3,049 research outputs found
영상 복원 문제의 변분법적 접근
학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. 강명주.Image restoration has been an active research area in image processing and computer vision during the past several decades. We explore variational partial
differential equations (PDE) models in image restoration problem. We start our discussion by reviewing classical models, by which the works of this dissertation are highly motivated. The content of the dissertation is divided
into two main subjects. First topic is on image denoising, where we propose non-convex hybrid total variation model, and then we apply iterative reweighted algorithm to solve the proposed model. Second topic is on image
decomposition, in which we separate an image into structural component and oscillatory component using local gradient constraint.Abstract i
1 Introduction 1
1.1 Image restoration 2
1.2 Brief overview of the dissertation 3
2 Previous works 4
2.1 Image denoising 4
2.1.1 Fundamental model 4
2.1.2 Higher order model 7
2.1.3 Hybrid model 9
2.1.4 Non-convex model 12
2.2 Image decomposition 22
2.2.1 Meyers model 23
2.2.2 Nonlinear filter 24
3 Non-convex hybrid TV for image denoising 28
3.1 Variational model with non-convex hybrid TV 29
3.1.1 Non-convex TV model and non-convex HOTV model 29
3.1.2 The Proposed model: Non-convex hybrid TV model 31
3.2 Iterative reweighted hybrid Total Variation algorithm 33
3.3 Numerical experiments 35
3.3.1 Parameter values 37
3.3.2 Comparison between the non-convex TV model and
the non-convex HOTV model 38
3.3.3 Comparison with other non-convex higher order regularizers 40
3.3.4 Comparison between two non-convex hybrid TV models 42
3.3.5 Comparison with Krishnan et al. [39] 43
3.3.6 Comparison with state-of-the-art 44
4 Image decomposition 59
4.1 Local gradient constraint 61
4.1.1 Texture estimator 62
4.2 The proposed model 65
4.2.1 Algorithm : Anisotropic TV-L2 67
4.2.2 Algorithm : Isotropic TV-L2 69
4.2.3 Algorithm : Isotropic TV-L1 71
4.3 Numerical experiments and discussion 72
5 Conclusion and future works 80
Abstract (in Korean) 92Docto
Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
We address the denoising of images contaminated with multiplicative noise,
e.g. speckle noise. Classical ways to solve such problems are filtering,
statistical (Bayesian) methods, variational methods, and methods that convert
the multiplicative noise into additive noise (using a logarithmic function),
shrinkage of the coefficients of the log-image data in a wavelet basis or in a
frame, and transform back the result using an exponential function. We propose
a method composed of several stages: we use the log-image data and apply a
reasonable under-optimal hard-thresholding on its curvelet transform; then we
apply a variational method where we minimize a specialized criterion composed
of an data-fitting to the thresholded coefficients and a Total
Variation regularization (TV) term in the image domain; the restored image is
an exponential of the obtained minimizer, weighted in a way that the mean of
the original image is preserved. Our restored images combine the advantages of
shrinkage and variational methods and avoid their main drawbacks. For the
minimization stage, we propose a properly adapted fast minimization scheme
based on Douglas-Rachford splitting. The existence of a minimizer of our
specialized criterion being proven, we demonstrate the convergence of the
minimization scheme. The obtained numerical results outperform the main
alternative methods
Phase and TV Based Convex Sets for Blind Deconvolution of Microscopic Images
In this article, two closed and convex sets for blind deconvolution problem
are proposed. Most blurring functions in microscopy are symmetric with respect
to the origin. Therefore, they do not modify the phase of the Fourier transform
(FT) of the original image. As a result blurred image and the original image
have the same FT phase. Therefore, the set of images with a prescribed FT phase
can be used as a constraint set in blind deconvolution problems. Another convex
set that can be used during the image reconstruction process is the epigraph
set of Total Variation (TV) function. This set does not need a prescribed upper
bound on the total variation of the image. The upper bound is automatically
adjusted according to the current image of the restoration process. Both of
these two closed and convex sets can be used as a part of any blind
deconvolution algorithm. Simulation examples are presented.Comment: Submitted to IEEE Selected Topics in Signal Processin
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