BEMD Based Cross Bilateral Filtering Technique for Speckle Reduction in Ultrasound Images

DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 20 |NUMBER: 1 |2022 |MARCH BEMD Based C oss Bila e al Fil e ing Technique o Speckle Reduc ion in Ul asound Images Bhawna GUPTA , Vinee KHANDELWAL Depa men o Elec onics and Communica ion Enginee ing, Jaypee Ins i u e o In o ma ion Technology, Sec o -62, 201309 Noida, U a P adesh, India bha[email p o ec ed], inee .khandelw[email p o ec ed] DOI: 10.15598/aeee. 20i1.4265 A icle his o y: Recei ed Jun 22, 2021; Re ised No 22, 2021; Accep ed Dec 28, 2021; Published Ma 31, 2022. This is an open access a icle unde he BY-CC license. Abs ac . In his pape , Bidimensional Empi ical Mode Decomposi ion (BEMD) based C oss Bila e al Fil e (CBF) echnique o speckle educ ion in ul a- sound images has been p oposed. The e e ence image is ob ained by denoising he noisy image using pixel- wise Wiene il e ing. Then, bo h he noisy image and he e e ence image a e decomposed in o a se o In- insic Mode Func ions (IMFs) and he esidue im- age using BEMD echnique. CBF is applied be ween noisy image IMFs and he co esponding e e ence im- age IMFs. The image is econs uc ed back wi h hese modi ied IMFs and he esidue. The p oposed me hod exploi s he edge in o ma ion in he e e ence image o imp o ing he quali y o he denoised image. The pe - o mance o he p oposed me hod has been es ed o eal ul asound images and simula ed images ha ing noise o di e en a iance. The expe imen al esul s show ha he p oposed algo i hm pe o ms be e han o he s a e-o -a me hods in e ms o Edge Keeping Index (EKI), Co ela ion Coe icien (CC), Figu e o Me i (FOM), S uc u al Simila i y (SSIM), Peak Sig- nal o Noise Ra io (PSNR) and Signal o Noise Ra io (SNR) o syn he ic images. The algo i hm gi es be - e pe o mance o eal ul asound images in e ms o Mean o Va iance Ra io (MVR) and Equi alen Num- be o Looks (ENL). Keywo ds BEMD, CBF, noise educ ion, speckle. 1. In oduc ion Wi h he ad ancemen o a ious image acqui ing ha d- wa e in applica ions like medical diagnosis, syn he ic ape u e ada s, o a ia ion, la ge numbe o images a e being acqui ed and u ilized. These digi al images a ailable in la ge magni ude a e a ec ed by noise due o a ious ex e nal as well as in e nal ac o s. One such widely used applica ion o diagnos ic pu poses is ul- asound image, whose pe cei ed quali y is deg aded by he exis ence o speckle noise which is imminen owing o he p esence o physical phenomenon such as sca e ing a he ime o image acquisi ion [1]. Due o he high equency cha ac e is ic o speckle noise, denoising algo i hms u ilized o imp o e he quali y o hese images ace he challenge o p ese ing he edge in o ma ion. Speckle educ ion in ul asound images is an essen ial s ep and a ge s imp o emen in he qual- i y o he image in e ms o PSNR, CC, SNR, FOM, SSIM, EKI, MVR and ENL [2], [3] and [4]. The s a e-o - he-a speckle educ ion algo i hms wo k in spa ial domain. The spa ial domain ech- niques mainly use local s a is ics o in o ma ion edun- dancy be ween simila pa ches and eplace he pixel alue by p ocessing he nea by pixel alues. Mos suc- cess ul amongs his ca ego y a e di usion-based il e s like Speckle Reducing Aniso opic Di usion (SRAD), De ail p ese ing aniso opic di usion (DPAD), Pe ona-Malik’s Aniso opic Di usion (PMAD) [5], [6], [7] and [8], Bila e al il e s [9] and [10], and pa ch- based me hods like Non Local Mean Fil e (NLM) [11], [12], [13] and [14] and Op imized Bayesian Nonlocal Mean il e (OBNLM) [15] and [16]. The pa ch selec- ion in pa ch-based me hods is icky so ha he noise emo al does no lose he edge in o ma ion while de- noising. The e o e, ecen wo ks [17], [18] and [19] use ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 95 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 20 |NUMBER: 1 |2022 |MARCH modi ied NLM and Block Ma ching and 3D il e ing (BM3D) algo i hms o educe speckle while ying o p ese e he edge in o ma ion. Amongs hese a ious me hods, he bila e al il e p oposed by Tomasi and Manduchi in 1998 [9] aims o denoise he image while p ese ing edge de ails by weigh a e aging he neighbo ing pixels based on hei spa ial dis ance and simila i y. I has been applied o a ious ields like image denoising [9] and [20], pho o- g aph enhancemen [21], o ange comp ession [22], as i is non-i e a i e, simple and deli e s a s able pe o - mance compa able o many o he il e s. The disad- an age o long unning ime o his me hod has been wo ked upon by a ious me hods [22], [23] and [24]. Bila e al il e ing has also been applied in wa ele do- main o denoising in [20], which ep esen s in e es ing esul s bu does no pe o m well o eal image denois- ing. In se e e noise cases, he pe o mance o non-local me hods is be e bu ha is a he cos o compu a- ion complexi y and limi a ion o o e smoo hening he image. High quali y denoised image by local p ocessing can be ob ained by join bila e al il e [21] and [25], which calcula es weigh s using ano he e e ence image. Ge ing high quali y p e-es ima ed e e ence image is a c ucial s ep in his me hod as he esul depends on he chosen e e ence image. Empi ical Mode Decomposi ion (EMD) in oduced in 1998 [26] is a e y powe ul algo i hm decomposing he signal in i s IMFs [27]. This decomposi ion is done based on hei oscilla ion in he spa ial domain. The basis unc ions calcula ed in his me hod a e signal- dependen and a se ies o IMFs a e es ima ed ia an i - e a i e p ocedu e known as si ing [28]. The EMD was in oduced in images in 2003 in [29] and he BEMD o images was in oduced in 2005 in [30]. The BEMD is also a signal-dependen adap i e echnique, decompos- ing he image in o a se ies o IMFs and a esidue. The low-o de IMFs a e he high- equency componen s and he high o de IMFs a e he low- equency componen s. The speckle noise has high equency cha ac e is ic, he e o e he low o de IMFs a e ha ing mo e noise componen s as compa ed o he high o de IMFs. Ac- co dingly, some BEMD based denoising algo i hms u i- lizes his ac o disca d he noise exis ing in he low o de IMFs [31], [32] and [33]. Bu his may no always be ue and a signi ican noise componen may also be p esen in u he IMFs as well. The CBF was in oduced in 2004 o denoise low-ligh image [21] and o enhance he ambien image ha ely on lash pho og aph in o ma ion [25]. These me hods a e based on Bila e al il e equa ion and exploi s he ac ha he Signal o-Noise Ra io (SNR) o he lash image is highe han ha o he no- lash image. Denois- ing algo i hms can exploi his echnique o images, whe e e e ence image is he one wi h highe SNR. As in mos o he cases, he o iginal noiseless image is no a ailable so choosing he co ec e e ence image is a challenge. Laplacian py amid has been u ilized o de- noising image using CBF in [34], whe e he e e ence image has been aken as he Wiene il e ed e sion o he noisy image. Some o he CBF based image de- noising algo