Th`ese Marouan BOUALI - Sites personnels de TELECOM ParisTech

More documents

Recommendations

Info

100 4. A Variational approach for the destriping issue Figure 4.12 – Optimal destriping using Tadmor et al. hierarchical decomposition approach. From left to right and top to bottom, noisy image from Terra band 30 and successive destriped results for iterations 1 to 7. The value λ 0 = 10 have been selected to ensure initial oversmoothing This iterated process provides a multiscale representation of I s where the successive terms u k extract details of the noise-free image I related to the scale λ 0 2 k , while sharper details associated with stripe and included in the finer scale λ 0 2 k+1 are isolated in the term v k . The original TNV hierachical decomposition was initially proposed as a multiscale framework in the context of ROF regularization but does not aim at removing noise from the images. In the later case, a stopping criteria is required so that the term ∑ j=k j=0 u j does not contain stripe details. This is discussed in section 4.6.3. TNV hierarchical decomposition is applied to a striped image extracted from Terra MODIS band 30 and illustrated in figure 4.12. The stripe noise extracted at each iteration is displayed in figure 4.13 4.6.2 Osher et al. iterative regularization method In the orignal ROF model, the term f − u can still contain fine edges and textures if the lagrange multiplier λ is not choosen carefully. To minimize the removal of structures from the estimate solution, [Osher et al., 2005] introduced an iterative refinement of the ROF model and proposed a generalization for other variational models based on the use of Bregman distances. In the case of ROF regularization, the iterative methodology follows three steps : Step 1 : Solve the original ROF model : {∫ ∫ u 1 = inf u∈BV (Ω) |∇u| + λ Ω Ω (f − u) 2 } (4.101)
101 Figure 4.13 – From left to right and top to bottom, extracted stripe noise using Tadmor et al. hierarchical decomposition approach for iterations 1 to 8. This leads to a decomposition of the image f as f = u 1 + v 1 where v 1 is the estimated noisy component. Step 2 : Inject the noise estimated in the first step v 1 in the fidelity term and solve : {∫ ∫ u 2 = inf u∈BV (Ω) |∇u| + λ Ω Ω (f + v 1 − u) 2 } (4.102) This correction step provides a decomposition of the form f + v 1 = u 2 + v 2 Step 3 : Solve : {∫ ∫ } u k+1 = inf |∇u| + λ (f + v k − u) 2 u∈BV (Ω) Ω Ω (4.103) where v k is obtained after k iterations as v k = v k−1 + f − u k . This iterated methodology is extended by Osher et al. to other inverse problems by considering a general variational model of the form : inf {J(u)+H(u, f)} (4.104) u where J(u) is a convex non negative regularizing functional and H(u, f) the fidelity term. The general case consists of iteratively solving : u k+1 = inf u {J(u)+H(u, f)− < u, p k >} (4.105) where < ., . > is the duality product and p k is a subgradient of J at u k . The adaptation to the UVDM is straightforward. Replacing J(u) with λT V y (u) and H(u, f) with TV x (u−f),
Page 1:
École Doctorale d’Informatique,
Page 5:
5 Résumé Nou abordons dans cette
Page 8 and 9:
8 TABLE DES MATIÈRES 3.5 Frequency
Page 10 and 11:
10 TABLE DES MATIÈRES
Page 12 and 13:
12 1. Introduction A common issue f
Page 14 and 15:
14 1. Introduction
Page 16 and 17:
16 2. Remote Sensing with MODIS In
Page 18 and 19:
18 2. Remote Sensing with MODIS Fig
Page 20 and 21:
Page 22 and 23:
Page 24 and 25:
24 2. Remote Sensing with MODIS any
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
30 2. Remote Sensing with MODIS Mai
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
38 2. Remote Sensing with MODIS
Page 40 and 41:
40 3. Standard destriping technique
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51: 50 3. Standard destriping technique
Page 72 and 73: Table 3.4 - Noise Reduction (NR), I
Page 74 and 75: 74 4. A Variational approach for th
Page 102 and 103: 102 4. A Variational approach for t
Page 112 and 113: 112 5. Application : Restoration of
Page 124 and 125: - Alaska Labrador Siberia Restorati
Page 128 and 129: 128 Conclusion
Page 130 and 131: 130 BIBLIOGRAPHIE A. Chambolle. An
Page 132 and 133: 132 BIBLIOGRAPHIE E. Hochberg, S. A
Page 134 and 135: 134 BIBLIOGRAPHIE P. Perona and J.
show all

Th`ese Marouan BOUALI - Sites personnels de TELECOM ParisTech

Create successful ePaper yourself

Delete template?

Save as template?