Lossless Compression Schemes of Vector Quantization Indices Using State Codebook

Transcription

1 74 JOURNAL OF SOFTWARE, VOL. 4, NO. 4, JUNE 009 Lossless Comressio Schemes of Vector Quatizatio Idices Usig State Codebook Chi-Che Chag Deartmet of Iformatio Egieerig ad Comuter Sciece, Feg Chia Uiversity, Taiwa, R.O.C. Guei-Mei Che 1 Deartmet of Comuter Sciece ad Iformatio Egieerig, Natioal Chug Cheg Uiversity, Taiwa, R. O. C. ckm90@cs.ccu.edu.tw, Chia-Che Li Deartmet of Comuter Sciece ad Iformatio Maagemet, Providece Uiversity, Taiwa, R. O. C. mhli3@u.edu.tw Abstract I a memoryless vector quatizatio system, each image block is ideedetly ecoded as a corresodig idex ad the a idex table will be geerated. I this aer, we roose two ovel schemes to comress the idex table without itroducig extra ecodig distortio. Both our schemes exloit the characteristic that the blocks of images are highly correlated to fid the same or similar idex from the eighborig idices i the comressio rocess. To icrease the comressio, the ricial comoet aalysis (PCA) techique is also emloyed to sort the codewords i the codebook for miimizig the differece of eighborig idices. I additio, our secod scheme excludes the reetitive idices from the search ath to further decrease the bit rate. Simulatio results show that our schemes are suerior to SOC ad traditioal memoryless VQ o the comressio rate. Idex Terms Vector quatizatio system, SOC, PCA I. INTRODUCTION Vector quatizatio (VQ) is a effective comressio scheme of digital images for the urose of trasmissio ad storage [3,1]. The major advatages of VQ are that the comressio rate is very high ad the hardware of decoder is very simle. I a VQ system, some stadard images are first divided ito smaller blocks for traiig a codebook, icludig reresetative codewords (multidimesioal vectors), by usig some reviously roosed techiques such as LBG algorithm [9]. The reresetative codebook will be further referred i the both ecodig ad decodig rocess. I the ecodig rocess, iut vectors (multi-dimesioal vectors) of the origial images are the idividually quatized to the closest codewords i the codebook. Comressio is achieved by trasmittig or storig the idices of closest codewords istead of the origial ixels. I the decodig rocess, recostructio of the images ca be imlemeted by usig idex-based codebook look-u rocedure. The VQ scheme [3] ca be maily classified ito two categories: memoryless VQ ad memory VQ. I a memory VQ, image blocks are ecoded deedetly such as fiite-state VQ (FSVQ) [, 6]. FSVQ emloys the reviously ecoded blocks to make a selectio oly from the sub-codebook of a much smaller size. Therefore, it may itroduce some extra codig distortio. There are several other related techiques such as redictive VQ (PVQ) [4,5] ad address VQ (AVQ) [11]. PVQ ca be regarded as a extesio of vector quatizatio. AVQ is based o exloitig the iter-block correlatio by ecodig a grou of blocks together usig a addresscodebook. But i geeral, most of the memory VQ schemes are very comlicated for hardware imlemetatio ad require more comutatioal cost tha memoryless VQ. O the cotrary, memoryless VQ schemes exloit the high correlatio ad the satial redudacy betwee eighborig ixels; meawhile, they igore the satial redudacy betwee eighborig image blocks. I other words, each image block is ecoded ideedetly, while its corresodig idex is set to the decoder. Several efficiet techiques have bee roosed, such as idexcomressed VQ (ICVQ) [13], redictive mea search algorithm (PMS) [10], ad search-order codig (SOC) [7], etc. The SOC scheme further achieves the goal of comressio i the idex domai rather tha i the ixel domai. Its mai cocet is to search the same idex from the eighborig idices of the curret rocessig idex ad the use search-order codes as the ecoded codes. Comressio ca be achieved whe the legth of biary reresetatio of search-order codes is shorter tha the umber of bits required by the origial idex value. It has bee roved that SOC is efficiet i imrovig the image comressio rate [7]. I this aer, we roose two ovel schemes to further comress the VQ idex table of images based o the SOC scheme without losig ay image quality by the origial