i hms combine Non-local Means [35] and mul i-sized 2D ha d h esholding [36] o signi ican e- sul s. Mos o he high- equency componen s o he image con ain de ail in o ma ion such as edges. Mos o he noise is also in high equency, he e o e, hese algo i hms hough gi ing good denoising pe o mance, loose impo an edge de ails. These de ails a e o im- po ance o diagnos ic pu poses when dealing wi h ul- asound images. This pape in oduces a hyb id echnique whe ein he high SNR e e ence image is calcula ed using Wiene il e ing he noisy image. The IMF’s a e com- pu ed o bo h noisy image and e e ence image. The edge in o ma ion in he e e ence image IMFs is a c u- cial in o ma ion ha is impo an om he poin o iew o diagnosis. The p oposed echnique u ilizes his edge in o ma ion in e e ence image o ob aining a be - e quali y denoised image in e ms o edge de ails. To achie e his, a CBF is applied be ween he noisy image IMFs and he co esponding e e ence image IMFs o ge despeckled image. This helps in p ese ing he edge in o ma ion while denoising he ul asound image. The emainde o he pape is o ganized as ollows. Sec ion 2. , p o ides a b ie o e iew o BEMD al- go i hm along wi h CBF algo i hm. In Sec. 3. , he p oposed denoising me hod is desc ibed. The pe o - mance e alua ion o he p oposed me hod is illus a ed in Sec. 4. , and Sec. 5. p esen s he conclusions. 2. Backg ound 2.1. Bidimensional Empi ical Mode Decomposi ion BEMD is an adap i e echnique which can be applied o images o decompose hem in o a se o a ious IMFs and a esidue. The s eps o calcula ion o he IMFs and he esidue a e as illus a ed he e. Le he obse ed image be deno ed by o(x, y). This being an i e a i e p ocess, le he esidue o he m h IMF be ep esen ed by m(x, y), which is aken as he inpu o he calcula ion o he nex IMF. Le he inpu image aken o he gene a ion o m h numbe IMF, m= 1, . . . , M a he k h i e a ion o he si ing p ocess, k= 0, . . . , K −1in wo spa ial dimensions (x, y), be deno ed by im,k(x, y). 1. Ini ializing he si ing p ocess o he calcula ion o he i s IMF wi h m= 1 and k= 0,im,k(x, y) ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 96 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 20 |NUMBER: 1 |2022 |MARCH is aken o be he obse ed image. i.e i1,0(x, y) = o(x, y). 2. Local maxima and minima o im,k(x, y)a e ex- ac ed. 3. Using he applica ion speci ic spline in e pola ion o all local maxima, calcula e he uppe en elope ue(x, y). Also, using he in e pola ion o all local minima, calcula e he lowe en elope le(x, y). 4. The mean en elope en m,k(x, y)is calcula ed om he uppe and lowe en elopes ob ained in s ep 3. en m,k(x, y) = ue(x, y) + lu(x, y) 2.(1) 5. The mean en elope en m,k(x, y)is sub ac ed om he inpu signal o calcula ing he upda ed signal o he nex i e a ion. im,k(x, y) = im,k−1−(x, y)en m,k(x, y), k→k+ 1.(2) 6. Calcula e he s anda d de ia ion ε, om he esul ob ained in s ep 5. ε= M−1 X x=0 N−1 X y=0 |im,k(x, y)−im,k−1(x, y)|2 i2 m,k−1(x, y).(3) 7. I he s anda d de ia ion εcalcula ed in s ep 6 is less han a p ede ined alue (usually 0.2–0.3), hen he esul o s ep 5 is he equi ed m h IMF om(x, y), else epea s eps 2–6. om(x, y) = im,k(x, y).(4) 8. The esidue o he m h IMF is de ined as: m(x, y) = im,0(x, y)−om(x, y).(5) 9. Fo he calcula ion o he nex IMF his esidue calcula ed in s ep 8 is aken as he inpu signal and going back o s ep 2 again. im+1,0(x, y) = m(x, y).