Efficient VLSI Implementation of Modified Dual Tree Discrete Wavelet Transform Based on Lifting Scheme

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1 Austalan Jounal of Basc and Appled Scences, 9(7) August 05, Pages: ISSN: Austalan Jounal of Basc and Appled Scences Jounal home page: Effcent VLSI Implementaton of Modfed Dual Tee Dscete Wavelet Tansfom Based on Lftng Scheme S. Senthl Kuma and R. Radhakshnan Assocate Pofesso, Depatment of Electoncs and Communcaton Engneeng, SVS College of Engneeng, Combatoe, Taml Nadu, Inda Pncpal, Vdhya Mandh Insttute of Technology, Eode, Taml Nadu, Inda A R T I C L E I N F O Atcle hstoy: Receved 3 June 05 Accepted 5 August 05 Avalable onlne Septembe 05 Keywods: Dscete wavelet tansfoms; Modfed dual tee dscete wavelet tansfoms; lftng Algothm; mage compesson A B S T R A C T In past few decades, dual tee dscete wavelet tansfom (DT-DWT) has become an open actve eseach aea fo mage pocessng applcatons. Nowadays; lftng based DT-DWT seeks moe attenton due to ts lowe computatonal complexty and shft nvaance popety. Nevetheless, VLSI mplementaton of lftng based DT-DWT futhe needs to be mpoved fo low powe and hgh speed mage pocessng applcatons. In ths atcle, an effcent VLSI mplementaton of modfed lftng based DT-DWT s poposed. In poposed appoach, two eal valued lftng based fltes ae used to mplement dual tee stuctue n whch sx hgh pass bands (.e., two HH, two HL and two LH) and two low pass bands (LL) ae obtaned. Next, hgh fequency components (HH and HH) as well as low pass bands (LL and LL) ae meged togetheas sngle sub bands HHm and LLm espectvely. In synthess secton, the ognal mage s ecoveed usng LL m, HH m, and LHand HL wthout consdeng the two hgh pass bands (HLand LH).Hence, the poposed appoach geatly educes the hadwae equements and consumes less powe than the DT-DWT wthout affectng the mage qualty. Expement was caed out and tested on vaous test mages usng Xlnx ISE and MATLAB R00a. The expement esults nfeed that the poposed appoach s well suted fo mage compesson. 05 AENSI Publshe All ghts eseved. To Cte Ths Atcle: S. Senthl Kuma and R. Radhakshnan., Effcent VLSI Implementaton of Modfed Dual Tee Dscete Wavelet Tansfom Based on Lftng Scheme. Aust. J. Basc & Appl. Sc., 9(7): 58-66, 05 INTRODUCTION In cuent yeas, dscete wavelet tansfom (DWT) s wdely used fo mage pocessng applcatons because of ts ablty to epesent the sgnal n dffeent scale, hghest enegy compacton, mult esoluton, and hghe compesson ato. Howeve, the ealzaton of DWT demands hghe computatonally complexty and moe memoy stoage whch ae not appopate fo hgh speed and low powe mage/vdeo pocessng applcatons (Tnku Achaya and Chatal Chakabat, 006). Sweldens (996) and Daubeches (998) poposed a lftng based DWT whch eques fewe athmetc computatons. In lftng-based DWT (LDWT) scheme, the wavelet flte matx s dvded nto successve matces ncludng dagonal, uppe tangula and lowe tangula matces. Then, the wavelet fltes ae mplemented usng banded matces multplcatons (Sweldens, 996 and Daubeches, 998). Seveal lftng based DWT achtectues have been poposed fo mage pocessng applcatons. These achtectues may nclude folded lftng based DWT (Anda et al., 00), systolc aay DWT (Huang et al., 00), and ecusve lftng based DWT (Xong et al., 006). Convesely, the lftng based achtectues clam lage amount of fame buffes to stoe the ntemedate LL output and also eque complex contol path. Anda et al., (00) poposed block based achtectue whch eques lage embedded memoy and longe output latency. In combned lnebased achtectue (Dllen et al., 003), hadwae esouces ae not effectvely utlzed and t needs to be futhe optmzed. In addton, the DWT and lftng based DWT ae suffeed by shft nvaance and lack of dectonal selectvty (Mohanty and Mehe, 0) whch affects the qualty of epoduced mage. Kngsbuy (000) and Selesnck et al (005) poposed a DT-DWT to solve the shft vaance poblem and to mpove dectonal selectvty. Futhemoe, a fully shft-nvaant lftng based statonay wavelet tansfom (LSWT) has been poposed by Lee.et.al (000). On the othe hand, both DT-DWT and LSWT needs moe lftng hadwae and consume moe powe, whch ae Coespondng Autho: S. Senthl Kuma, Assocate Pofesso, Depatment of Electoncs and Communcaton Engneeng, SVS College of Engneeng, Combatoe, Taml Nadu, Inda E-mal: sentheeyan@yahoo.co.n

