238 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
Image Restoration Using Joint Statistical Modeling in Space-Transform Domain
This paper presents a novel strategy for high-fidelity image restoration by
characterizing both local smoothness and nonlocal self-similarity of natural
images in a unified statistical manner. The main contributions are three-folds.
First, from the perspective of image statistics, a joint statistical modeling
(JSM) in an adaptive hybrid space-transform domain is established, which offers
a powerful mechanism of combining local smoothness and nonlocal self-similarity
simultaneously to ensure a more reliable and robust estimation. Second, a new
form of minimization functional for solving image inverse problem is formulated
using JSM under regularization-based framework. Finally, in order to make JSM
tractable and robust, a new Split-Bregman based algorithm is developed to
efficiently solve the above severely underdetermined inverse problem associated
with theoretical proof of convergence. Extensive experiments on image
inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise
removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions
on Circuits System and Video Technology (TCSVT). High resolution pdf version
and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM
Group-based Sparse Representation for Image Restoration
Traditional patch-based sparse representation modeling of natural images
usually suffer from two problems. First, it has to solve a large-scale
optimization problem with high computational complexity in dictionary learning.
Second, each patch is considered independently in dictionary learning and
sparse coding, which ignores the relationship among patches, resulting in
inaccurate sparse coding coefficients. In this paper, instead of using patch as
the basic unit of sparse representation, we exploit the concept of group as the
basic unit of sparse representation, which is composed of nonlocal patches with
similar structures, and establish a novel sparse representation modeling of
natural images, called group-based sparse representation (GSR). The proposed
GSR is able to sparsely represent natural images in the domain of group, which
enforces the intrinsic local sparsity and nonlocal self-similarity of images
simultaneously in a unified framework. Moreover, an effective self-adaptive
dictionary learning method for each group with low complexity is designed,
rather than dictionary learning from natural images. To make GSR tractable and
robust, a split Bregman based technique is developed to solve the proposed
GSR-driven minimization problem for image restoration efficiently. Extensive
experiments on image inpainting, image deblurring and image compressive sensing
recovery manifest that the proposed GSR modeling outperforms many current
state-of-the-art schemes in both PSNR and visual perception.Comment: 34 pages, 6 tables, 19 figures, to be published in IEEE Transactions
on Image Processing; Project, Code and High resolution PDF version can be
found: http://idm.pku.edu.cn/staff/zhangjian/. arXiv admin note: text overlap
with arXiv:1404.756
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