Variational Image Restoration

Transcription

1 Variational Image Restoration Yuling Jiao School of and Statistics and Mathematics ZNUFE Dec 30, 2014

2 Outline 1 1 Classical Variational Restoration Models and Algorithms 1.1 Variational Image Restoration Modeling 1.2 Algorithms for min u J (u) = F (Ku, f ) + λr(u) 2 2 Proposed Model and Algorithm 3 3 Numerical Results 3.1 Denoising 3.2 Deblurring 3.3 Inpainting (ZNFUE) Dec 30, / 118

3 1 Classical Variational Restoration Models and Algorithms

4 Variational Image Restoration Modeling f = Ku n, f Y, u X, K L(X, Y ). +, n is gaussian =, n is multiplicative n(u), n is image dependent I, Denoising convolution, Deblurring K = projection, Inpainting upsample, Zomming Dec 30, / 118

5 oringal image Dec 30, / 118

6 SNR 3.84dB,PSNR 7.89dB June 5, / 118

7 SNR 16.92dB,PSNR 29.45dB,It: 28 June 5, / 118

8 oringal image June 5, / 118

9 SNR 1.72dB,PSNR 11.99dB June 5, / 118

10 SNR 24.47dB,PSNR 35.64dB,It: 51 June 5, / 118

11 original image June 5, / 118

12 inpainted June 5, / 118

13 Variational Image Restoration Modeling Recover u from observed f by MAP: } u = arg max {P u f u u = arg min u { = arg max u { Pf u (f u)p u (u)} P f (f ) } log P f u (f u) + log P u (u) eg: restoration f = u + n with Gaussian distributed n and Gaussian prior of u, i.e., ( P f u (f u) exp f ) u 2 L 2 2σ 2 n and ( P u (u) exp ) u 2 L 2 2σ 2. u June 5, / 118

14 Variational Image Restoration Modeling Then u is recovered by min u f u 2 L 2 (Ω) + λ u H 1 (Ω) (Tikhonov regularization). So, one can recover u by the regularized variational form Then, min J (u) = F (Ku, f ) + λr(u). u proper data fitting term + proper regularization term+ fast algorithm + proper regularization parameter = good restoration June 5, / 118

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16 Variational Image Restoration Modeling Data Fitting Term F (Ku, f ) 1 2 Ku f 2 L 2 (Ω), Gaussian Ku f G, texture Ku f L 1 (Ω), outlier F = Ku f log Ku, poisson Ω Ω Ku + f Ku, multiplicative (Ku f ) 2, sample Ω u 2 (Ku f ) 2 Ku, ultrasound Ω (WHU) June 5, / 118

17 Variational Image Restoration Modeling Regularization Term (prior of u) u L2 (Ω), Tikhonov regularizer, 1960 s u H 1 (Ω), Tikhonov regularizer, 1960 s u, Γ M S, Mumford-Shar regularizer, 1980 s u TV (Ω), TV regularizer, 1992, Osher Wu L1 (Ω), Wavelet regularizer, 1990 s R(u) = u E, Euler s elastica regularizer, 1980 s, M-S u TV 2 (Ω), TV 2 regularizer, 2000 s, Scherzer u HOR : M, Reduced TV 2 regularizer, 2004, T.Chan u ICTV (Ω), Inf-conv regularizer, 1997, Lions, Chambolle u TGV (Ω),... Tgv regularizer, 2010, Kunisch (WHU) June 5, / 118

18 Variational Image Restoration Modeling u L 2 (Ω) convex differentiable but no geometrical information and poor noise killing u H 1 (Ω) convex differentiable but do not keep jumps u(x, y), (x, y) Ω, Ω = (a, b) (c, d), for a.e y (c, d), u(, y) H 1 (a, b) H ölder(1/2). Mumford-Shar λ ] [(1 v i+0.5,j )(u i+1,j u i,j ) 2 +(1 v i,j +0.5 )(u i,j +1 u i,j ) 2 +µ i,j i,j R M S (u, Γ) = λ u 2 + µ Γ h Ω\Γ ensure spatial regularity and keep edges but non-convex (v i+0.5,j + v i,j +0.5 ) (WHU) June 5, / 118