2 59 S. Senthl Kuma et al, 05 Austalan Jounal of Basc and Appled Scences, 9(7) August 05, Pages: undesable fo hgh speed and low powe mage pocessng applcatons. Hence, an effectve VLSI mplementaton of modfed lftng based dual tee dscete wavelet tansfom has been poposed n ths atcle to mpove the system pefomance of dual tee wavelet tansfom by suppessng the fequency components ncludng LH and HL fo econstucton. MATERIALS AND METHODS Lftng scheme: The fundamental dea behnd the lftng scheme s that nstead of usng scalng functons on the fne level to buld a wavelet, t uses an old, smple wavelet and scalng functons on the same level to synthesze a new wavelet. The wavelet fltes ae mplemented usng lftng steps such as splt, pedct, update and nomalze. Hee, the splt phase splts the ognal sgnal X() nto even and odd pats. The pedcton step pedcts the hgh pass detaled sub band coeffcents and the update stage gves low pass appoxmaton sub band flte coeffcents.in9/7 lftng scheme, the mplementaton of D-DWT eques two pedctons, two updates and one scalng. A basc 9/7 lftng-based DWT stuctue s descbed n Fg.. The nput sgnal X () s decomposed nto two pats such as X( ) ) and X( ). Then, the fst stage of lftng opeaton s executed as follows (Tnku Achaya and Chatal Chakabat, 006): p( ) X( ) X( ) X( ) () u( ) p( ) p( ) X ( ) () Whee, p () and u () epesent the fst pedcted and updated coeffcents, and ae the fst level lftng constants. In poposed appoach, = and = ae used fo fst stage lftng pocess. The second stage of pedct and update of lftng pocess s gven by: p( ) u( ) u( ) p( ) (3) u( ) p( ) p( ) u( ) (4) p () Whee, and u () epesent the second lftng pedcted and updated coeffcents, and ae the second level lftng constants and ts typcal values ae , espectvely. The scalng s pefomed usng the nomalzaton paametes K and K. In pactce, the typcal value of nomalzaton facto K s The nomalzaton s done as follows: u( ) Ku( ) (5) p( ) p( ) K (6) Fg. : 9/7 Lftng stuctue fo 9/7 flte. Lftng based Dual Tee dscete wavelet tansfom: In case of DWT, small shfts n the nput sgnal o mage can cause sgnfcant changes n the dstbuton of sgnal/mage enegy acoss scales n the DWT coeffcents. In addton to that the DWT s not able to dscmnate spectal featues n dffeent oentatons (UfukBal, 0). In DT-DWT, dectonal selectvty and shft vaance poblems ae elmnated by pocessng the same nput sgnal usng two dffeent eal valued lftng based DWT fltes and one of the wavelet fltes s an appoxmate Hlbet tansfom of the othe. In ths appoach, DWT algothm s mplemented usng eal fltes wthout complex athmetc opeatons. The evese opeaton s done at the synthess pat to ecove the ognal mage. The analyss and synthess sectons of lftng based dual tee dscete tansfom (DT- DWT)ae llustated n Fg -3. Modfed Lftng based Dual Tee dscete wavelet tansfom: The objectve of mage compesson s to explot the edundant featues to educe the memoy stoage. As DT-DWT s a edundant tansfom, t ntoduces addtonal edundancy though t acheves good dectonal selectvty. Hence, the edundancy must be educed wthout sacfcng pefect econstucton and t can be accomplshed by smply emovng the nsgnfcant complex coeffcents (Reeves et al., 00). Though, nose shapng algothm (NSA) helps to educe the numbe of coeffcents, t eques moe bnay data fo epesentaton (Reeves et al., 00). Theefoe, the modfed lftng based dual tee stuctue has been modfed and pesented n ths atcle. At the analyss pat, the low fequency sub bands (LL &LL) as well as hgh fequency sub bands (HH & HH) ae meged as sngle sub bands such as LL m and HH m espectvely and the ognal mage s econstucted at the synthess pat by usng LL m, HH m, HL and LH sub bands. Ths stuctue eques less numbe of lftng hadwae and theeby

3 60 S. Senthl Kuma et al, 05 Austalan Jounal of Basc and Appled Scences, 9(7) August 05, Pages: educng the powe consumpton as well as athmetc computatons than the D-DWT. Fg.4 demonstates the analyss secton of modfed lftng based dual tee stuctue. Fg. : Analyss Secton of Lftng based DT-DWT stuctue. Fg. 3: Synthess Secton of Lftng based DT-DWT stuctue.

