PSO AND GA BASED NEIGHBOR EMEDDING SUPER RESOLUTION

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1 THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Serie A, OF THE ROMANIAN ACADEMY Volume 16, Number 1/2015, PSO AND GA BASED NEIGHBOR EMEDDING SUPER RESOLUTION Saeid FAZLI 1, Maryam TAHMASEBI 2 1 Zanjan Univeriy, Reearch Iniue of Modern Biological Techniue, Zanjan, Iran 2 Zanjan Univeriy, Eng. Faculy, Elecrical De., Zanjan, Iran m.ahmaebi@znu.ac.ir In hi aer a novel echniue for Neighbor embedding ingle image uer reoluion (SR) i rooed. Given a low-reoluion image, i high-reoluion image i reconruced from a e of raining image, which are comoed of one or more low-reoluion and correonding highreoluion image air. In hi aer we rooe a new aroach o a ingle image uer-reoluion hrough neighbor embedding uing Geneic Algorihm (GA) and Paricle Swarm Oimizaion (PSO). GA and PSO are ued for ach ize, overla and K neare neighbor arameer uning of neighbor embedding uer reoluion by maximizing he PSNR a a fine value. Exerimen how ha he ue of GA and PSO for finding he arameer of neighbor embedding mehod i more accurae han eing he arameer a random. Alo, i can be een from he reul ha he rooed mehod increae he average of PSNR 2.2db in comaring wih Bicubic inerolaion, bu he PSNR difference beween PSO and GA are no ignifican. Key word: neighbor embedding, geneic algorihm (GA), aricle warm oimizaion (PSO). 1. INTRODUCTION The uer-reoluion (SR) mehod can be divided ino wo clae: one cla i mulile-frame SR [1, 2, ec.], which generae a high-reoluion (HR) image from mulile low-reoluion (LR) image of he ame cene. The oher one i ingle-frame SR [3, 4, 5, 6, ec.],which generae a HR image from a ingle LR image, wih he hel of raining e image. In hi aer, we focu on he ingle-image SR roblem. Neighbor embedding algorihm ha been widely ued in examle-baed uer-reoluion reconrucion from a ingle frame, which aume ha neighbor ache embedded are conained in a ingle manifold. Chang e al. (2004) fir rooe he neighbor embedding uer-reoluion mehod, which aume he ache of high- and low-reoluion image, can form manifold wih imilar local geomery in he wo differen feaure ace. Fir, hey comue he reconrucion weigh of each low-reoluion ach neighbor in low-reoluion raining image e by minimizing he reconrucion error. Second, hey eimaed he high-reoluion embedding from he raining image air by reerving local geomery. Finally, hey enforce local comaibiliy beween adjacen high-reoluion ache. According o he udy-baed uer reoluion algorihm, he raining e i ofen a ube of all ache of one or everal image. Wih a good ach elecing raegy, he generaliy and reliabiliy of he uerreoluion algorihm will be largely imroved. If he ize of he ach i oo mall, he raining e i enlarged and more ache of he inu image would be calculaed; if he ach i oo large in ize, he maching error i magnified and he acuired high-reoluion image i low in ualiy. Addiionally, he local ach informaion i no enough o redic he deailed informaion of he high-reoluion, bu he effec of he aial neighborhood hould be aken ino accoun. So, during he roce of breaking he low-freuency image by raer can order, every ach hould be arially overlaed by i neighbor o kee he accordance of he ace neighborhood [7]. In hi aer, we aly boh he PSO and GA aroache for oimizing he value of ach ize, overla and K neare neighbor in Neighbor Embedding mehod in order o obain higher PSNR han Bicubic inerolaion. Inead of uing he uer reoluion roblem direcly wih highly comuaionally comlex algorihm, geneic algorihm and aricle warm oimizaion can be alied o find he oimal

