401 research outputs found
Variational models for multiplicative noise removal
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Όλ¬Έ (λ°μ¬)-- μμΈλνκ΅ λνμ μμ°κ³Όνλν μ리과νλΆ, 2017. 8. κ°λͺ
μ£Ό.This dissertation discusses a variational partial differential equation (PDE) models for restoration of images corrupted by multiplicative Gamma noise. The two proposed models are suitable for heavy multiplicative noise which is often seen in applications. First, we propose a total variation (TV) based model with local constraints. The local constraint involves multiple local windows which is related a spatially adaptive regularization parameter (SARP). In addition, convergence analysis such as the existence and uniqueness of a solution is also provided. Second model is an extension of the first one using nonconvex version of the total generalized variation (TGV). The nonconvex TGV regularization enables to efficiently denoise smooth regions, without staircasing artifacts that appear on total variation regularization based models, and to conserve edges and details.1. Introduction 1
2. Previous works 6
2.1 Variational models for image denoising 6
2.2.1 Convex and nonconvex regularizers 6
2.2.2 Variational models for multiplicative noise removal 8
2.2 Proximal linearized alternating direction method of multipliers 10
3. Proposed models 13
3.1 Proposed model 1 :exp TV model with SARP 13
3.1.1 Derivation of our model 13
3.1.2 Proposed TV model with local constraints 16
3.1.3 A SARP algorithm for solving model (3.1.16) 27
3.1.4 Numerical results 32
3.2 Proposed model 2 :exp NTGV model with SARP 51
3.2.1 Proposed NTGV model 51
3.2.2 Updating rule for in (3.2.1) 52
3.2.3 Algorithm for solving the proposed model (3.2.1) 55
3.2.4 Numerical results 62
3.2.5 Selection of parameters 63
3.2.6 Image denoising 65
4. Conclusion 79Docto
λΉκ°μ°μμ μ‘μ μμ 볡μμ μν κ·Έλ£Ή ν¬μ νν
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Όλ¬Έ(λ°μ¬)--μμΈλνκ΅ λνμ :μμ°κ³Όνλν μ리과νλΆ,2020. 2. κ°λͺ
μ£Ό.For the image restoration problem, recent variational approaches exploiting nonlocal information of an image have demonstrated significant improvements compared with traditional methods utilizing local features. Hence, we propose two variational models based on the sparse representation of image groups, to recover images with non-Gaussian noise. The proposed models are designed to restore image with Cauchy noise and speckle noise, respectively. To achieve efficient and stable performance, an alternating optimization scheme with a novel initialization technique is used. Experimental results suggest that the proposed methods outperform other methods in terms of both visual perception and numerical indexes.μμ 볡μ λ¬Έμ μμ, μμμ λΉκ΅μ§μ μΈ μ 보λ₯Ό νμ©νλ μ΅κ·Όμ λ€μν μ κ·Ό λ°©μμ κ΅μ§μ μΈ νΉμ±μ νμ©νλ κΈ°μ‘΄ λ°©λ²κ³Ό λΉκ΅νμ¬ ν¬κ² κ°μ λμλ€. λ°λΌμ, μ°λ¦¬λ λΉκ°μ°μμ μ‘μ μμμ 볡μνκΈ° μν΄ μμ κ·Έλ£Ή ν¬μ ννμ κΈ°λ°ν λ κ°μ§ λ³λΆλ²μ λͺ¨λΈμ μ μνλ€. μ μλ λͺ¨λΈμ κ°κ° μ½μ μ‘μκ³Ό μ€νν΄ μ‘μ μμμ 볡μνλλ‘ μ€κ³λμλ€. ν¨μ¨μ μ΄κ³ μμ μ μΈ μ±λ₯μ λ¬μ±νκΈ° μν΄, κ΅λ λ°©ν₯ μΉμλ²κ³Ό μλ‘μ΄ μ΄κΈ°ν κΈ°μ μ΄ μ¬μ©λλ€. μ€ν κ²°κ³Όλ μ μλ λ°©λ²μ΄ μκ°μ μΈ μΈμκ³Ό μμΉμ μΈ μ§ν λͺ¨λμμ λ€λ₯Έ λ°©λ²λ³΄λ€ μ°μν¨μ λνλΈλ€.1 Introduction 1
2 Preliminaries 5
2.1 Cauchy Noise 5
2.1.1 Introduction 6
2.1.2 Literature Review 7
2.2 Speckle Noise 9
2.2.1 Introduction 10
2.2.2 Literature Review 13
2.3 GSR 15
2.3.1 Group Construction 15
2.3.2 GSR Modeling 16
2.4 ADMM 17
3 Proposed Models 19
3.1 Proposed Model 1: GSRC 19
3.1.1 GSRC Modeling via MAP Estimator 20
3.1.2 Patch Distance for Cauchy Noise 22
3.1.3 The ADMM Algorithm for Solving (3.7) 22
3.1.4 Numerical Experiments 28
3.1.5 Discussion 45
3.2 Proposed Model 2: GSRS 48
3.2.1 GSRS Modeling via MAP Estimator 50
3.2.2 Patch Distance for Speckle Noise 52
3.2.3 The ADMM Algorithm for Solving (3.42) 53
3.2.4 Numerical Experiments 56
3.2.5 Discussion 69
4 Conclusion 74
Abstract (in Korean) 84Docto
The Application of Preconditioned Alternating Direction Method of Multipliers in Depth from Focal Stack
Post capture refocusing effect in smartphone cameras is achievable by using
focal stacks. However, the accuracy of this effect is totally dependent on the
combination of the depth layers in the stack. The accuracy of the extended
depth of field effect in this application can be improved significantly by
computing an accurate depth map which has been an open issue for decades. To
tackle this issue, in this paper, a framework is proposed based on
Preconditioned Alternating Direction Method of Multipliers (PADMM) for depth
from the focal stack and synthetic defocus application. In addition to its
ability to provide high structural accuracy and occlusion handling, the
optimization function of the proposed method can, in fact, converge faster and
better than state of the art methods. The evaluation has been done on 21 sets
of focal stacks and the optimization function has been compared against 5 other
methods. Preliminary results indicate that the proposed method has a better
performance in terms of structural accuracy and optimization in comparison to
the current state of the art methods.Comment: 15 pages, 8 figure
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