(6) S eps 2–9 a e epea ed un il esidue calcula ed has no mo e ex ema poin s. Thus, o o al o ‘M’ IMFs and he las esidue M, he o iginal signal can be ep- esen ed as: o(x, y) = M X m=1 =im(x, y) + M(x, y).(7) The high o de IMFs a e co esponding o he low equency while low o de IMFs, a e co esponding o he high equency. 2.2. C oss Bila e al Fil e CBF algo i hm is explained he e in b e i y o he sake o illus a ion. Le Inand I deno e he noisy image and he e e ence image, espec i ely. The unc ion gd a enua es he il e ke nel weigh s in spa ial domain on he basis o he dis ance be ween he pixels. Also, he edge s opping unc ion gese s weigh s on he basis o in ensi y di e ence be ween he pixels. Then he alue o he pixel a loca ion qusing CBF can be calcula ed as: ICBF q=1 n(q)X q′∈Ω gd(∥q−q′∥)qe(I q −I q′)Inq′, (8) whe e n(q)is he no maliza ion ac o gi en by: nq=X q′∈Ω gd(∥q−q′∥)qe(I q −I q′),(9) and Ωis he window size. The dis ance scaling unc- ion gdis Gaussian unc ion as gi en in Eq. (10), whe e s anda d de ia ion σdcon ols i s wid h and he a i- able xin equa ion is Euclidean dis ance be ween qand q′∈Ω. g(x) = exp −x2 2σ2 d.(10) The edge s opping unc ion geis also Gaussian unc- ion as gi en in Eq. (11) below whe e s anda d de ia- ion σeis con olling i s wid h. ge(I q −I q′) = exp −1 2I (q)−I (q′) σe2!. (11) The s anda d de ia ion σdis ob ained as in con en- ional Bila e al il e ing. Also, as he e e ence image has less noise, σeis no se e y la ge. E en when he alue o σeis aken small and ixed alue o σeis aken o all images, he edge s opping unc ion geensu es ha p ope weigh s a e chosen wi hou o e -blu ing o unde -blu ing he images. 3. BEMD Based C oss-Bila e al Fil e ing This sec ion in oduces he p oposed BEMD based c oss bila e al il e o speckle educ ion in Ul asound images. The o iginal image has speckle noise as well as he i al edge in o ma ion in he high equency compo- nen s and his is e lec ed in he low o de IMFs o he image. Re e ence image is ob ained a e p ocessing he o iginal image wi h Wiene il e . This e e ence image is being decomposed using BEMD algo i hm o ge a se o IMFs. Ob ained low o de IMFs e ain ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 97 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 20 |NUMBER: 1 |2022 |MARCH Residue IMF1 IMF2 IMF M Residue IMF1 IMF2 IMF M Residue IMF1 IMF2 IMF M O iginal Image Re e ence Image Bidimensional Empi ical Mode Decomposi�on C oss Bila e al Fil e ing Wiene Fil e ing Denoised Image Fig. 1: Block Diag am o he p oposed scheme. dominan edge in o ma ion as noise componen has been educed p io ly. Also, he high o de IMFs will ha e he smoo h egion in o ma ion a e he educ ion o noise. Hence, he p oposed echnique u ilizes he dominan edge in o ma ion in he low o de IMFs o il e ed image and he noise ee non-edge in o ma ion in he high o - de IMFs o his e e ence image. The algo i hm applies he CBF be ween he same le el IMFs o he o iginal image and he il e ed image e e ed o as e e ence image. This helps in p ese ing he edge de ails while emo ing he speckle noise om he ul asound im- age as well as educes he blu ing in he smoo h e- gions. The block diag am o he p oposed algo i hm is as shown in Fig. 1. The s eps in he p oposed algo i hm a e as ollows: 1. Calcula e he BEMD o he o iginal ul asound image o(x, y)which has speckle noise. 