19 Variational Image Restoration Modeling u TV { } Du := sup u gdx : p C0 (Ω, R2 ), p 1. Ω Ω Denote the Rodon measure Ω Du by u TV. Important property: Du = u + u + d h 1 and Du = dsdl Γ Γ Ω {u=l} edge preserving convex but non differentiable and cause stair case Euler s elastica (α + β κ 2 )ds Γ + u E = (α + β κ 2 )dsdl = (α + β( u {u=l} Ω u )2 ) Du preserve both jumps and smoothness but nonconvex (WHU) June 5, / 118

20 Variational Image Restoration Modeling u TV 2 u TV 2 { } := sup u 2 vdx : v C0 (Ω, S 2 2 ), v F 1 Ω convex, take care of flatten domain but blur the the boundary. u M u TV 2 { } := sup u vdx : v C0 (Ω), v 1 Ω convex, weaker smoothness but also do not keep jump since u L 1 (Ω) and u M (Ω) u W 1,1 (Ω) (WHU) June 5, / 118

21 Variational Image Restoration Modeling u ICTV (Ω) { } u ICTV (Ω) := inf α u v v TV (Ω) + β v TV 2 (Ω) { = inf α v sup p 1 p C 0 (Ω,R2 ) Ω (u v) pdx + β sup q 1 q C 0 (Ω,S 2 2 ) = sup inf. and inf is attained when α p = p,q v β 2 q Ω } v 2 qdx convex and utilizing structure of the image preserve both smoothness and constant jump (WHU) June 5, / 118

22 Variational Image Restoration Modeling u GTV (Ω) u GTV (Ω) := sup u 2 qdx (let p = q in u ICTV ) q α Ω q β q C 0 (Ω,S 2 2 ) Wu L 1 (Ω) W can be FT, let, dictionary... natural images can be sparsely approximate under let bases large let coefficients appear at the singularities different let has different vanishing moment let transform can be seen as an multi-differential operator which can detect the underling regularity of the image adaptively (WHU) June 5, / 118

23 Variational Image Restoration Modeling HOR MODEL TO REDUCE STAIR CASE A. Chambolle and P. Lions min u 1+u 2 λ 1 u 1 TV + λ 2 H (u 2 ) F L 1 + K (u 1 + u 2 ) f 2 L 2 T. Chan, S. Esedoglu, and F. Park min λ 1 u 1 u TV + λ 2 u 2 p 1+u 2 L 1 + K (u 1 + u 2 ) f 2 L, p = 1, 2 2 T. Chan, A. Marquina, and P. Mulet min u λ 1 u TV + λ 2 Φ( u ) (Lu) 2 L 1 + Ku f 2 L 2 (WHU) June 5, / 118

24 Variational Image Restoration Modeling K. Kunisch,K. Bredies, and T. Pock min u,v λ 1 ε(v) + λ 2 u v L 1 + Ku f 2 L 2 Osher, S, Tai, X.C.,Rahman, T min τ TV + 1 τ f 2, s.t. τ = 0 τ 2λ L 2 min u u TV u, τ τ, s.t. Ku f L 2 σ(n) L 2 (WHU) June 5, / 118

25 Variational Image Restoration Modeling Tight Frames Let X L 2 (R) to be countable, X is a tight if f 2 2 = < f, h > 2, f L 2 (R). h X It is equivalent to f = h X < f, h > h, f L 2 (R). Representation of f in terms of h is not unique. The sequence {< f, h >} is called the canonical frame coefficients. (WHU) June 5, / 118

26 Variational Image Restoration Modeling Wavelet Frames A wavelet system is the collection of the dilations and the shifts of a finite set Ψ L 2 (R) X (Ψ) = {2 k/2 ψ(2 k x j ) : ψ Ψ, k, j Z} Theorem X (Ψ) is a tight frame iff its "dual Gramian" is the identity, i.e., ^ψ(2 k ω) 2 = 1, ψ Ψ k Z a.e and ^ψ(2 k ω) ^ψ(2 k (ω + (2j + 1)2π)) = 0, a.e j Z. ψ Ψ k=0 (WHU) June 5, / 118

27 Variational Image Restoration Modeling Wavelet Frame from Multiresolution Analysis Start with a function refinable ψ L 2 (R) with mask h 0, i.e. φ(x ) = 2 k Z h 0 (k)φ(2x k). Let Ψ = {ψ 1, ψ 2,, ψ r }, where ψ i (x ) = 2 k Z h i (k)φ(2x k), with wavelet masks h i. (WHU) June 5, / 118

