015 8th Internatonal Congress on Image and Sgnal Processng (CISP 015) Dscrete Cosne Transform Optmzaton n Image Compresson Based on Genetc Algorthm LIU Yuan-yuan 1 CHE He-xn 1 College of Communcaton Engneerng, Jln Unversty, JLU Changchun Jln, Chna 1 College of nformaton technology, Jln Agrcultural Unversty, JLAU Changchun Jln, Chna Abstract Based on the basc prncples and characterstcs of dscrete cosne transform (DCT), we propose a DCT optmzaton method usng genetc algorthm n order to mprove the effcency of mage compresson. Frst, we calculate the error between the reconstructed mage and ts orgnal one. Then, n order to optmze DCT transform matrx coeffcents, we use genetc algorthm to fnd optmal soluton by mnmzng the mean square error. Fnally, we use the optmzed transform kernel to process mages. Expermental results ndcate that the PSR of the reconstructed mages has been mproved usng the proposed optmzaton DCT n both cases of mage block 4 4 and 8 8. Keywords-DCT optmzaton; Genetc algorthm; Image compresson; Mean square error I. ITRODUCTIO Wth the rapd progress of modern scence and technology, mage nformaton s wdely used n computer systems and multmeda communcatons. Accordngly, the requrements of data processng are gettng hgher and hgher. Image nformaton, especally hgh-defnton mage s carryng huge amount of nformaton, however, the storage and processng of mages for communcaton devces are under tremendous pressure. A large number of requrements for real-tme transmsson of multmeda nformaton n varous communcaton networks are also a great challenge even under the exstng hgh communcaton transmsson rate. Therefore, effcent mage compresson plays a crucal role n such cases. At present, the most-wdely-used method of mage compresson s based on dscrete cosne transform (DCT) [1] []. Orgnal mage has strong correlaton. Therefore, most energy wll concentrate on a few coeffcents after performng DCT on the mage [3]. We can acheve the goal of mage compresson by keepng the sgnfcant coeffcents of man energy. And n some new mage or vdeo codng methods the nteger transform form of DCT [4] s adopted, whch use smlar transformaton coeffcents. In order to get hgher compresson rato, some DCT coeffcents wll not be recovered n the decoder, therefore, the reconstructed mage s often dfferent from the orgnal mage. Subjectvely, we hope the dfference or dstorton s smaller. A genetc algorthm n processng of mage compresson s ZHAO Yan 1 SU Hong-yan 3 School of Electronc and Informaton Engneerng, Changchun Unversty of Scence and Technology, CUST Changchun Jln, Chna. 3 Luyuanyuan1980@16.com proposed n [5] and [6], whch s based on the premse that the approxmate extent s the maxmum between reconstructed and orgnal mages. We put forward an optmzaton DCT method of mage compresson based on genetc algorthms, whch adopts adaptve optmzed correcton by applyng genetc algorthms to the tradtonal DCT coeffcent regardng mage features such as texture and edge nformaton. Our method breaks the unfed bondage of the tradtonal DCT matrx coeffcent, acheves the goal of mprovng the effect of mage compresson. II. TRADITIOAL DCT ALGORITHM Two-dmensonal dscrete cosne transform [7] s F( u, v) where u (x 1) v (x 1) f ( x, y) ( u) ( v) cos( ) cos( ) 1 1 1 x0 y0 1 ( u), ( v) u, v 0 u. v 1,,..., 1 Tradtonal mage compresson method s as follows: Let orgnal mage matrx s f, DCT matrx s, reserved coeffcent matrx s M, the transformed coeffcent matrx s obtaned by F C f C 1 The coeffcent matrx L after strppng off nsgnfcant coeffcents s gven by L F M 3 In the decoder, the reconstructed mage matrx f s obtaned by 1 f C L C 4 Ths processng s smple and general, however the transform effect depends on transform matrx and the reserved coeffcent matrx. The retenton of the coeffcent s certan n most practcal applcatons, so the whole processng 978-1-4673-9098-9/15/$31.00 015 IEEE 199