2. Denoise he o iginal noisy image wi h pixel-wise Wiene il e [37] o calcula e he e e ence im- age. The noise componen has o be addi- i e while applying his il e , so he mul iplica- i e speckle noise is con e ed o addi i e noise η(n1, n2)applying log ans o ma ion. Assuming ha η(n1, n2)is ha ing ze o mean and a iance σ2 η, Wiene il e es ima es he local mean and a i- ance a ound each pixel o he chosen IMF. µe=1 NK X x,yϵw o(x, y),(12) σ2 e=1 NK X x,yϵw o2(x, y)−µ2 e,(13) whe e wis he window co esponding o he N×K neighbo hood o each pixel in he IMF. This il e hen c ea es a pixel-wise es ima e gi en as: oe(x, y) = µe+σ2 e−σ2 η σ2 e (o(x, y)−µe).(14) 3. Calcula e he BEMD o he e e ence image calcu- la ed in s ep 2. 4. Apply CBF on all he IMFs o he o iginal image aking he co esponding il e ed image IMFs as he e e ence componen . 5. Recons uc he image om he ou pu IMFs ob- ained in s ep 4 o ge he inal denoised image. ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 98 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 20 |NUMBER: 1 |2022 |MARCH IMF 1 IMF 2 IMF 3 IMF 4 IMF 5 IMF 6 IMF 7 IMF 8 IMF 9 Noisy Image (a) IMF 1 IMF 2 IMF 3 IMF 4 IMF 5 IMF 6 IMF 7 IMF 8 IMF 9 Fil e ed Image (b) Fig. 2: (a) Noisy e us image and i s BEMD IMFs and (b) Fil e ed e us image and i s BEMD IMFs. IMF 1 IMF 2 IMF 3 IMF 4 IMF 5 IMF 6 IMF 7 IMF 8 IMF 9 Noisy Image (a) IMF 1 IMF 2 IMF 3 IMF 4 IMF 5 IMF 6 IMF 7 IMF 8 IMF 9 Fil e ed Image (b) Fig. 3: (a) Noisy kidney image and i s BEMD IMFs and (b) Fil e ed kidney image and i s BEMD IMFs. The pseudo code o he algo i hm is as shown below: •Read he noisy image Inand esize i o a s anda d size as pe he da ase : Hsize = 256; •Calcula e he IMFs o noisy image In: [im , Res] = emd(In); •Wiene Fil e he noisy image o ob ain il e ed image I : I = wiene 2(In); •Calcula e he IMFs o il e ed image: [im 2, Res2] = emd(I ); •Modi y IMFs using CBF aking dis ance sigma (sigmad), edge s opping sigma (sigmae), ke nel size (ksize): Fo i e a ion i = 1 : size (im ,2); –Compu e x(i) = im (:,i); Fo i e a ion i = 1 : size (im 2,2); –Compu e y(i) = im 2 (:,i); Fo i e a ion i = 1 : size (x,2); –Calcula e cb _ou 1(i) = c oss_bila e al_ il (x(i), y(i), sigmad, sigmae, ksize); and de ail1(i) = x(i) - cb _ou 1(i); •Recons uc he image: Reco e = 0; Reco e 1 = 0; Fo i e a ion i = 1 : size (cb _ou 1,2); –Calcula e Reco e 1 = Reco e 1 + cb _ou 1(:,i) + de ail1(:,i); Reco e = Reco e 1 + Res; 4. Expe imen al Resul s The kidney and e us syn he ic images ob ained us- ing Field II simula ion p og am [38] ha e been used in ou expe imen s ha we e pe o med on MATLAB. The speckle noise has been added o he image wi h σ2= 0.1,0.2, and 0.3. BEMD algo i hm is applied on he noisy syn he ic e us image o ob ain he IMFs and he esidue. ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 99 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 20 |NUMBER: 1 |2022 |MARCH O iginal Image Noisy Image Fil e ed Image (a) O iginal Image O iginal Image Noisy Image Fil e ed Image (b) Noisy image O iginal Image Noisy Image Fil e ed Image (c) Fil e ed Image Denoised Image (d) Denoised Image Fig. 4: Syn he ic e us image o σ2= 0.1. Figu e 2(a) shows he BEMD IMFs o noisy syn- he ic e us image, ha a e ob ained o noise a iance σ2= 0.1. The spline in e pola ion ha is used in ou case is a cubic spline. The low o de IMFs can be seen o ha e high equency componen s co espond- ing o noise and edges o he image. As he Wiene il e gi es op imal pe o mance o addi i e noise, he mul iplica i e speckle was con e ed o addi i e noise using log- ans o ma ion be o e adding o he syn he ic image. Pixel-wise Wiene il e