2 JOURNAL OF SOFTWARE, VOL. 4, NO. 4, JUNE VQ ecodig. To attai our goal, at first, we rearrage the order of the codewords i a codebook by usig the ricile comoet aalysis (PCA) techique [1, 8] such that eighborig image blocks are likely to be ecoded by similar idices. Furthermore, the cocet of state codebook is the exloited to kee the closest codewords of these similar idices i the codebook. The mai idea behid our schemes is that we try to search a same idex with the curret rocessig idex from state codebook, if we could ot directly fid a same idex from the eighborig idices. Besides, our secod scheme excludes the reetitive idices from the search ath to further imrove our first scheme. Simulatio results idicate that both our ewly roosed schemes achieve sigificat reductio of bit rate without losig ay image quality by the origial VQ ecodig. This aer is orgaized as follows. Sectio resets a brief review of some related works, icludig the PCA techique [8] ad SOC algorithm [7]. I Sectio 3, the roosed schemes shall be described i detail. Fially, i Sectio 4, simulatio results shall be give, followed by some coclusios i Sectio 5. II. RELATED WORKS For the urose of miimizig the differece of eighborig idices, the ricial comoet aalysis techique showed i Subsectio A will be first exloited to sort the codewords i a codebook. Ad the, the VQ ad search-order codig (SOC) scheme will be described i Subsectios B ad C, resectively. A. The Pricial Comoet Aalysis (PCA) Techique PCA is a efficiet techique for sortig multidimesioal vectors. The cocet of PCA is to fid a secial axis oto which all multi-dimesioal vectors ca be rojected. Through these rojectios, the corresodig rojected oits o the secial axis ca kee the greatest relative differeces betwee ay two multi-dimesioal vectors. It meas that sortig of multidimesioal vectors ca be achieved by sortig their corresodig rojected oits. Now the mai roblem is how to fid the secial rojectio axis. A algorithm which has bee roosed by Lee et al. [8] for fidig the secial axis is as follows: Algorithm of PCA Problem: For m give multi-dimesioal vectors V, V, 1 K, V m, each vector is of dimesios. The outut is a secial rojectio axis D = d, d K, d ), called as first ricial 1 ( 1 comoet directio, where d 1 such i= 1 i = that V 1, V, K, V, ca be rojected oto D m 1. Ad all rojected oits ca kee their greatest relative differeces betwee each other. Ste 1: I order to elimiate ifluece from the differet measure, we must first ormalize the differece measure if V, V, 1 K, V, do ot have the same m differece measure. Ste : Comute the covariace matrix C accordig to all ormalized multi-dimesioal vectorsv, V, 1 K, V. m Ste 3: Fid all eigevalues of the covariace matrix C ad deote them as λ, λ, 1 K, λ, where λ1 λ K λ. Comute D, D, 1 K, D which are the corresodig eigevectors of λ, λ, 1 K, λ. Ste 4: Outut the secial axis, D1 = ( d1, d K, d ), called as first ricial comoet directio. Oce the secial rojectio axis D1 = ( d1, d K, d ) was geerated, for each give multi-dimesioal vector Vi = ( vi, 1, vi,, K, vi, ), where i = 1,,..., m, comute its rojected oit oto D1 = ( d1, d, K, d ) by usig the exressio v i, 1 d1 + vi, d + K + vi, d. Sortig of the multi-dimesioal vectors ca the be erformed accordig to sortig of their rojectio oits. B. Review of Vector Quatizatio Algorithm I recet years, there is a exlosive growth i the etworks for trasmittig digital media or other tyes of files. With the raid develomet of the etwork techologies, digital media ca be trasmitted directly via the comuter etwork. Therefore, how to reduce the amout of the trasmitted data becomes a imortat issue. To hadle this issue, data comressio is emloyed. Data comressio is a critical techique to dimiish the amout of data such as images, audio, ad