performance wll be determned by the transform matrx. Accordng to (1), f the sze of the transform block s known, the transform matrx C s constant. There s larger dstorton between the reconstructed mage and ts correspondng orgnal one due to the process of transformaton, compresson and nverse transform. The reason s that the transform blocks are defnte and the transform matrx s kept constant. In other words, no matter what mages are processed, the same transform matrx s used, whch means mage characterstcs are not fully consdered. Therefore, we need to optmze the tradtonal DCT method to mnmze the dfference between the reconstructed mage and the orgnal mage. III. OPTIMAL DCT ALGORITHM In the proposed method, the least square method s used to optmze DCT matrx. The error caused by mage compresson s 1 e( n) E f f E C L C f E 5 To mnmze the mean square error [8], we have E e( n) C 0 6 BecauseC s a matrx, (6) becomes to take the dervatve of each element n the matrx s as follows. 7 The optmzed DCT matrxc OPT can be worked out usng (7). The optmzed dscrete cosne transform s referred to as ODCT n ths paper. Replacng C wth C, and then OPT repeatng the orgnal tradtonal DCT process to complete the mage compresson based on ODCT. The whole transform process s shown n Fgure 1. IV. GEETIC ALGORITHM FOR THE OPTIMAL SOLUTIO We propose to perform tradtonal DCT optmzaton by mnmzng the mean square error between the orgnal mage and the reconstructed mage. However, (6) s actually the process of solvng the optmal soluton wth smultaneous equatons for each pxel of mage blocks. Ths process has two characterstcs: Frst, the optmal soluton s the solutons of equatons, whch s not a sngle soluton and requres the smultaneous processng of multple nformaton n parallel. Second, the adjacent pxels n mage blocks are related, the optmzaton process s not determnstc, and we know exactly what the optmal soluton appears near the DCT coeffcents. Accordngly we need to adopt certan rules to gude the solutons. Thus, we use the optmal soluton method based on genetc algorthm to search [9]. AEncodng Frst, the mage nformaton data s expressed as the genotype strng structure data of the genetc space. These dfferent combnatons of strng structure data consttute dfferent ponts. We adopt bnary encodng. Assume the value ranges from a to b, then the codng accuracy s calculated as follows. b a x l 8 1 where l s the strng length of the strng structure data, then the -th test data decodng s X a l b 1 ( b a) ( 1) 9 l l The larger the value nterval selected, the greater we may select the optmal value, the better mage effect s. B Generaton of the ntal populaton There are M numbers of randomly generated ntal strng structure data, each strng structure data s an ndvdual, whch consttute a populaton. These M numbers of strng structure data are the ntal pont of teratons, whch denotes the number of ndvduals n the populaton. In order to avod premature or neffcency and other phenomena caused by napproprate values, M takes the range from 0 to 100 n our method. Fgure1. Block dagram of ODCT algorthm It needs to be noted that ODCT matrx s determned by approxmaton degree of the orgnal mage and the reconstructon mage. So the optmal results can be obtaned by the method of multple approxmate optmzatons. CAssessment test of adaptve values Adaptve functon ndcates the unque merts, whch follows the prncple of smplfcaton, and t s desgned to reduce the complexty of algorthm to accelerate the speed of obtanng the optmal value. In the proposed method, the adaptve functon s the error functon of mage compresson [10] as n (5). 00
DSelecton The purpose of selecton s to select superor ndvduals from the current populaton and gve them the opportunty for the next generaton of breedng offsprng. Ths paper adopts roulette wheel selecton method [11] and selects the next generaton of ndvdual based on the prncple of survval of the fttest. Gven the objectve functon, f ( b ) s called the ftness of ndvdualb. The number of selected ndvduals P for the next generaton s gven by P f ( b ) b s selected n n f(b j ) j1 10 Obvously, the hgher the ftness of ndvduals s, the larger the number of breedng n the next generaton s, on the contrary, a smaller number of breedng the next generaton s, or even to be elmnated. Ths produces descendants who have strong abltes to adapt the envronment. From the