Th`ese Marouan BOUALI - Sites personnels de TELECOM ParisTech

More documents

Recommendations

Info

104 4. A Variational approach for the destriping issue supported by quantitative measurements reported in tables 4.1 and 4.2. Although the UVM was derived intuitively by combining edge-preserving models and gradient field integration approaches, similar results can be achieved with slightly different variational models. These are based on the minimization of the following energy functionals : E 1 (u) =TV x (u − f)+λT V (u) (4.110) ∫ ( ) ∂ (u − f) 2 E 2 (u) = + λT V (u) (4.111) Ω ∂x ∫ ( ) ∂ (u − f) 2 E 3 (u) = + λT V y (u) (4.112) ∂x Ω In the model (4.112), the L 1 -norm on the x-gradient is replaced by the L 2 -norm. This modification does not cause bluring artifacts as the edges are still preserved by the regularizing term which includes the L 1 -norm of the y-gradient. Nevertheless, the original UVDM is more suited to isolate striping due to the L 1 -norm being weaker than the standard L 2 -norm (L 2 (Ω) ∈ L 1 (Ω)). For u-components holding the same ID index and derived from (4.112) and the UVDM, the noisy component v extracted with the UVDM contains more stripe-related texture. This feature comes in handy in the TVN hierarchical decomposition where the destriped image is obtained by progressively extracting striping from oversmoothed u estimates. The L 1 -norm in the fidelity term then ensures a minimal number of iterations compared to the L 2 -norm. The model (4.110) replaces the regularizing term of the UVM model with the commonly used TV-norm which provides similar results than the UVM but increases the computational cost required for the minimization of its energy functional. This drawback, together with the use of L 2 -norm in the fidelity term are both present in the variational model (4.111). From a denoising perspective, the UVDM and models (4.110), (4.111), (4.112) satisfy the destriping requirements imposed in chapter 3, namely complete stripe removal without blur/ringing artifacts. In fact, both TVN and/or Osher et al. iterative procedures ensure that the ID index of the optimally destriped image is close to 1. This emphazises the importance of a suitable fidelity term which, for all destriping models described above, takes into account the unidirectional property of striping.
105 17500 23500 Mean value 16500 15500 Mean value 23000 22500 14500 0 100 200 300 400 500 Line Number 22000 0 100 200 300 400 500 Line Number 17500 23500 Mean value 16500 15500 Mean value 23000 22500 14500 0 100 200 300 400 500 Line Number 22000 0 100 200 300 400 500 Line Number 17500 23500 Mean value 16500 15500 Mean value 23000 22500 14500 0 100 200 300 400 500 Line Number 22000 0 100 200 300 400 500 Line Number Figure 4.15 – Cross-Track profiles for Terra MODIS band 30 (Left) and band 33 (Right). From top to bottom : Original image, histogram matching with IMAPP and proposed UVDM
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:
Page 52 and 53:
Page 54 and 55: 54 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 100 and 101: 100 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?