28 Variational Image Restoration Modeling Matrix Representation Let rows of W be a frame, i.e. W T W = I. Decomposition: c = Wf. Reconstruction: f = W T c. W can be generated by tight frame filters obtained via UEP. Framelet Based Balanced Model { 1 min K W T c f p c p + α (I WW T )c } 2 + β c L p (Ω) 2 l 2 l 1, p = {1, 2} (WHU) June 5, / 118

29 Algorithms for min u J (u) = F (Ku, f ) + λr(u) First Optimization then Discretization first derive Euler-Lagrange equation { F (Ku, f ) + λ R(u) = 0 B.D. then time marching: u = F (Ku, f ) λ R(u) t u(0, ) = f B.C. it does work but high nonlinearity + nonsmoothness = bad CFL condition (slow) (WHU) June 5, / 118

30 Algorithms for min u J (u) = F (Ku, f ) + λr(u) First Discretization and Optimization (based on operator splitting,alternative direction,nesterov s acceleration ) State-of-the-Art-Methods Augmented-Lagrangian-Type Methods Forward-Backward Splitting Nesterov s acceleration A Unified Primal-Dual Algorithm (WHU) June 5, / 118

31 Algorithms for min u J (u) = F (Ku, f ) + λr(u) Augmented-Lagrangian-Type Methods minimize subject to H (u) + G(v) Au + Bv = b Algorithm 1 ADMM(GADM) Require: v 0 R Nv, λ 0 R N b, τ > 0 1: for k = 0, 1, do 2: u k+1 = arg min u H (u)+ < λ k, Au > + τ 2 b Au Bv k u u k 2 Q 3: v k+1 = arg min u G(u)+ < λ k, Bv > + τ 2 b Au k+1 Bv v v k 2 P 4: λ k+1 = λ k + τ(b Au k+1 Bv k+1 ) 5: end for (WHU) June 5, / 118

32 Algorithms for min u J (u) = F (Ku, f ) + λr(u) minimize subject to H (u) + G(v) Au + Bv = b Algorithm 2 AMA Require: λ 0 R N b, τ > 0 1: for k = 0, 1, do 2: u k+1 = arg min u H (u)+ < λ k, Au > 3: v k+1 = arg min u G(u)+ < λ k, Bv > + τ 2 b Au k+1 Bv 2 4: λ k+1 = λ k + τ(b Au k+1 Bv k+1 ) 5: end for (WHU) June 5, / 118

33 Algorithms for min u J (u) = F (Ku, f ) + λr(u) Forward-Backward Splitting minimize J (x ) Algorithm 3 Gradient Descent 1: for k = 0, 1, do 2: x k+1 = x k + τ J (x k ) 3: end for F = H + G Algorithm 4 FBS 1: for k = 0, 1, do 2: x k+1 = J τ G (x k τ H (x k )) 3: end for (WHU) June 5, / 118

34 Algorithms for min u J (u) = F (Ku, f ) + λr(u) Nesterov s acceleration minimize J (x ) Algorithm 5 Nesterov s Optimal Gradient Descent Require: α 0 = 1, x 0 = y 1 R N, τ < 1/L( F ) 1: for k = 1, 2, 3, do 2: x k = y k τ J (y k ) 3: α k+1 = (1 + 4α 2 k + 1)/2 4: y k+1 = x k + (α k 1)(x k x k 1 )/α k+1 5: end for (WHU) June 5, / 118

35 Algorithms for min u J (u) = F (Ku, f ) + λr(u) J = H + G Algorithm 6 FISTA Require: y 1 = x 0 R N, α 1 = 1, τ < 1/L( G) 1: for k = 1, 2, 3, do 2: x k = J τ G (y k τ H (y k )) 3: α k+1 = (1 + 4α 2 k + 1)/2 4: y k+1 = x k + α k 1 α k+1 (x k x k 1 ) 5: end for (WHU) June 5, / 118

36 Algorithms for min u J (u) = F (Ku, f ) + λr(u) minimize subject to H (u) + G(v) Au + Bv = b Algorithm 7 Fast AMA Require: α 0 = 1, λ 1 = ^λ 0 R N b, τ < ρ(a T A) 1: for k = 0, 1, 2, do 2: u k = arg min H (u)+ < ^λ k, Au > 3: v k = arg min G(v)+ < ^λ k, Bv > + τ 2 b Au k Bv 2 4: λ k = ^λ k + τ(b Au k Bv k ) 5: α k+1 = ( α 2 k )/2 6: ^λ k+1 = λ k + α k 1 α k+1 (λ k λ k 1 ) 7: end for (WHU) June 5, / 118