video. Oe of the most commo ad oular data comressio techiques is VQ, which was roosed by Gray i 1984 [3] ad is a imortat techique for lowbit-rate image comressio. I the followig, the detail of VQ, which will be alied to our roosed method, is itroduced. VQ cosists of three stes: (1) codebook desig, () the ecodig hase ad (3) the decodig hase. At first, a codebook K which is comosed of the most reresetative codewords must be costructed. The K will be emloyed i both the ecodig hase ad the decodig hase. Geeratig a erfect codebook from a large amout of traiig set is a essetial work i VQ. Eve though may codebook desig algorithms have bee roosed, the most famous oe is LBG algorithm which was reseted by Lide, Buzo ad Gray i 1980 [9]. LBG algorithm for desigig the codebook is a iterative algorithm that slits the traiig sets ad udates the codebook iteratively. A erfect codebook is geerated by a good iitial guess ad a fast covergece to obtai the most reresetative codewords. I the ecodig hase, the iut image S is divided ito may o-overlaig square blocks of size ixels, ad each of them stads for a -dimesio vector. The set of vectors is rereseted by S = S S,...,, where m is the umber of vectors i S. { } 1, S m

3 76 JOURNAL OF SOFTWARE, VOL. 4, NO. 4, JUNE 009 Suose that the fiite set = { k i = 0,1,, 1} K i K is the codebook of size, where ki ( ki, ki, ), K k = is 1 i the ith codeword. Thereuo, VQ ca be regarded as a maig fuctio Q from a -dimesio Euclidea sace R to a fiite subset K R : Q : R K. The ecoder desigs a desired maig fuctio Q such that the Euclidea distace betwee the iut vector S j ad the maed codeword ( S j ) kx Q = is the shortest. The Euclidea distace is ofte used to measure the distortio ad defied as follows. ( s k ) = mi ( s k ), for1 j m, ad1 x ja a= 1. xa ja ta t = 1 a= 1 As a result, the corresodig distortio is miimal. The, as show i Figure 1, the idex x of codeword k x which is maed from the iut vector is trasmitted to the decoder rather tha the iut vector Sj. Owig to that the iut vector is relaced by the idex of k x, the umber of bits used for reresetig the idex x of the codeword k x is smaller tha that of the iut vector Sj. Thus, the origial image is comressed. For examle, assume that the size of the codebook is set to be 56, ad each codeword is rereseted by a 16-dimesio vector i geeral. Ad, b, defied the umber of the required bits for oe ixel, is alied to measure the comressio ratio. The b value of the comressed image is 0.5 sice the umber of bits used for reresetig the codeword is eight i the above examle. I terms of image comressio, the good comressio ratio is rovided by VQ. value of the recovered image. Note that the greater the PSNR value of the recostructed image is, the worse the comressio ratio will be. C. Review of the Search-Order Codig Algorithm The roosed search-order codig (SOC) algorithm [7] is a techique to further achieve image comressio o the idex table of VQ [3] ad does ot cause codig distortio agai. Its mai cocet is based o two image characteristics: the eighborig blocks are highly corresodig to the same idices ad a image is geerally ecoded block by block i a raster sca order (i.e. from left to right ad from to to bottom). For a idex table, SOC searches the reviously geerated VQ idices ad uses the corresodig search-order codes as the comressio codes if ay revious idex matches the curret idex. Comressio ca be achieved whe the search-order codes which are biary reresetatios are less tha the origial VQ idex. Now the roblems are to fid the matched oe of revious idices with the curret (b) Figure. Search aths of SOC (a) SSP = 1 (b) SSP = 4. Figure 1. The ecodig hase of VQ. I the decodig hase, the codebook of the decoder is idetical to that of the ecoder. The decoder receives each idex x which is trasmitted by the ecoder, ad a easy look-u table oeratio is erformed to fid the corresodig codeword k x. As a result, the codeword k x is emloyed to recostruct the iut vector Sj. The