2 96 Saeid Fazli, Maryam Tahmaebi 2 arameer of neighbor embedding mehod and romoe he ouu reul. Exerimenal reul how ha hi aroach can effecively obain high reoluion image and make he uer-reoluion algorihm of he image more racical. Thi aer i organized a follow. In ecion 2 we give a review of neighbor embedding algorihm for uer-reoluion. In ecion 3 we ouline he mehodology of hi geneic algorihm and aricle warm oimizaion o olve he neighbor embedding uer reoluion arameer, followed by he exerimen and analyi in ecion 4. The concluion i exlained in ecion REVIEW OF NEIGHBOR EMBEDDING FOR SUPER-RESOLUTION RECONSTRUCTION The idea of neighbor embedding for uer-reoluion reconrucion wa fir rooed by Chang e al. [8]. A follow, we will give a brief formulaion of neighbor embedding for image uer-reoluion. The arge high-reoluion image Y of a low-reoluion image X i eimaed uing a raining e of one or more low reoluion image X and he correonding high-reoluion imagey. Each low- or highreoluion image rereen a a e of mall overlaing image ache. X and Y have he ame number of ache, and each low-reoluion image in X and he correonding high-reoluion image in Y alo have he ame number of ache. The e of image ache denoe correonding o x, y, x and y a N { x }, = 1 { y } N, = 1 { x } N and = 1 { y } N. = 1 { y } N. Obviouly, = 1 N and N deend on he ach ize and he degree of overla beween adjacen ache. Neighbor embedding mehod for SR reconrucion can be ummarized in five e [8]. (a) For each ach x in image X do. (b) Find he e N of K neare neighbor in X. (c) Calculae he reconrucion weigh of he neighbor for minimizing he error of reconrucing x ε = 2 x w x. (1) x N In he euaion (1), w i he weigh for x, ubjec o he following conrain in he euaion (2) w = 1 and w = 0 for any x N. x N (2) (d) Comue he high-reoluion embedding neare neighbor and he reconrucion weigh. y x N (e) Conruc he arge high-reoluion image y uing he aroriae high-reoluion feaure of he K = Σ w y. (3) Y. 3. PROPOSED ALGORITHM In hi ecion, we will decribe he idea of he rooed mehod. Our neighbor embedding mehod ha only hree arameer ha we have exlored o oimize hem. The fir arameer i he number of K neare neighbor for neighbor embedding. The econd and hird arameer are he ach ize and he degree of overla beween adjacen ache. Our aim i o find he be e of value for hee hree arameer which

3 3 PSO and GA baed neighbor embedding uer reoluion 97 can roduce he oimal reul (beer PSNR). In hi aer, PSO and GA are ued o oimize he ach ize, overla and K neare neighbor arameer of he neighbor embedding mehod. We rooe he ue of aricle warm oimizaion and geneic algorihm echniue ha eed u he convergence and reduce he comuaion ime Deermining neighbor embedding arameer uing geneic algorihm Alhough GA ared much earlier han 1975, Holland (1975) i he key lieraure ha inroduced GA o broader audience. In GA, he oluion are rereened a chromoome. The chromoome (a ring of gene ha rereen a oluion) are evaluaed for fine value and hey are ranked from be o wor baed on fine value. The roce i accomlihed by reeaing alicaion of hree geneic oeraor: elecion, croover, and muaion. Fir, he beer offring are eleced o become aren o roduce new chromoome. To acuae he remaining of he fie, he chromoome wih beer fine value are eleced wih higher robabiliie han he chromoome wih weaker fine. The elecion robabiliie are uually defined uing he relaive ranking of he fine value. A oon a he aren chromoome are eleced, he croover oeraor incororae he chromo ome of he aren o roduce new offring (erurbaion of old oluion). Since ronger (fier) individual are being eleced more ofen, here i a rend ha he new oluion may become very imilar afer everal generaion, and he variey of he oulaion may decline; and hi could lead o oulaion agnaion [9]. Poulaion ize, number of generaion, croover and muaion rae arameer effec on he GA algorihm. Grea number of generaion (i.e. houand) and greaer oulaion ize (i.e. hundred) increae he likelihood of obaining a global oimum oluion, bu ignificanly increae roceing ime. Croover among aren chromoome i a common naural roce, and he variaion of aren informaion roduce children (offring). Veru croover, muaion i an uncommon roce ha reemble a udden change o a child (offring). Thi can be done by randomly elecing one chromoome from he oulaion and hen arbirarily changing ome of i informaion. The rofi of muaion i ha i randomly inroduce new geneic maerial o he evoluionary roce, robably hereby avoiding agnaion around local minima [10]. More deail on he mechanim of GA can be found in Goldberg [11] and Al-Tababai and Alex [12]. The flowchar of he geneic algorihm i given in Fig.1. Fig. 1 Flowchar for geneic algorihm. In GA every individual in he oulaion ge an evaluaion of i adaaion (fine) o he environmen. The elecion elec he be gene comoiion alo referred a individual, which hrough croover and muaion hould acuae o beer oluion in he nex oulaion. Our cheme of Neighbor embedding mehod via GA can be ummarized a follow. 1) Generae iniial oulaion (Iniialize ach ize, overla and K arameer randomly wihin heir range and correonding random velociie).

4 98 Saeid Fazli, Maryam Tahmaebi 4 2) For each Paricle i=1 o P do 3) Calculae PSNR a a fine value hrough neighbor embedding a decribed in ecion(2) 4) End for 5) While (Terminaion condiion rue) do 6) Selecion beween all individual in he curren oulaion are choe hoe, who will coninue and by mean of croover and muaion will roduce offring oulaion 7) Croover he individual choen by elecion recombine wih each oher and new individual will be creaed. The goal i o ge offring individual ha inheri he be oible combinaion of he characeriic (gene) of heir aren 8) Muaion by mean of random change of ome of he gene, i i uored ha even if none of he individual conain he neceary gene value for he exreme, i i oible o reach he exreme 9) New generaion he elie individual choen from he elecion are combined wih hoe who aed he croover and muaion, and form he nex generaion. 10) End while 3.2. Deermining Neighbor Embedding Parameer Uing Paricle Swarm Oimizaion PSO wa fir inroduced by Kennedy and Eberhar [13] a an oimizaion mehod for coninuou nonlinear funcion. PSO i a biologically inired algorihm moivaed by a ocial analogy. The warm i iniialized wih a grou of random aricle and i hen earche for oima by udaing hrough ieraion. In every ieraion, each aricle i udaed by following wo be value. The fir one i he be value of each aricle achieved o far. Thi value i known a oluion. The econd one i ha, be oluion racked by any aricle among all generaion of he warm. The be fine value i known a oluion. Thee wo be value are reonible o drive he aricle o move o new beer oiion. Afer finding he wo be value [14], a aricle udae i velociy and oiion wih he hel of he following euaion (4, 5): v + = W v + c r (be X ) + c r ( gbe X )i. (4) 1 h i i 1 1 i i 2 2 i i X = X + v, (5) i i i where X i and vi denoe he oiion and velociy of i h aricle a ime inance. Maximum and minimum h value for w i e o wo and zero reecively, which i ame for all aricle. W i ineria weigh a inan of ime, c 1 and c 2 are oiive acceleraion conan in range [0, 2], r 1 and r2 are