4 6 S. Senthl Kuma et al, 05 Austalan Jounal of Basc and Appled Scences, 9(7) August 05, Pages: In poposed appoach, ntally an nput mage s decomposed up to a desed level by two sepaable D DWT banches usng lftng scheme such as, tee and tee, whose fltes ae specfcally desgned to meet the Hlbet pa equement. At each level of decomposton, sx hgh-pass sub bands as well as two low-pass sub bands ae geneated. Next, the HH and HHsub bands ae lnealy combned as HHm. Smlaly the low-pass sub bands of each tee ae combned as LLm. Fnally, the econstucted mage s obtaned at the synthess pat by nvetng the pocess pefomed at the analyss secton. Let us assume that and be the scalng and wavelet functons of eal tee. Let and be the scalng and wavelet functons of magnay tee. The poduct of φ (.) along the fst coodnate and Ψ (.) along the second coodnate coespond to LH sub band. Smlaly, wavelets (LH, HL, HH) assocated wth DWT ae gven by (Ankt and Bhuane, 0), ( ) ( ) j ( ) ( ) ( ) ( ) j ( ) ( ) ( ) ( ) j ( ) ( ) ( ) ( ) j ( ) ( ) ( ) ( ) j ( ) ( ) ( ) ( ) j ( ) ( ) ( ) ( ) j ( ) ( ) ( ) ( ) j ( ) ( ) ( ) ( ) j ( ) ( ) ( ) ( ) ( ) j ( ) ( ) ( ) ( ) ( ) j ( ) ( ) ( ) ( ) ( ) j ( ) ( ) ( ) ( ) ( ) j ( ) j * ( ) ( ) j ( ) j * ( ) ( ) j ( ) j * * ( ) ( ) j ( ) j ( ) ( ) j ( ) j * ( ) ( ) j ( ) j * ( ) ( ) j ( ) j * * ( ) ( ) j ( ) j ( ) ( ) j ( ) j * ( ) ( ) j ( ) j * ( ) ( ) j ( ) j * * ( ) ( ) j ( ) j (7) (8) (9) (0) () () (3) (4) (5) (6) (7) (8) Real-dual tee dscete wavelet tansfom consdes only the eal pat of the complex wavelets (Ankt and Bhuane, 0) fo the analyss secton and t s mplemented usng two sepaate lftng based DDWT. It poduces eghtsub bands such as HH, HL, LH, HL, LH, HH, LL and LL as follows: j ) ( ) ( j ) (, ) ( ) ( ), j j,, (, (, ) ( ) ( ), j j,, (, j ) ( ) ( ) j (, ) ( ) ( ),3 j j,3, (, j ) ( ) ( ) j (9) Real-dual tee dscete wavelet tansfom s a edundant and two tmes expensve. Thus, the poposed stuctue combnes the two hgh pass bands as well two low pass bands as a sngle component such as HHm and LLm espectvely. Futhe, t pefoms the synthess opeaton wthout consdeng two hgh pass bands and as a esult, the hadwae equement s educed by a facto of fo synthess opeaton. The modfed synthess secton s shown n Fg.5.

5 6 S. Senthl Kuma et al, 05 Austalan Jounal of Basc and Appled Scences, 9(7) August 05, Pages: Fg. 4: Analyss secton of modfed Lftng based dual tee dscete wavelet tansfom (Poposed). Fg. 5: Synthess secton of modfed Lftng based dual tee dscete wavelet tansfom (Poposed). Expemental Results and Dscussons: In ths secton, the pefomance of poposed appoach s qualtatvely analyzed and the numecal esults of pefomance metcs ae dscussed. Expement was conducted on Intel Pentum IV 3.0-GHz CPU and -GB RAM usng Xlnx ISE desgn sut 4.5 and MATLAB 00. The poposed appoach was tested on test mages ncludng lvng oom.tff, house.tff, lake.tff and Jet plane.tff wth mage sze of 5 5 and the paametes ncludng Aveage Absolute Dffeence (ABSDIFF), Peak Sgnal to Nose Rato (PSNR) (Llan et al., 0 and Amhamed et al., 00), Image Fdelty (IMFID) and Mean Squae Eo (MSE) (Llan et al., 0 and Amhamed et al., 00), ae consdeed fo pefomance compason. These paametes ae calculated as follows. MN ABSDIFF o( x, y) ( x, y) MN x0 y0 (0) 55 MN PSNR 0log 0 MN o( x, y) ( x, y) x0 y0 MN o( x, y) ( x, y) x0 y0 IMFID o( x, y) MN MSE o( x, y) ( x, y) MN x0 y0 () () (3) The qualty of econstucted mage s analyzed usng the above metcs. Peak Sgnal-to-Nose Rato (PSNR) measues the nose powe wth espect to peak sgnal powe and t s often pefeed as pefomance metc fo mage compesson. PSNR must be hgh fo bette mage qualty. The ognal and econstucted mages of poposed method ae