origial image is recostructed by reeatig the above rocesses for all the received idices. The comutatio load of VQ is quite low such that it is suerior to other comressio techiques. VQ rovides the good comressio ratio ad the good image quality of the recostructed image. The size of codebook ca be adjusted to be larger if we wat get the higher PSNR idex ad geerate the relative search-order codes. Accordig to the raster sca order, the curret idex is deoted as a search ceter (SC) ad oe of revious ecodig idices is the startig search oit (SSP). For examle, i Figure, there are two 7 7 idex tables, where the black dot is the SC ad startig search oit (SSP) is defied i Figure 3. It is obvious that these two idex tables (show i Figures (a) ad 1(b)) demostrate two differet search aths for searchig a same idex value with the SC. The solid boudary squares are the search oits (SP) which are reviously ecoded based o the raster sca order. I other words, o-search oits ca ot be cosidered i a search ath because they are ecoded after SC. Note that i each search, it must search the SPs alog the search ath, 1st level, d

4 JOURNAL OF SOFTWARE, VOL. 4, NO. 4, JUNE level,, ad so o, util the first same idex is foud or oe of the SPs is matched. I Figure 3, there are four startig search oits (SSP) defied by the SOC algorithm. To start a search, the SSP must be determied at first. Ad the four SPs i the 1st level will be searched for. If ay same idex is foud, the search-order codes will be set to the decoder. Otherwise, the SPs i the d level will be cosidered. If oe of the SPs is matched, the origial idex value of SC is set. To distiguish the search-order codes from the origial idex value by the decoder, a extra bit, called a idicator, is also set to the decoder i the frot of them. Figure 3. Four startig search oits (SSP). Based o our observatio, there are usually may reetitio idices i the eighborhood of the SC. A reetitio idex meas that its idex value is equal to the revious SP alog the search ath. If they are excluded i a search ath, it will icrease the robability of fidig the matched oe. For examle, i Figure 4, the idex of (3,3), which equals to 7, is the SC ad SSP equals to 1. Here the reetitio idices are (,) ad (3,1), which are equal to 9 ad 3, resectively. Oce they are icluded, the matched idex of (,1), which also equals to 7 will be lost i this search because the umber of bits assiged to search-order codes,, is limited. I this examle, is equal to. If we igore the reetitio idices, we ca fid the corresodig search-order codes, 11, of the SC. Figure 4. A 4 4 idex table for showig the exclusio of reetitio oits. I the decodig rocess, the decodig order is also i the raster sca order. After received the comressio codes, the decoder ca distiguish the search-order codes form the origial idex value accordig to its idicator. The the similar search rocedure with the ecodig rocess is erformed. Note that the values of SSP ad are equal to those of the ecodig rocess. Whe the idex table is recovered, the image ca be recostructed by usig the traditioal VQ codebook look-u rocedure. III. THE PROPOSED SCHEME I this sectio, we roose two schemes based o the SOC algorithm i imrovig comressio rate of images. The first scheme exloits the basic state codebook to kee the closest codewords, ad the secod scheme imroves the state codebook for further reducig the bit rate. They will be described i Subsectio A ad B i detail, resectively. A. The Basic State Codebook Scheme By the SOC algorithm, it just searches the same idex value aroud the curret rocessig idex. I other words, SOC igores the similar idices, if it fails to fid the same oe. For the urose of further icreasig the comressio rate, our scheme fids the similar idices aroud the curret ecodig idex ad the ecodes it as the shorter legth tha its origial idex value. To make sure the differece of eighborig idices is miimal, we aly the ricial comoet aalysis (PCA) techique to sort the codewords i