perspectve of gettng the optmzaton soluton, t s a process of choosng the soluton whch s closer to the optmal one. unchanged when ODCT populatons change from 40 to 60. Ths ndcates the number of populatons has reached saturaton pont bascally and that s enough for carryng out genetc algorthm optmzaton. Therefore, the optmal populaton sze s 40 for 4 4 mage block, and 60 for 8 8 mage block. It s worthy of menton that n the case of 8 8 mage block, when the number of populaton sze s 10 and the PSRs of the reconstructed mages usng ODCT and DCT are equal, whch ndcates that the populaton sze 10 s not suffcent to process genetc optmzaton algorthm, resultng n a "premature" phenomenon whch should be avoded n the genetc optmzaton algorthm. ECrossover Crossover operaton s the most mportant genetc manpulaton n genetc algorthms. We can get a new generaton of ndvduals through crossover operaton, and the new ndvduals contan ndvdual characterstcs of ther parents. FMutaton We select an ndvdual randomly n the populaton. For the selected ndvduals, the values of a strng structure of data n the strng are changed randomly wth a certan probablty. Lke n the bologcal communty, the probablty of occurrence mutaton s really low n the encodng. It s usually rangng from 0.001 to 0.01. Mutaton provded an opportunty for the new generaton. Mutaton wll affect the populaton ftness agan. The optmal matrx ODCT s obtaned by the above steps, and the process of repeatng conventonal DCT s solved. As shown n Fgure 1, the optmzed ODCT mage compresson s accomplshed. Fgure. PSR comparson results wth dfferent block szes usng DCT and ODCT for varng populaton sze ) Strng sze The results of usng dfferent strng sze are shown n Fgure 3. It can be seen that the qualty of the reconstructed mage for both cases are stable when the strng sze s larger than 8. And the curve of 8 8 block s relatvely flatter than that of 4 4 block. It llustrates that larger blocks are not senstve to the change of strng sze, whch results n the relatvely small perturbaton of the algorthm. Therefore the optmal strng sze of the proposed method s 8. V. EXPERIMETAL RESULTS AD AALYSIS AParameter settngs In the optmzaton process, ODCT matrx results depend on parameters of genetc optmzaton algorthm. The effect of mage compresson vares wth the expermental parameters, whch s shown from Fgure to Fgure 5. 1) Populaton sze As can be seen from Fgure, for 4x4 and 8x8 mage blocks, the PSR of reconstructed mages s essentally Fgure3. PSR comparson results wth dfferent block szes usng ODCT for varng strng sze 01
3) Crossover probablty The performance of the proposed method usng dfferent crossover probablty s shown n Fgure 4. The curves show that the crossover probablty s 0.7 for 4 4 block and 0.8 for 8 8 blocks. The reconstructed mage effect n dfferent cases are bascally stable, so the smaller the mage blocks, the less the requred crossover probablty. We select 0.8 as the crossover probablty n our method. probablty s 0.8, varaton probablty s 0.01 and the number of teratons s 0. The results of experments wth dfferent block szes are shown n Fgure 6 and Table 1. a b Fgure 4. PSR comparson results wth dfferent block szes usng ODCT for varng crossover probablty 4) Mutaton probablty Fgure 5 presents the PSR results of mage compresson usng ODCT wth dfferent mutaton probablty. It shows that the reconstructed mage effects are bascally stable, when mutaton probablty s 0.007 for 4 4 blocks and 0.008 for 8 8 blocks. Consequently, the smaller the mage block s, the less the requred stable mutaton probablty s. c d athe reconstructed mage of 4x4 block usng DCT bthe reconstructed mage of 4x4 block usng ODCT cthe reconstructed mage of 8 8 block usng DCT dthe reconstructed mage of 8 8 block usng ODCT Fgure6. Comparson results of reconstructed Lenna mage usng DCT and ODCT TABLE I. COMPARISO RESULTS OF PSR USIG DCT AD ODCT DCT ODCT Block sze PSR Compresson rato% PSR Compresson rato% 4 4 35.1450 81.5 36.4994 80.7 8 8 31.1835 38.3 33.907 359 Fgure5. PSR comparson results wth dfferent block szes usng ODCT for varng mutaton probablty BExpermental comparson