚．非连续正交函数［M］．北京：科学出版社，2011.
23	ZHANG Y， CAI Z， XIONG G ．A new image compression algorithm based on non-uniform partition and U-system［J］．IEEE Transactions on Multimedia，2020，23：1069-1082.
24	ZHANG Y， CAI Z， YE B ．An image importance partition-based compression method for COVID-19 computed tomography scan［J］．IEEE Transactions on Industrial Informatics，2022，18（7）：4596-4607.
25	熊刚强，齐东旭．基于U-正交变换的图像编码算法［J］．中国图象图形学报，2010，15（11）：1569-1577.
	XIONG Gangqiang， QI Dongxu ．Algorithm of image encoding based on U-orthogonal transform［J］．Journal of Image and Graphics，2010，15（11）：1569-1577.
26	CHAM W K ．Development of integer cosine transforms by the principle of dyadic symmetry［J］．IEE Proceedings I：Communications，Speech and Vision，1989，136（4）：276-282.
27	WANG Z.New algorithm for the slant transform［J］．IEEE Transactions on Pattern Analysis and Machine Intelligence，1982，4（5）：551-555.
28	YUAN X， CAI Z ．ICHV：a new compression approach for industrial images［J］．IEEE Transactions on Industrial Informatics，2021，18（7）：4427-4435.
29	Computer Vision Group ．Test images ［EB/OL］．（2014-03-13）［2023-11-01］．.

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

[1]	Lan Tian Gu Xue-mai Guo Qing Wang Zhen-yong. A Novel Adaptive Rate Control Algorithm for H. 264 Frame Layer [J]. Journal of South China University of Technology (Natural Science Edition), 2008, 36(9): 100-106.
[2]	Shi Min Xie Sheng-li. A Prediction-based Vector Quantization Method for Image Coding [J]. Journal of South China University of Technology (Natural Science Edition), 2006, 34(1): 18-23.
[3]	Wo Yan Han Guo-qiang Zhang Bo . Fast Wavelet Image Coding Algorithm Based on Combining Iterations and Significant Subband [J]. Journal of South China University of Technology(Natural Science Edition), 2003, 31(9): 17-21,25.