the codebook that geerated by the origial VQ ecodig. I additio, the raster sca order (i.e., from left to right ad to to bottom) is also alied i our scheme to sca the idex table. I our first roosed ecodig scheme, all the idices i the idex table shall be classified ito three grous. I the first grou, it cotais the idices that ca be ecoded as search-order codes by usig SOC. I the secod grou, it cotais the idices that ca be ecoded by usig state codebook. The state codebook is a much smaller subcodebook of the origial VQ codebook (i.e., suer codebook) ad cosists of the idices of the closest codewords. Note that the codewords i the origial VQ codebook have bee sorted by the PCA techique, the closest codewords of each codeword may aear earby. It is easy to fid the similar idices for the curret idex. Furthermore, the state codebook is geerated i real-time i the both ecodig ad decodig rocesses. It is ot ecessary to store the state codebooks. I the third grou, it cotais the rest idices excluded from the first ad secod grou i the idex table. I order to distiguish these three grous i the comressio codes by the decoder, a extra idicator (oe or two bits) should be added i the frot of the comressio codes of each idex. To begi the ecodig rocess, all the idices i the idex table shall be ecoded sequetially. For the curret rocessig idex, we first check whether this idex belogs to the first grou or ot. The SOC algorithm is executed to search aroud this idex for fidig a same oe i the redefied search order. If the result is ositive, this idex is classified ito the first grou. The, the comressio codes of this idex are a idicator lus search-order codes. Accordig to our simulatio results, the idicator i the first grou is oe bit istead of two bits, achieves better comressio rate. If the curret rocessig idex does ot belog to the first grou, we further check whether this idex belogs to the secod grou or ot. If this idex does ot belog

5 78 JOURNAL OF SOFTWARE, VOL. 4, NO. 4, JUNE 009 to the first grou, the similar idices with the curret idex may exist i the redefied search ath. I our scheme, we search a same idex with the curret idex from the closest codewords of those similar idices. It meas that the state codebook will be geerated i realtime ad cosists of several closest codewords. Sice the codebook has bee sorted by PCA techique, the closest codewords of each idex i the codebook must aear earby. Note that the umber of those similar idices which we wat to search for is redefied ad deotes as i the arameter,. The umber of closest codewords of j each similar idex is also redefied ad deotes as. i j Hece, the size of state codebook will be. Oce we fid a same idex with the curret idex i the state codebook, the curret idex is classified ito the secod grou. The comressio codes of this idex are a idicator lus the idex, which is corresodig to the foud same idex, of the state codebook. Here the idicator is two bits ad the umber of bits of the idex for the state codebook is i + j. Figure 5. A examle of 4 4 idex table for geeratig the state codebook For the examle of Figure 5, first, we assume that the umber of bits of search-order codes, m, equals to ad search directio, SSP, equals to 1 by executig the SOC algorithm. We ca fid that the curret idex (3,3) does ot belog to the first grou because we ca ot fid a same idex i the redefied search ath. Here its similar eighborig idices are the idices of (3,), (,), (,4) ad (3,1), which equal to 55, 54, 5 ad 46. Now we start to check whether the curret idex belogs to the secod grou or ot. Assume that i = ad j =, the the size of the state codebook will be = 16. The state codebook is show i Table 1, where we defie that there are j / idices of the closest codewords above each similar idex ad j / oes below it. TABLE I. THE STATE CODEBOOK OF FIGURE 5 From Table I, the same idex with the curret idex i the state codebook was foud at the idex, 1110, of the state codebook. It meas that the curret idex belogs to the secod grou. Therefore, i this examle, the comressio codes of the curret idex (3,3), which equals to 47, are two bits idicator lus Oce o match is foud i the state codebook for the curret idex, the curret idex belogs to the third grou. Its comressio codes will be a two-bit idicator lus its