random value generaed in he range [0, 1], be i i he be oluion of i h individual aricle, g be i he be aricle obained over all generaion o far [14]. Baed on he above PSO model, we denoe a a oulaion marix. The oulaion wih hree X i arameer for h i aricle a ime inance include ach ize, overla and K neare neighbor. The PSO algorihm earche for he be oluion hrough an ieraive roce. A every ieraion, he fine of each aricle i evaluaed uing he fine value (PSNR). If i i he be value he aricle ha achieved o far, he aricle ore ha value a eronal be. The be fine value achieved by any aricle during curren ieraion i ored a global be. Our algorihm of Neighbor embedding mehod via PSO can be ummarized a follow: 1) Generae iniial oulaion wih hree arameer for each aricle include ach ize, overla and K neare neighbor. (Iniialize arameer ach ize, overla and K randomly wihin heir range and correonding random velociie). 2) For each Paricle i = 1 o P do 3) Evaluae PSNR a a fine value hrough neighbor embedding a decribed in ecion(2) 4) End for

5 5 PSO and GA baed neighbor embedding uer reoluion 99 5) While (Terminaion condiion rue) do 6) Udae velociy according o he euaion (4) 7) Udae laen oiion according o he euaion (5) 8) For each Paricle i=1 o P do 9) Calculae PSNR a a fine value a menioned above 10) If he fine value i beer han he be fine value (be) in hiory 11) Se curren value a new be 12) End for 13) Udae global be by chooing he aricle wih he be fine value of all he aricle a he gbe 14) End while 4. EXPERIMENTAL RESULTS AND EVALUATIONS In hi ecion, we will how he erformance of he rooed mehod and erform comarion beween he PSO and GA, wih he ame fixed oulaion, and Bicubic inerolaion. For examle-baed image uer-reoluion, raining e i imoran for reconrucion ualiy of high-reoluion image. The rooed mehod i eed on four image (Fig. 2). For all he exerimen, when any one image i een a a eing image, he re ac a he generaion of raining amle. To ge inu LR image, each HR i degraded by blurring, and down-amled wih facor 2 o roduc a eing inu image. A menioned above, we ue PSO and GA for finding neighbor embedding arameer. The conan arameer for PSO algorihm ued in our exerimen can be een in Table 1. There are hree arameer ha we exlore hem by PSO and GA. We find an oimal value of K for all our exerimen. For he lowreoluion image, we find M M ache wih an overla of N ixel beween adjacen ache. If we wan o magnify a low reoluion image by S ime in each dimenion, hen we ue SM * SM ache in he highreoluion image wih an overla of SN ixel beween adjacen ache. In our exerimen, he range of hee arameer i eleced for ach ize [3, 6], overla [1, 4] and K [1, 5]. Objecively, eak-ignalo-noie raio (PSNR) i exloied a a fine value. The PSNR i defined a in he following euaion 2552 PSNR = 10log10. (6) MSE In Table 2, we comare he PSNR value beween bicubic inerolaion and neighbor embedding uing PSO and GA for four eing image. For all eing image, he reul how ha PSO and GA achieve beer PSNR value han Bicubic inerolaion mehod, bu he difference beween PSO and GA are no ignifican. In Table 3, we how deail abou eing image and oimal value obained for hree arameer. Moreover, we exlore he effec of number of ieraion for convergence and how ha PSO algorihm ha high endency for remaure convergence and GA ha medium endency, he reul can be een in Table 4. Figure 3 how he reul of alying differen uer reoluion mehod o a Lena image o obain 2 magnificaion. A i can be een, our mehod give he be reul han bicubic inerolaion. (a) (b) (c) (d) Fig. 2 Teing image: a) Lena; b) Head; c) Ha; d) Sarfih.