ing u ilizing 8-neighbo hood o local egion calcula ion was applied o he noisy image. The BEMD algo i hm was hen applied on his il e ed image o ge he IMFs which a e shown in Fig. 2(b) along wi h esidual image. I can be no ed ha he low o de IMFs o he il e ed image a e now ep esen ing he dominan edge de ails. As he Wiene il e has denoised he image, so IMFs o his il e ed image a e aken as he e e ence. CBF on all he IMFs o he noisy image and he co espond- ing IMFs o he il e ed image has been applied o ge he modi ied IMFs. Based on ex ensi e expe imen s pe o med on di e en images, he alue o dis ance sigma σd, edge s opping sigma σeand ke nel size a e unde aken as 1.8, 2.5, and 5, espec i ely o bes e- sul s. These modi ied IMFs along wi h he esidue o he inpu image a e u ilized o econs uc he denoised image in which he edge in o ma ion has been e ained. O iginal Image Noisy Image Fil e ed Image (a) O iginal Image O iginal Image Noisy Image Fil e ed Image (b) Noisy image O iginal Image Noisy Image Fil e ed Image (c) Fil e ed Image O iginal Image Noisy Image Denoised Image (d) Denoised Image Fig. 5: Syn he ic kidney image o σ2= 0.1. Figu e 4 shows he syn he ic e us image, i s noisy e - sion o σ2= 0.1, il e ed e e ence image and he i- nal econs uc ed denoised image. As can be seen, he denoised image is pe cep ually o he same quali y as ha o he o iginal image. Following he simila p oce- du e esul s o he syn he ic kidney image a e ob ained which a e shown in Fig. 3 and Fig. 5, espec i ely. I is wo h no ing ha he esul s p o ided by he p oposed echnique a e pe cep ually e y pleasing. Table 2, Tab. 3,Tab. 4, Tab. 5, Tab. 6 and Tab. 7 shows he compa ison o a ious pa ame e s ob ained o a ying alues o σ o he wo Field II syn he ic images, e us and kidney. As can be no iced, he p o- posed algo i hm pe o ms be e han he exis ing ech- niques in e ms o EKI and PSNR, o noise a iance σ2= 0.1,0.2and 0.3. The alues ob ained o EKI pa- ame e gi es be e esul s e en a highe noise a i- ances, clea ly showing be e edge keeping capabili y o he p oposed algo i hm. Also, as seen in he esul ables, p oposed echnique gi es compa able esul s wi h he exis ing echniques in e ms o SNR, CC, SSIM and FOM o σ2= 0.1. A he same ime, as can be analyzed om he alues ob ained by expe imen a ion ha he scheme is gi ing compa able esul s in e ms o hese pa ame e s o highe alues o σ2= 0.2and σ2= 0.3also. Thus, we can summa ize ha he echnique pe o ms accep ably well e en a highe noise le els. ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 100 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 20 |NUMBER: 1 |2022 |MARCH O iginal Image Noisy Image P oposed EMD BEMD BEMD Th esholding CBF Th esholding Enhanced BEMD Laplacian CBF NLM CBF Con en ional EMD Bila e al SRAD NLM OBNLM PMAD (a) (b) (c) (d) (e) ( ) (g) (h) (i) (j) (k) (l) (m) (n) (o) Fig. 6: Syn he ic kidney: (a) O iginal image, (b) Noisy image o σ2= 0.1, Denoised images using he me hods, (c) P oposed EMD echnique, (d) BEMD [31], (e) BEMD Th esholding [32], ( ) CBF Th esholding [36], (g) Enhanced BEMD [33], (h) Laplacian CBF [34], (i) NLM CBF [35], (j) Con en ional EMD [30], (k) Bila e al [9], (l) SRAD [5], (m) NLM [11], (n) OBNLM [16] and (o) PMAD [7]. Tab. 1: S uc u al Simila i y (SSIM) o a ious echniques. Technique MVR ENL P oposed echnique 18.81 ±2.63 5.41 ±2.37 BEMD [31] 18.51 ±3.76 5.25 ±2.79 BEMD h esholding [32] 18.13 ±4.02 5.18 ±2.82 CBF h esholding [36] 17.89 ±4.54 