6 JOURNAL OF SOFTWARE, VOL. 4, NO. 4, JUNE origial VQ idex value. Note that each idex i the idex table will be just classified ito oly oe grou. A detail descritio of the roosed algorithm is give as follows: The Proosed Ecodig Algorithm Iut: Each block of a image usig the raster sca order. Outut: The comressio codes of the iut image. Ste 1: Aimig at the curret rocessig block, exloit traditioal VQ ecodig scheme to geerate its corresodig idex. If the idex belogs to the first grou, a oe-bit idicator ( 0 is commoly i use) lus the search-order codes are oututted as its comressio codes ad go to Ste 4. Otherwise, go to Ste. Ste : If the idex belogs to the secod grou, a twobit idicator ( 10 is commoly i use) lus the idex of the state codebook are oututted ad go to Ste 4. Otherwise, go to Ste 3. Ste 3: The idex belogs to the third grou. A two-bit idicator ( 11 is commoly i use) lus the origial VQ idex value are oututted. Ad the go to Ste 4. Ste 4: Reeat Stes 1 to 4 util all the blocks i the iut image are rocessed. As for the decoder, the decodig rocess is also i the raster sca order. Accordig to the idicator of each idex of the received comressio codes, the decoder ca distiguish each grou. If the idicator idicates the first grou, the idex will be recovered by usig the SOC algorithm. O the cotrary, if the idicator idicates the secod grou, the same state codebook with the revious ecodig rocess will be geerated for recoverig this idex. Fially, if the idicator idicates the third grou, the idex will be recovered by usig its origial VQ idex value. B. The Otimized State Codebook Scheme This imrovemet is desiged o the observatio that there may exist some reetitio idices i the basic state codebook reseted i Subsectio 3.1. The reetitio idex sigifies a idex whose value is equal to that of revious idices that have bee stored i the state codebook ad the similar idices searched i the redefied search ath. For the examle of Table 1, the reetitio idices are 0101, 0111, 1010 ad Due to these reetitios, the search rocedure of the state codebook will yield redudat search ad thereby decrease the codig efficiecy. Therefore, the exclusio of reetitio idices will icrease the ossibility for fidig matched idex from the otimized state codebook j because the umber of closest codewords,, the same defiitio with Subsectio 3.1 is limited. Figure 6. A examle of 4 4 idex table for geeratig the otimized state codebook For the examle of Figure 6, the curret idex (3,3), which equals to 61, will be classified ito the third grou if we do ot exclude reetitio idices from the state codebook. Table shows the otimized state codebook of the curret idex (3,3). I this case, (3,3) will be classified ito the secod grou because the matched idex is Accordig to the simulatio results, Both the basic state codebook ad otimized state codebook schemes sigificatly achieve lower bit rate tha the SOC scheme. TABLE II. THE OPTIMIZED STATE CODEBOOK OF FIGURE 6

7 80 JOURNAL OF SOFTWARE, VOL. 4, NO. 4, JUNE 009 umber of idices classified ito the first grou, secod grou ad third grou, resectively. (a) Airlae (b) Lea (c) Peers (d) Sailboat (e) Tiffay (f) Toys Figure 7. Stadard images of ixels IV. EXPERIMENTAL RESULTS Exerimets have bee erformed for the two roosed lossless idex comressio schemes usig several moochrome stadard images with 56 gray levels show i Figure 7. As for our codebook, which was desiged by usig six stadard images, Airlae, Boat, Lea, Sailboat, Tiffay ad Toys, of ixels with 56 gray levels ad the wellkow LBG algorithm [9]. I our exerimets, the size of each image block is 4 4 ixels. The comarisos of comressio rate betwee each scheme shall be show with