139 research outputs found
A Convex Variational Model for Restoring Blurred Images with Multiplicative Noise
Abstract. In this paper, a new variational model for restoring blurred images with multiplicative noise is proposed. Based on the statistical property of the noise, a quadratic penalty function technique is utilized in order to obtain a strictly convex model under a mild condition, which guarantees the uniqueness of the solution and the stabilization of the algorithm. For solving the new convex variational model, a primal-dual algorithm is proposed and its convergence is studied. The paper ends with a report on numerical tests for the simultaneous deblurring and denoising of images subject to multiplicative noise. A comparison with other methods is provided as well. Key words. Convexity, deblurring, multiplicative noise, primal-dual algorithm, total variation regularization, variational model. AMS subject classifications. 52A41, 65K10, 65K15, 90C30, 90C4
Bregman Cost for Non-Gaussian Noise
One of the tasks of the Bayesian inverse problem is to find a good estimate
based on the posterior probability density. The most common point estimators
are the conditional mean (CM) and maximum a posteriori (MAP) estimates, which
correspond to the mean and the mode of the posterior, respectively. From a
theoretical point of view it has been argued that the MAP estimate is only in
an asymptotic sense a Bayes estimator for the uniform cost function, while the
CM estimate is a Bayes estimator for the means squared cost function. Recently,
it has been proven that the MAP estimate is a proper Bayes estimator for the
Bregman cost if the image is corrupted by Gaussian noise. In this work we
extend this result to other noise models with log-concave likelihood density,
by introducing two related Bregman cost functions for which the CM and the MAP
estimates are proper Bayes estimators. Moreover, we also prove that the CM
estimate outperforms the MAP estimate, when the error is measured in a certain
Bregman distance, a result previously unknown also in the case of additive
Gaussian noise
๋น๊ฐ์ฐ์์ ์ก์ ์์ ๋ณต์์ ์ํ ๊ทธ๋ฃน ํฌ์ ํํ
ํ์๋
ผ๋ฌธ(๋ฐ์ฌ)--์์ธ๋ํ๊ต ๋ํ์ :์์ฐ๊ณผํ๋ํ ์๋ฆฌ๊ณผํ๋ถ,2020. 2. ๊ฐ๋ช
์ฃผ.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.์์ ๋ณต์ ๋ฌธ์ ์์, ์์์ ๋น๊ตญ์ง์ ์ธ ์ ๋ณด๋ฅผ ํ์ฉํ๋ ์ต๊ทผ์ ๋ค์ํ ์ ๊ทผ ๋ฐฉ์์ ๊ตญ์ง์ ์ธ ํน์ฑ์ ํ์ฉํ๋ ๊ธฐ์กด ๋ฐฉ๋ฒ๊ณผ ๋น๊ตํ์ฌ ํฌ๊ฒ ๊ฐ์ ๋์๋ค. ๋ฐ๋ผ์, ์ฐ๋ฆฌ๋ ๋น๊ฐ์ฐ์์ ์ก์ ์์์ ๋ณต์ํ๊ธฐ ์ํด ์์ ๊ทธ๋ฃน ํฌ์ ํํ์ ๊ธฐ๋ฐํ ๋ ๊ฐ์ง ๋ณ๋ถ๋ฒ์ ๋ชจ๋ธ์ ์ ์ํ๋ค. ์ ์๋ ๋ชจ๋ธ์ ๊ฐ๊ฐ ์ฝ์ ์ก์๊ณผ ์คํํด ์ก์ ์์์ ๋ณต์ํ๋๋ก ์ค๊ณ๋์๋ค. ํจ์จ์ ์ด๊ณ ์์ ์ ์ธ ์ฑ๋ฅ์ ๋ฌ์ฑํ๊ธฐ ์ํด, ๊ต๋ ๋ฐฉํฅ ์น์๋ฒ๊ณผ ์๋ก์ด ์ด๊ธฐํ ๊ธฐ์ ์ด ์ฌ์ฉ๋๋ค. ์คํ ๊ฒฐ๊ณผ๋ ์ ์๋ ๋ฐฉ๋ฒ์ด ์๊ฐ์ ์ธ ์ธ์๊ณผ ์์น์ ์ธ ์งํ ๋ชจ๋์์ ๋ค๋ฅธ ๋ฐฉ๋ฒ๋ณด๋ค ์ฐ์ํจ์ ๋ํ๋ธ๋ค.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
Multiscale hierarchical decomposition methods for images corrupted by multiplicative noise
Recovering images corrupted by multiplicative noise is a well known
challenging task. Motivated by the success of multiscale hierarchical
decomposition methods (MHDM) in image processing, we adapt a variety of both
classical and new multiplicative noise removing models to the MHDM form. On the
basis of previous work, we further present a tight and a refined version of the
corresponding multiplicative MHDM. We discuss existence and uniqueness of
solutions for the proposed models, and additionally, provide convergence
properties. Moreover, we present a discrepancy principle stopping criterion
which prevents recovering excess noise in the multiscale reconstruction.
Through comprehensive numerical experiments and comparisons, we qualitatively
and quantitatively evaluate the validity of all proposed models for denoising
and deblurring images degraded by multiplicative noise. By construction, these
multiplicative multiscale hierarchical decomposition methods have the added
benefit of recovering many scales of an image, which can provide features of
interest beyond image denoising
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