5.23 ±2.33 Enhanced BEMD [33] 18.02 ±4.93 5.14 ±2.64 Laplacian CBF [34] 17.95 ±4.82 5.11 ±2.18 NLM CBF [35] 17.63 ±4.22 5.01 ±2.13 Con en ional EMD [30] 17.91 ±5.32 5.01 ±2.54 Bila e al [9] 15.42 ±5.16 3.96 ±2.32 SRAD [5] 17.66 ±4.52 4.87 ±2.35 NLM [11] 17.01 ±4.14 4.91 ±2.15 OBNLM [16] 17.81 ±4.71 4.95 ±2.61 PMAD [7] 16.39 ±6.21 4.33 ±2.79 Figu e 6 shows he isual esul s ob ained by a ious denoising algo i hms applied on he kidney image co - up ed by a speckle o a iance 0.1. I is clea ly isible ha he p oposed echnique is able o con ol he o e smoo hness sho coming o some algo i hms and also has be e pe cep ual quali y in e ms o he edges in he image. Fo he sake o comple eness, he e icacy o p oposed echnique is also e alua ed by pe o ming expe imen s on he eal ul asound image da abase aken om [39]. The eal images ha e h ee se s o da a namely kid- ney, li e , and gall bladde images, each ha ing a ound 85 images. Th ee egions we e selec ed andomly o all h ee se s and he MVR and ENL ha e been calcu- la ed. The Fig. 7(a) shows he eal li e ul asound im- age, whe e h ee andomly selec ed egions a e ma ked which a e used o he calcula ion o MVR and ENL alues. The Fig. 7(b) and Fig. 7(c) depic s he MVR and ENL plo s ob ained o selec ed egions in he eal li e image da abase o compa ing he pe o mance o ou p oposed me hod wi h ha o exis ing one. I is wo h no ing ha ou p oposed me hod wo ks ai ly well compa ed o he o he s. Table 1 shows he MVR and ENL mean alues along wi h he s anda d de ia ion o he eal li e ul a- sound image da abase. Two di e en egions we e se- lec ed in each US image o MVR and ENL calcula- ion. These egions we e andomly selec ed mainly in homogeneous and edge egions o a pa icula US im- age. Recons uc ed US images we e ob ained o all he il e s and MVR and ENL alues we e calcula ed in hese egions. I is o be no ed ha he bes MVR and ENL alues a e ob ained o he p oposed il e . Based on he esul s, he nex candida e in e ms o he pe o mance was Laplacian CBF compa ed o he exis ing me hods in e ms o MVR and ENL alues. Simila expe imen s we e pe o med on kidney and gall bladde eal ul asound image da a se s also, how- e e , due o pauci y o space we ha e shown MVR and ENL plo s o li e da abase only. The esul s ob ained o he o he se s a e also in conjunc ion wi h he e- sul s shown he e. ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 101 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 20 |NUMBER: 1 |2022 |MARCH (a) MVR1 MVR2 MVR3 0 5 10 15 20 25 P oposed echnique BEMD BEMD h esholding CBF h esholding Enhanced BEMD Laplacian CBF NLM CBF Con en io nal BEMD Bila e al SRAD NLM OBNLM PMAD (b) P oposed echnique 0 1 2 3 4 5 6 7 8 ENL1 ENL2 ENL3 BEMD BEMD h esholding CBF h esholding Enhanced BEMD Laplacian CBF NLM CBF Con en io nal BEMD Bila e al SRAD NLM OBNLM PMAD (c) Fig. 7: (a) Real li e image wi h selec ed egions, (b) MVR plo and (c) ENL plo . Tab. 2: Co ela ion Coe icien (CC) o a ious echniques. Technique CC Noise a iance σ2 Syn he ic e us image Syn he ic kidney image 0.1 0.2 0.3 0.1 0.2 0.3 P oposed echnique 0.95342 0.93070 0.92330 0.93840 0.92590 0.88210 BEMD [31] 0.95834 0.93007 0.92193 0.94284 0.90968 0.87969 BEMD h esholding [32] 0.95038 0.92852 0.91310 0.92435 0.88928 0.82736 CBF h esholding [36] 0.94911 0.90321 0.88398 0.91329 0.82987 0.77120 Enhanced BEMD [33] 0.95201 0.92654 0.87511 0.92643 0.88321 0.82101 Laplacian CBF [34] 0.93750 0.90440 0.89230 0.90760 0.85880 0.77830 