bit rate (bits/ixel, i.e., b) system. I other words, the bit rate of the roosed scheme is give by ( + m) + NO ( + i + j) NO1 1 + NO3 ( + log N c ) BR = M N where N c : codebook size; M N : image size; m, i, j : the same defiitios as i Sectio 3; NO 1, NO, NO 3 : the total TABLE III. BIT RATE OF THE PROPOSED SCHEMES AND THE SOC ALGORITHM USING A VQ CODEBOOK WITH 56 CODEWORDS. Schemes Images SOC (=) [7] Scheme 1 Scheme Airlae Lea Peers Sailboat Tiffay Toys Note: Scheme 1 is the basic state codebook scheme ad scheme is the otimized state codebook scheme. Table III shows the comariso of the bit rate by usig our desiged codebook with 56 codewords. Note that for the traditioal memoryless VQ, the bit rate is 0.5 bits/ixel for codebook of size 56. I Table III, the imlemetal arameters of SOC, ad SSP, equal to ad 1 suggested by the authors [7]. The former meas the umber of bits assiged to the search-order codes is ad the latter meas the startig search oit is 1. I additio,

8 JOURNAL OF SOFTWARE, VOL. 4, NO. 4, JUNE our Scheme 1 ad Scheme are desiged usig the basic state codebook ad the otimized state codebook roosed i Subsectio 3.A ad 3.B, resectively. Here, the arameters, m, i, j, are,, 3, which are redefied. From Table III, the bit rates of our schemes are obviously less tha that of the SOC scheme. Furthermore, the bit rate of Scheme is also less tha Scheme 1 sice the exclusio of the reetitio idices i the state codebook. TABLE IV. BIT RATE OF THE PROPOSED SCHEMES AND THE SOC ALGORITHM USING A VQ CODEBOOK WITH 51 CODEWORDS. Schemes SOC (=) Scheme 1 Scheme Images [7] Airlae Lea Peers Sailboat Tiffay Toys Note: Scheme 1 is the basic state codebook scheme ad scheme is the otimized state codebook scheme. Table IV ad V show the exerimetal results i which the arameters are chose the same with Table 3, excet the size of codebook are 51 ad 104, idividually. Note that for codebook of sizes 51 ad 104, the bit rates of the traditioal memoryless VQ scheme are ad From the exerimet, it is obvious that our scheme 1 ad still reset better erformace tha the SOC algorithm ad traditioal memoryless VQ scheme o matter eve i the worse sceario. TABLE V. BIT RATE OF THE PROPOSED SCHEMES AND THE SOC ALGORITHM USING A VQ CODEBOOK WITH 104 CODEWORDS. Schemes Images SOC (=) [7] Scheme 1 Scheme Airlae Lea Peers Sailboat Tiffay Toys Note: Scheme 1 is the basic state codebook scheme ad scheme is the otimized state codebook scheme. V. CONCLUSIONS Two ewly schemes have bee roosed for VQ idex comressio. They are desiged based o the observatio that the high correlatio of eighborig blocks i a image. I order to emloy this characteristic, the oly thig we eed to do is sortig of the codewords i a codebook. With the hel of the PCA techique, this aim is easily attaied. To icrease the comressio rate, both our schemes first uses the search-order codig algorithm to fid the same oe i the eighborig idices. After that, the techique of rocessig the similar idices is to exloit state codebook for recordig of the closest codewords of these similar idices. Hece, for geeratig the comressio codes ad recoverig the origial idex, the idex-based state codebook look-u rocedure will be erformed. Besides, to further reduce the bit rate, our scheme excludes the reetitive idices from the search ath. Our exerimets rove the scheme ideed reset better erformace tha both of the SOC scheme ad our scheme 1. Comarig to the traditioal memoryless VQ system ad the SOC algorithm, both our roosed schemes truly achieve the goal of reducig the bit rate ideed. REFERENCES [1] C. C. Chag, D. C. Li ad T. S. Che, A imroved VQ codebook search algorithm usig Pricial Comoet Aalysis, J. Vis. Commu. Image Reresetatio, Vol. 8, No. 1, 1997, [] J. Foster, R. M. Gray ad M. O. Duham, Fiite-state vector quatizatio for waveform codig, IEEE Tras. o Iformatio Theory, Vol. IT-31, May 1985, [3] R. M. Gray, Vector quatizatio, IEEE ASSP Mag., Vol. 1, No., Ar. 1984, [4] R. M. Gary ad Y. Lide, Vector