results In order to compare the performance of the proposed ODCT method wth the tradtonal DCT method, Lenna mage s used n our experments for mage compresson. The parameters used n our method are: the populaton sze s 40, the length of ndvdual and chromosome s 8, crossover Expermental results n Table 1 show that compresson performance usng the proposed ODCT s better than that of usng DCT obvously. Comparng cases of 4 4 and 8 8 blocks n Table 1, the larger the blocks sze are, the better the performance s. The reason s that the optmzaton process for larger blocks are more comprehensve for fndng ODCT transform matrx coeffcents. We use dfferent types of mages n our experments for further comparson of the proposed method wth the correspondng state of art methods based on DCT. The mages we use here are Stonebrd, Rverstreet, Rangutter and Cameraman. The comparson results of usng DCT, the proposed ODCT and ADCT [1] are shown n Table. Table 0
shows that the ODCT method has a better compresson effect. TABLE II. COMPARISO RESULTS OF PSR USIG DIFFERET MATHODS Images DCT ADCT [1] ODCT Stonebrd 8.9113 9.765 30.335 Rverstreet 9.05 3.381 33.657 Rangutter 4.4659 5.57 6.013 Cameraman 4.18 5.81 6.638 Error.Journal on Communcatons.Vol.1,Issues1,December 000, pp.1-4. [9] Ek Peng Chew, Chong Jn Ong, Km Hee Lm. Varable perod adaptve genetc algorthm.computers & Industral Engneerng, Vol.4,Issuse -4,Aprl 00,pp. 353-360. [10] U.M. Al-Saggaf, M. Monuddn, M. Arf, A. Zergune. The q-least Mean Squares algorthm.sgnal Processng.Avalable onlne 3 December 014. In Press. [11] XIA Gu-me, ZEG Jan-chao. A Stochastc Partcle Swarm Optmzaton Algorthm Based on the Genetc Algorthm of Roulette Wheel Selecton.Computer Engneerng and Scence.Vol.9,Issuse 6,June,007, pp.51-54. [1] K.Saraswathy, D.Vathyanathan and R.Seshasayanan. A DCT Approxmaton wth Low Complexty for Image Compresson. Internatonal conference on Communcaton and Sgnal Processng, Inda.013,pp.465-468. VI. COCLUSIO In ths paper, amng at the mprovng dscrete cosne transform (DCT) matrx n mage compresson, the genetc algorthm s used to optmze the tradtonal DCT. By testng wth dfferent mage blocks and parameter optmzaton, the deal settng of optmzaton parameters and blocks are determned. Expermental results show that for the mages wth lne edge and texture feature, our DCT optmzaton method based on genetc algorthm for mage compresson can reach the best effects when small block processng s used, the number of populaton s from 40 to 60, the length of the strng s 8, the crossover probablty s from 0.7 to 0.8, and the mutaton probablty s from 0.007 to 0.008. ACKOWLEDGMET Ths work s supported partly by atonal atural Scence Foundaton of Chna 61171078 and 6171315, and by scence and technology development project of Jln provnce 015004007Y. REFERECE [1] Fefe Zhang, We Xe, Guoru Ma. Hgh dynamc range compresson and detal enhancement of nfrared mages n the gradent doman.infrared Physcs & Technology. Vol. 67, ovember 014, pp. 441-454. [] Je We. Image segmentaton based on stuatonal DCT descrptors.pattern Recognton Letters, Vol. 3, Issues 13, January 00, pp. 95-30. [3] Dae-Yeon Km, Yung-Lyul Lee. A fast ntra predcton mode decson usng DCT and quantzaton for H.64/AVCOrgnal.Sgnal Processng: Image Communcaton, Vol. 6, Issues 89, October 011, pp. 455-465. [4] D.J. Duh, J.H. Jeng, S.Y. Chen. DCT based smple classfcaton scheme for fractal mage compresson.image and Vson Computng. vol. 3, Issues 13,ovember 005, pp. 1115-111. [5] TIA Yng, YUA We-q. Applcaton of the Genetc Algorthms n Image Processng.Journal of Image and Graphcs. Vol. 1, Issues 3, March 007, pp. 389-396. [6] Snehamoy Chatterjee, Ashs Bhattacherjee. Genetc algorthms for feature selecton of mage analyss-based qualty montorng model: An applcaton to an ron mne. Engneerng Applcatons of Artfcal Intellgence. Vol. 4, Issues 5,August 011,pp.786-795. [7] Rafael C.Gonzalez,Rchard E.Woods,Steven L.Eddns. Dgtal Image Processng Usng MATLAB. Publshng House of Electroncs Industry.Bejng.pp.39-51. [8] CAO J-hua, WAG Zhao-hua. The Interpolaton Algorthms of Pcture Error Conceal Ment Based on Mnmum Mean Square 03