37 Algorithms for min u J (u) = F (Ku, f ) + λr(u) minimize H (u) + G(v) subject to Au + Bv = b Algorithm 8 Fast ADMM Require: v 1 = ^v 0 R Nv, λ 1 = ^λ 0 R N b, τ > 0 1: for k = 1, 2, 3, do 2: u k = arg min H (u)+ < ^λ k, Au > + τ 2 b Au B ^v k 2 3: v k = arg min G(v)+ < ^λ k, Bv > + τ 2 b Au k Bv 2 4: λ k = ^λ k + τ(b Au k Bv k ) 5: if E k > 0 then 6: α k+1 = ( α 2 k )/2 7: ^v k+1 = v k + α k 1 α k+1 (v k v k 1 ) 8: ^λ k+1 = λ k + α k 1 α k+1 (λ k λ k 1 ) 9: else 10: α k+1 = 1, ^v k+1 = v k, ^λ k+1 = λ k 11: end if 12: end for (WHU) June 5, / 118

38 Algorithms for min u J (u) = F (Ku, f ) + λr(u) A Unified Primal-Dual Algorithm min F (Kx ) + G(x ), max x X ( ) G ( K y) + F (y) y Y min max < Kx, y > +G(x ) F (y) x X y Y Initialization: Choose τ, σ > 0, θ [0, 1], (x 0, y 0 ) X Y and set x 0 = x 0. Iterations (n 0): Update x n, y n, x n as follows: y n+1 = (I + σ F ) 1 (y n + σk x n ) x n+1 = (I + τ G) 1 (x n τk y n+1 ) x n+1 = x n+1 + θ(x n+1 x n ) (WHU) June 5, / 118

39 Algorithms for min u J (u) = F (Ku, f ) + λr(u) min x Ω Du + λ 2 u g 2 2 min max < u, div p > X + λ u X p Y 2 u g 2 2 δp(p) F (p) = δp(p) G(u) = λ 2 u g 2 2 p = (I + σ F ) 1 ( p) p i,j = p i,j max(1, p i,j ) (WHU) June 5, / 118

40 Algorithms for min u J (u) = F (Ku, f ) + λr(u) min u Ω Du + λ u g 1 min max < u, div p > X +λ u g u X p Y 1 δp(p) ũ i,j τλ u = (I + τ G) 1 (ũ) ũ i,j + τλ g i,j if ũ i,j g i,j > τλ if ũ i,j g i,j < τλ if ũ i,j g i,j τλ (WHU) June 5, / 118

41 Algorithms for min u J (u) = F (Ku, f ) + λr(u) min u Ω Du + λ 2 Au g 2 2 min max < u, div p > X + λ u X p Y 2 Au g 2 2 δp(p) u = (I + τ G) 1 (ũ) u = arg min u u ũ 2τ F 1( τλf(g)f(k A ) + F(ũ) τλf(k A ) λ 2 k A u g 2 2 ) (WHU) June 5, / 118

42 Algorithms for min u J (u) = F (Ku, f ) + λr(u) min u X Φu 1 + λ 2 Au g 2 2 min u X Φu 1 + λ 2 u = (I + τ G) 1 (ũ) u i,j = ũ i,j ũ i,j +τλg i,j 1+τλ i,j D\I if (i, j ) I else (u i,j g i,j ) 2 (WHU) June 5, / 118

43 2 Proposed Model and Algorithm

44 Proposed Model and Algorithm Proposed Model { } 1 min u p Ku f p L p (Ω) + α u TV + β ωwu l, p = {1, 2}, = {a, i} 1 there exist at least one minimizer. convex, utilizes edge preserving property of total variation and the adaptivity of the framlet transform to the underlying regularity of image. Therefore, preserve both jumps and smoothness. (WHU) June 5, / 118

45 Proposed Model and Algorithm Algorithm:(ADMM for Fixed α and β) 1 min u 2 Ku f 2 L 2 (Ω) + α u TV + β ωwu l (P) 1 min max u,v,z p,q L(u, v, z ; p, q) (PD) L(u, v, z ; p, q) = 1 2 Ku f 2 + u v, p + r 2 u v α v 1 + Wu z, q + s 2 Wu z β ωz 1 (WHU) June 5, / 118