6 63 S. Senthl Kuma et al, 05 Austalan Jounal of Basc and Appled Scences, 9(7) August 05, Pages: shown n Fg.6. Fom Fg.6, t can be seen that, the qualty of econstucted mage s appecable and t s an exact eplca of the ognal mage. The pefomance of poposed stuctue s quanttatvely evaluated based on the metcs ncludng ABSDIFF, PSNR, IMFID and MSE and plotted n Fg.7 (a)-(d). The pefomance of poposed appoach s compaed wth the othe exstng technques and t s noted n Table I-V. It s obseved that the modfed lftng based DT-DWT out pefoms than othe exstng technques. The poposed appoach s also smulated usng Xlnx ISE desgn sut 4.5 and the esults ae epoted n Table VI. It s noted that the poposed stuctue s well suted fo low powe and hgh speed mage pocessng applcatons. Fg. 6: Ognal and econstucted mages of poposed appoach. Table I: Pefomance compason of ABSDIFF (Absolute dffeence). Absolute dffeence(absolute dffeence) Images lvng oom house lake Jetplane DWT LWT DTWT Poposed Table II: Pefomance compason of PSNR. PSNR Images lvng oom house lake Jetplane DWT LWT DTWT Poposed Table III: Compason of mage fdelty. IMAGE FIDELITY Images lvng oom house lake Jet plane DWT -5.48E LWT -7.79E DTWT -5.48E Poposed -4.05E E E E-04 Table IV: Pefomance compason of MSE. MEAN SQUARE ERROR (MSE) Images lvng oom house lake Jet plane DWT LWT DTWT Poposed Table V: Oveall pefomance compason of poposed appoach wth exstng System. Method ABSDIFF PSNR IMFID MSE Tme Complexty (Sec) Analyss secton Tme Complexty (Sec) Synthess Secton DWT E

7 PSNR (n db) Absolute dffeence 64 S. Senthl Kuma et al, 05 Austalan Jounal of Basc and Appled Scences, 9(7) August 05, Pages: LWT E DTWT E Poposed E Table VI: Paamete Compason of Poposed and Exstng System. Paamete Lftng based DT-DWT Modfed lftng based DT-DWT Analyss Synthess Analyss Synthess Powe (mw) Delay (ns) Regstes Memoy Buffes FF/Latches DWT LWT DTWT Poposed-DSLS Sample Images Fg. 7(a): Absolute dffeence vs. Sample mages DWT LDWT DT-DWT Poposed Fg. 7(b): PSNR vs. Sample mages Sample mages

8 Mean Squae Eo Image Fdelty 65 S. Senthl Kuma et al, 05 Austalan Jounal of Basc and Appled Scences, 9(7) August 05, Pages: x DWT LDWT DT-DWT Poposed Fg. 7(c): Image Fdelty vs. Sample mages Sample mages Compason of MSE DWT LWT DTWT Poposed-DSLS Fg. 7(d): Mean Squae Eo vs. Sample mages. Fg. 7(a)-(d) Compason of test esults Sample Images Concluson: In ths pape, a novel modfed lftng based DT- DWT has been poposed fo low powe and hgh speed mage compesson applcatons. An nput mage s dvded nto two banches of tees and lftng based DWT usng 9/7 flte s appled to each tee at the analyss secton. Eght sub bands such ashh, HL, LH, HL, LH, HH, LL and LL ae geneated. The hgh-pass sub bands (HH and HH) and low-pass sub bands (LL and LL) ae lnealy combned to poduce HHm and LLm. The econstucted mage s obtaned at the synthess pat wthout consdeng two hgh pass bands (LH and HL) and thus the hadwae complexty, powe and athmetc computatons ae educed to some extent. Expement was conducted on fou test mages usng Xlnx ISE desgn sut 4.5 and MATLAB 00.The pefomance was evaluated based on the compesson and achtectual paametes. Test esults show that the modfed lftng based DT-DWT s best suted fo low powe and hgh speed mage pocessng applcatons wthout sacfcng the dectonal and shft nvaant featues. REFERENCES Tnku Achaya and Chatal Chakabat, 006. A Suvey on Lftng-based Dscete Wavelet

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