NLM CBF [35] 0.94880 0.89530 0.87020 0.91020 0.83980 0.76430 Con en ional EMD [30] 0.95102 0.92555 0.87480 0.92645 0.87332 0.81060 Bila e al [9] 0.91368 0.84291 0.78464 0.84947 0.74776 0.67000 SRAD [5] 0.94191 0.87916 0.81739 0.91540 0.82920 0.75551 NLM [11] 0.93126 0.87093 0.82044 0.87618 0.78484 0.71328 OBNLM [16] 0.95155 0.90697 0.86630 0.90923 0.83734 0.77571 PMAD [7] 0.94638 0.88481 0.82668 0.90595 0.80801 0.72333 ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 102 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 20 |NUMBER: 1 |2022 |MARCH Tab. 3: Signal o Noise Ra io (SNR) o a ious echniques. Technique SNR Noise a iance σ2 Syn he ic e us image Syn he ic kidney image 0.1 0.2 0.3 0.1 0.2 0.3 P oposed echnique 14.0920 12.8840 11.4910 15.5620 13.9340 12.4030 BEMD [31] 14.0620 12.6740 11.4590 15.6020 13.6940 12.4430 BEMD h esholding [32] 13.7653 12.1382 11.2891 15.1528 12.9726 12.0628 CBF h esholding [36] 12.7261 9.9268 8.2108 12.6753 11.4367 8.9624 Enhanced BEMD [33] 13.9211 11.2167 10.3427 14.4563 12.2731 10.3821 Laplacian CBF [34] 13.7400 12.9200 11.3230 14.5660 13.8250 12.3670 NLM CBF [35] 12.6540 9.8660 8.0320 12.4530 11.3450 8.0630 Con en ional EMD [30] 13.9140 11.0110 10.2900 14.2440 12.0820 10.2030 Bila e al [9] 10.7200 7.9790 6.4897 10.7320 8.0182 6.5425 SRAD [5] 12.6000 9.2820 7.3429 13.7580 10.2860 8.4398 NLM [11] 11.7240 8.8585 7.3089 11.7650 8.9261 7.3852 OBNLM [16] 13.3050 10.3730 8.6871 13.3320 10.4920 8.8753 PMAD [7] 12.9410 9.4890 7.5779 13.2020 9.6131 7.6633 Tab. 4: Figu e o Me i (FOM) o a ious echniques. Technique FOM Noise a iance σ2 Syn he ic e us image Syn he ic kidney image 0.1 0.2 0.3 0.1 0.2 0.3 P oposed echnique 0.88195 0.85261 0.81317 0.88341 0.85238 0.83860 BEMD [31] 0.82919 0.85146 0.81217 0.86334 0.86088 0.82560 BEMD h esholding [32] 0.81092 0.84838 0.80283 0.85392 0.84294 0.82934 CBF h esholding [36] 0.88392 0.82019 0.78291 0.85281 0.83827 0.77385 Enhanced BEMD [33] 0.83182 0.82791 0.79201 0.86389 0.83982 0.82739 Laplacian CBF [34] 0.88102 0.81890 0.77839 0.85930 0.83029 0.76321 NLM CBF [35] 0.88021 0.81820 0.77352 0.84920 0.82940 0.76429 Con en ional EMD [30] 0.82761 0.84320 0.78133 0.86112 0.83281 0.81143 Bila e al [9] 0.81285 0.74764 0.70383 0.77549 0.72620 0.69278 SRAD [5] 0.86349 0.78487 0.73090 0.83815 0.75237 0.73401 NLM [11] 0.87531 0.79219 0.75194 0.83151 0.78397 0.74317 OBNLM [16] 0.89364 0.84390 0.80875 0.88295 0.78922 0.76806 PMAD [7] 0.86438 0.79341 0.73724 0.85802 0.76742 0.71880 Tab. 5: Peak Signal o Noise Ra io (PSNR) o a ious echniques. Technique PSNR Noise a iance σ2 Syn he ic e us image Syn he ic kidney image 0.1 0.2 0.3 0.1 0.2 0.3 P oposed Technique 24.983 23.117 22.748 24.821 22.281 21.842 BEMD [31] 24.946 23.077 22.383 24.322 22.188 21.158 BEMD h esholding [32] 24.126 22.764 21.853 23.019 21.934 21.021 CBF h esholding [36] 24.421 21.839 22.210 23.583 21.021 21.012 Enhanced BEMD [33] 22.593 21.294 21.256 22.593 21.245 20.183 Laplacian CBF [34] 23.453 20.987 20.837 24.839 20.548 20.634 NLM CBF [35] 24.332 21.712 22.590 23.383 20.628 21.522 Con en ional EMD [30] 22.398 20.671 20.330 22.317 20.672 19.821 Bila e al [9] 21.056 18.009 16.260 19.025 15.992 14.254 SRAD [5] 23.058 19.463 17.260 22.192 18.459 16.398 NLM [11] 22.336 19.310 17.594 20.288 17.239 15.518 OBNLM [16] 24.002 21.030 19.306 21.971 19.054 17.350 PMAD [7] 23.539 19.837 17.690 21.730 17.878 15.686 ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 103