46 Algorithm for Proposed Model algorithm ( ) u 0 = f, v 0 = 0, z 0 = 0; p 0 = 0, q 0 = 0, given α 0, β 0 γ > 0 for l = 1, 2, 3,, for k = 1, 2, 3,, (u k, v k, z k ) = arg min u,v,z L α l 1,β l 1(u, v, z ; pk 1, q k 1 ) p k = p k 1 r(p k 1 u k ) q k = q k 1 s(q k 1 Wz k ) stop or k k + 1 end for α l = 1 γ+1 ( 1 2 β l = 1 γ+1 ( 1 2 stop or l l + 1 end for Ku k f βl 1 ωwu k l 1)/ u k 1 Ku k f αl 1 u k 1 )/ ωwu k l 1 (WHU) June 5, / 118

47 Algorithm Detail Alternative Direction Minimization for (u k, v k, z k ) = arg min u,v,z L α l 1,β l 1(u, v, z ; pk 1, q k 1 ) fix v = v k 1,z = z k 1, solving u k u k = arg min L α l 1,β l 1(u, v k 1, z k 1 ; p k 1, q k 1 ) u the optimal conditon is a linear systerm. fix u = u k, solving v k, z k v k = arg min L α l 1,β l 1(u k, v, z k 1 ; p k 1, q k 1 ) v z k = arg min z L α l 1,β l 1(u k, v k, z ; p k 1, q k 1 ) two close form solution defined by threshold functions. (WHU) June 5, / 118

48 Complexity and Convergence Computational Complexity: O(m n) or O(m n) log(m n) Convergence Analysis: Convergence for u k with fix α l, β l : X = R m n, Y = X X, Z = W (X ), A = [, W ] : X X Y Z F (u) = 1 2 Ku f 2 2 : X R, G(v) = α v 1 1 +β ωv 2 1 : Y Z : R then, min u,v F (u) + G(v), s.t. Au = v by ADMM is inner loop of algorithm ( ) Convergence for α l, β l : {α l }, {β l } are monotone in the same way depend on α 0, β 0. (WHU) June 5, / 118