6 100 Saeid Fazli, Maryam Tahmaebi 6 Table 1 Conan arameer for PSO Parameer Name Value Size of he warm 10 Maximum number of ieraion 10 Cogniive caling arameer(c1) 1.5 Social caling arameer(c2) 1.5 Fine value PSNR Image Table 2 Fine value of he enhanced image Bicubic inerolaion Quaniaive comarion (PSNR in db) Prooed GA PSO Lena Head Ha Sarfih Table 3 Deail abou original image and oimal value for arameer Image Size(M N) Mehod Low ach Overl K ize Lena PSO GA Head PSO GA Ha PSO GA Sarfih PSO GA Table 4 The effec of number of ieraion on convergence Image/Ieraion Mehod Number of Ieraion Lena PSO GA Head PSO GA Ha PSO GA Sarfih PSO GA

7 7 PSO and GA baed neighbor embedding uer reoluion 101 (a) (b) (c) (d) Fig. 3 The 2 magnificaion of he head image from a low-reoluion image: a) inu low-reoluion image; b) rue high-reoluion image; c) bicubic inerolaion; d) our mehod wih PSO; e) our mehod wih GA. (e) 5. CONCLUSION The uroe of hi aer i o ue geneic algorihm and aricle warm oimizaion oluion for deermining he hree arameer of neighbor embedding uer reoluion and obaining HR image. Wih hi goal, we earch for oimal value of ach ize, overla and K neare neighbor for higher PSNR value. Reul of he rooed echniue are comared wih Bicubic inerolaion echniue. The exerimenal reul how ha he rooed algorihm can achieve beer reul han Bicubic inerolaion. Moreover, in PSO, he mo imoran feaure i ha, i can roduce beer reul wih roer uning of arameer. I i alo rue for GA baed image enhancemen. In comarion o GA, PSO ake le ime o converge o oimum. Alo, we rove ha he rooed mehod increae he average of PSNR 2.2db in comaring wih Bicubic inerolaion. A a reul, we hink ha a PSO and GA aroache for uer reoluion roblem are worh generalizaion and furher inveigaion in oher alicaion. REFERENCES 1. M. ELAD, and A. FEUER, Suer-reoluion reconrucion of image euence, IEEE Tranacion on Paern Analyi and Machine Inelligence 21, 9, , G. H. COSTA, and J.C.M. BERMUDEZ, Saiical analyi of he LMS algorihm alied o uer-reoluion image reconrucion, IEEE Tranacion on Signal Proceing ED, 11, , Y.T. ZHUANG, J. ZHANG, and F. WU, Hallucinaing face: LPH uer-reoluion and neighbor reconrucion for reidue comenaion, Paern Recogniion, 40, , H. CHANG, D. YEUNG, and Y. XIONG, Suer-reoluion hrough neighbor embedding, Proceeding of he IEEE Comuer Sociey Conference on Comuer Viion and Paern Recogniion, 1, , J.S. PARK, and S.W. LEE, An examle-baed face hallucinaion mehod for ingle-frame low-reoluion facial image, IEEE Tranacion on Image Proceing, 17, 10, , T.M. CHAN, J.P. ZHANG, J. PU, and H. HUANG, Neighbor embedding baed uer-reoluion algorihm hrough edge deecion and feaure elecion, Paern Recogniion Leer, 30, , SHU ZHANG, Examle-baed Suer-reoluion, Maer of Comuing, Auralian Naional Univeriy, Engineering and Comuer Science College, H. CHANG, D.-Y. YEUNG, and Y. XIONG, Suer-reoluion hrough neighbor embedding, IEEE Comu. Soc. Conf. Comu. Vi. Paern Recogniion, 2004, VORATAS KACHITVICHYANUKUL, Comarion of Three Evoluionary Algorihm:GA, PSO, and DE, Indurial Engineering & Managemen Syem, 11, 3, , 2012.

8 102 Saeid Fazli, Maryam Tahmaebi EMAD ELBELTAGI, TAREK HEGAZY, DONALD GRIERSON, Comarion among five evoluionary-baed oimizaion algorihm, Advanced Engineering Informaic, Elevier, 2005, GOLDBERG D.E., Geneic algorihm in earch, oimizaion and machine Learning, Addion-Weley Publihing Co, AL-TABTABAI H., ALEX P.A., Uing geneic algorihm o olve oimizaion roblem in conrucion, Eng. Conr. Archi. Manage., 6, 2, , J. KENNEDY, R.C. EBERHART, Paricle warm oimizaion, IEEE Inernaional Conference on Neural Nework, Perh, , APURBA GORAI, ASHISH GHOSH, Gray-level Image Enhancemen by Paricle Swarm Oimizaion, IEEE, Naure & Biologically Inired Comuing, Received Aril 28, 2014