32,973 research outputs found
A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems
Non-Local Total Variation (NLTV) has emerged as a useful tool in variational
methods for image recovery problems. In this paper, we extend the NLTV-based
regularization to multicomponent images by taking advantage of the Structure
Tensor (ST) resulting from the gradient of a multicomponent image. The proposed
approach allows us to penalize the non-local variations, jointly for the
different components, through various matrix norms with .
To facilitate the choice of the hyper-parameters, we adopt a constrained convex
optimization approach in which we minimize the data fidelity term subject to a
constraint involving the ST-NLTV regularization. The resulting convex
optimization problem is solved with a novel epigraphical projection method.
This formulation can be efficiently implemented thanks to the flexibility
offered by recent primal-dual proximal algorithms. Experiments are carried out
for multispectral and hyperspectral images. The results demonstrate the
interest of introducing a non-local structure tensor regularization and show
that the proposed approach leads to significant improvements in terms of
convergence speed over current state-of-the-art methods
Improving Image Restoration with Soft-Rounding
Several important classes of images such as text, barcode and pattern images
have the property that pixels can only take a distinct subset of values. This
knowledge can benefit the restoration of such images, but it has not been
widely considered in current restoration methods. In this work, we describe an
effective and efficient approach to incorporate the knowledge of distinct pixel
values of the pristine images into the general regularized least squares
restoration framework. We introduce a new regularizer that attains zero at the
designated pixel values and becomes a quadratic penalty function in the
intervals between them. When incorporated into the regularized least squares
restoration framework, this regularizer leads to a simple and efficient step
that resembles and extends the rounding operation, which we term as
soft-rounding. We apply the soft-rounding enhanced solution to the restoration
of binary text/barcode images and pattern images with multiple distinct pixel
values. Experimental results show that soft-rounding enhanced restoration
methods achieve significant improvement in both visual quality and quantitative
measures (PSNR and SSIM). Furthermore, we show that this regularizer can also
benefit the restoration of general natural images.Comment: 9 pages, 6 figure
Variational models for multiplicative noise removal
학위논문 (박사)-- 서울대학교 대학원 자연과학대학 수리과학부, 2017. 8. 강명주.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
Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition
Hyperspectral images (HSIs) are often corrupted by a mixture of several types
of noise during the acquisition process, e.g., Gaussian noise, impulse noise,
dead lines, stripes, and many others. Such complex noise could degrade the
quality of the acquired HSIs, limiting the precision of the subsequent
processing. In this paper, we present a novel tensor-based HSI restoration
approach by fully identifying the intrinsic structures of the clean HSI part
and the mixed noise part respectively. Specifically, for the clean HSI part, we
use tensor Tucker decomposition to describe the global correlation among all
bands, and an anisotropic spatial-spectral total variation (SSTV)
regularization to characterize the piecewise smooth structure in both spatial
and spectral domains. For the mixed noise part, we adopt the norm
regularization to detect the sparse noise, including stripes, impulse noise,
and dead pixels. Despite that TV regulariztion has the ability of removing
Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian
noise for some real-world scenarios. Then, we develop an efficient algorithm
for solving the resulting optimization problem by using the augmented Lagrange
multiplier (ALM) method. Finally, extensive experiments on simulated and
real-world noise HSIs are carried out to demonstrate the superiority of the
proposed method over the existing state-of-the-art ones.Comment: 15 pages, 20 figure
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