quatizatio ad redictive quatizers for Gauss-Markov sources, IEEE Tras. o Commus., Vol. COM-30, Feb. 198, [5] H. M. Hag ad J. M. Woods, Predictive vector quatizatio of images, IEEE Tras. o Commus., Vol. COM-33, No. 11, Nov. 1985, [6] C. H. Hsieh ad J. S. Shue, Frame adative fiite-state vector quatizatio for image sequece codig, Image Commu., Vol. 7, Mar. 1995, [7] C. H. Hsieh ad J. C. Tsai, Lossless comressio of VQ idex with search-order codig, IEEE Tras. o Image Processig, Vol. 5, No. 11, 1996, [8] R. C. T. Lee, Y. H. Chi ad S. C. Chag, Alicatio of Pricial Comoet Aalysis to Multikey Searchig, IEEE Tras. o Software Egieerig, Vol. SE-, No. 3, 1976, [9] Y. Lide, A. Buzo ad R. M. Gray, A algorithm for vector quatizer desig, IEEE Tras. o Commus., Vol. 8, 1980, [10] K. T. Lo ad J. Feg, Predictive mea search algorithms for fast VQ ecodig of images, IEEE Tras. o Cosumer Electroics, Vol. 41, No., 1995, [11] N. M. Nasrabadi ad Y. Feg, Image comressio usig address-vector quatizatio, IEEE Tras. o Commus., Vol. 38, No. 1, 1990, [1] N. M. Nasrabadi ad R. A. Kig, Image codig usig vector quatizatio : A review, IEEE Tras. o Commus., Vol. 36, No. 8, Aug. 1988, [13] J. Shabehzadeh ad P. O. Oguboa, Idex-comressed vector quatizatio based o idex maig, IEE Proceedigs Visio, Image ad Sigal Processig, Vol. 144, 1997, Chi-Che Chag received his BS degree i alied mathematics i 1977 ad the MS degree i comuter ad

9 8 JOURNAL OF SOFTWARE, VOL. 4, NO. 4, JUNE 009 decisio scieces i 1979, both from the Natioal Tsig Hua Uiversity, Hsichu, Taiwa. He received his Ph.D i comuter egieerig i 198 from the Natioal Chiao Tug Uiversity, Hsichu, Taiwa. Durig the academic years of , he was o the faculty of the Deartmet of Comuter Egieerig at the Natioal Chiao Tug Uiversity. From , he was o the faculty of the Istitute of Alied Mathematics, Natioal Chug Hsig Uiversity, Taichug, Taiwa. From August 1989 to July 199, he was the head of, ad a rofessor i, the Istitute of Comuter Sciece ad Iformatio Egieerig at the Natioal Chug Cheg Uiversity, Chiayi, Taiwa. From August 199 to July 1995, he was the dea of the college of Egieerig at the same uiversity. From August 1995 to October 1997, he was the rovost at the Natioal Chug Cheg Uiversity. From Setember 1996 to October 1997, Dr. Chag was the Actig Presidet at the Natioal Chug Cheg Uiversity. From July 1998 to Jue 000, he was the director of Advisory Office of the Miistry of Educatio of the R.O.C. From 00 to 005, he was a Chair Professor of Natioal Chug Cheg Uiversity. Sice February 005, he has bee a Chair Professor of Feg Chia Uiversity. I additio, he has served as a cosultat to several research istitutes ad govermet deartmets. His curret research iterests iclude database desig, comuter crytograhy, image comressio ad data structures. Guei-Mei Che received her MS degree i comuter sciece ad iformatio egieerig i 003 from Natioal Chug Cheg Uiversity, Taiwa, R. O. C. Her research iterests iclude image comressio ad image rocessig. Chia-Che Li received her BS degree i iformatio maagemet i 199 from the Tamkag Uiversity, Taiei, Taiwa. She received both her MS degree i iformatio maagemet i 1994 ad Ph.D. degree i iformatio maagemet i 1998 from the Natioal Chiao Tug Uiversity, Hsichu, Taiwa. Dr. Li served as Visitig Associate Professor at the Busiess School of the Uiversity of Illiois at Urbaa Chamaig durig the eriod of August 006 to July 007. The visitig scholarshi was aoited ad sosored by the Miistry of Educatio, Taiwa. Durig her visit, she worked with Professor Klara Nahrstedt at the Deartmet of Comuter Sciece o coy detectio ad the collaboratio cotiues. Dr. Li is curretly a rofessor of the Deartmet of Comuter Sciece ad Iformatio Maagemet, Providece Uiversity, Sha-Lu, Taiwa. Sice August 008, she is the Associate Dea of Academic Affairs of Providece Uiversity. She is also a member of IEEE ad a member of ACM. Her research iterests iclude image ad sigal rocessig, image hidig, mobile aget, ad electroic commerce.