49 3 Numerical Results

50 Denoising oringal image (WHU) June 5, / 118

51 Denoising observed image,psnr 23.70dB (WHU) June 5, / 118

52 Denoising tv restoration,psnr 34.29dB, CPU 0.84s (WHU) June 5, / 118

53 Denoising balanced restoration,psnr 31.53dB, CPU 2.17s (WHU) June 5, / 118

54 Denoising chan 4th ordr restoration,psnr 35.25dB, CPU 8.33s (WHU) June 5, / 118

55 Denoising tgv restoration,psnr 35.72dB, CPU 27.69s (WHU) June 5, / 118

56 Denoising tv frame restoration,psnr 33.95dB, CPU 5.44s (WHU) June 5, / 118

57 Denoising oringal image (WHU) June 5, / 118

58 Denoising observed image,psnr 23.47dB (WHU) June 5, / 118

59 Denoising tv restoration,psnr 28.35dB, CPU 0.39s (WHU) June 5, / 118

60 Denoising balanced restoration,psnr 27.10dB, CPU 4.47s (WHU) June 5, / 118

61 Denoising chan 4th ordr restoration,psnr 28.01dB, CPU 8.19s (WHU) June 5, / 118

62 Denoising tgv restoration,psnr 28.07dB, CPU 26.92s (WHU) June 5, / 118

63 Denoising tv frame restoration,psnr 28.23dB, CPU 5.97s (WHU) June 5, / 118

64 Denoising oringal image (WHU) June 5, / 118

65 Denoising observed image,psnr 22.82dB (WHU) June 5, / 118

66 Denoising tv restoration,psnr 26.19dB, CPU 0.83s (WHU) June 5, / 118

67 Denoising balanced restoration,psnr 25.72dB, CPU 2.78s (WHU) June 5, / 118

68 Denoising chan 4th ordr restoration,psnr 25.98dB, CPU 8.94s (WHU) June 5, / 118

69 Denoising tgv restoration,psnr 25.58dB, CPU 23.84s (WHU) June 5, / 118

70 Denoising tv frame restoration,psnr 26.21dB, CPU 6.45s (WHU) June 5, / 118

71 Denoising oringal image (WHU) June 5, / 118

72 Denoising observed image,psnr 24.10dB (WHU) June 5, / 118

73 Denoising tv restoration,psnr 32.14dB, CPU 0.52s (WHU) June 5, / 118

74 Denoising balanced restoration,psnr 30.38dB, CPU 5.44s (WHU) June 5, / 118

75 Denoising chan 4th ordr restoration,psnr 31.46dB, CPU 12.97s (WHU) June 5, / 118

76 Denoising tgv restoration,psnr 32.19dB, CPU 16.27s (WHU) June 5, / 118

77 Denoising tv frame restoration,psnr 31.86dB, CPU 9.28s (WHU) June 5, / 118

78 Deblurring oringal image (WHU) June 5, / 118

79 Deblurring observed image,psnr 16.60dB (WHU) June 5, / 118

80 Deblurring tv restoration,psnr 33.12dB, CPU 2.78s (WHU) June 5, / 118

81 Deblurring balanced restoration,psnr 30.57dB, CPU 24.53s (WHU) June 5, / 118

82 Deblurring tv frame restoration,psnr 30.93dB, CPU 13.80s (WHU) June 5, / 118

83 Deblurring oringal image (WHU) June 5, / 118

84 Deblurring observed image,psnr 18.13dB (WHU) June 5, / 118

85 Deblurring tv restoration,psnr 29.44dB, CPU 2.88s (WHU) June 5, / 118

86 Deblurring balaced restoration,psnr 28.84dB, CPU 18.69s (WHU) June 5, / 118

87 Deblurring tv frame restoration,psnr 29.08dB, CPU 7.86s (WHU) June 5, / 118

88 Deblurring oringal image (WHU) June 5, / 118

89 Deblurring observed image,psnr 18.55dB (WHU) June 5, / 118

90 Deblurring tv restoration,psnr 24.72dB, CPU 2.84s (WHU) June 5, / 118

91 Deblurring balanced restoration,psnr 24.33dB, CPU 27.03s (WHU) June 5, / 118

92 Deblurring tv frame restoration,psnr 23.92dB, CPU 11.19s (WHU) June 5, / 118

93 Deblurring oringal image (WHU) June 5, / 118

94 Deblurring observed image,psnr 18.32dB (WHU) June 5, / 118

95 Deblurring tv restoration,psnr 27.39dB, CPU 1.70s (WHU) June 5, / 118

96 Deblurring blanced restoration,psnr 27.53dB, CPU 24.80s (WHU) June 5, / 118

97 Deblurring tv frame restoration,psnr 27.55dB, CPU 11.50s (WHU) June 5, / 118

98 Inpainting oringal image (WHU) June 5, / 118

99 Inpainting observed image,psnr 21.68dB (WHU) June 5, / 118

100 Inpainting tv restoration,psnr 43.01dB, CPU 95.63s (WHU) June 5, / 118

101 Inpainting balanced restoration,psnr 31.60dB, CPU 34.14s (WHU) June 5, / 118

102 Inpainting tvframe restoration,psnr 42.20dB, CPU s (WHU) June 5, / 118

103 Inpainting oringal image (WHU) June 5, / 118

104 Inpainting observed image,psnr 14.27dB (WHU) June 5, / 118

105 Inpainting tv restoration,psnr 27.82dB, CPU 13.03s (WHU) June 5, / 118

106 Inpainting balanced restoration,psnr 27.35dB, CPU 32.02s (WHU) June 5, / 118

107 Inpainting tgframe restoration,psnr 27.65dB, CPU s (WHU) June 5, / 118

108 Inpainting oringal image (WHU) June 5, / 118

109 Inpainting observed image,psnr 18.86dB (WHU) June 5, / 118

110 Inpainting tv restoration,psnr 34.27dB, CPU 11.02s (WHU) June 5, / 118

111 Inpainting balanced restoration,psnr 31.20dB, CPU 9.03s (WHU) June 5, / 118

112 Inpainting tvframe restoration,psnr 32.32dB, CPU 47.75s (WHU) June 5, / 118

113 Inpainting oringal image (WHU) June 5, / 118

114 Inpainting observed image,psnr 23.05dB (WHU) June 5, / 118

115 Inpainting tv restoration,psnr 27.24dB, CPU 55.55s (WHU) June 5, / 118

116 Inpainting balanced restoration,psnr 26.82dB, CPU 29.52s (WHU) June 5, / 118

117 Inpainting tvframe restoration,psnr 26.85dB, CPU s (WHU) June 5, / 118

118 Thank you!