273 research outputs found
Joint group and residual sparse coding for image compressive sensing
Nonlocal self-similarity and group sparsity have been widely utilized in
image compressive sensing (CS). However, when the sampling rate is low, the
internal prior information of degraded images may be not enough for accurate
restoration, resulting in loss of image edges and details. In this paper, we
propose a joint group and residual sparse coding method for CS image recovery
(JGRSC-CS). In the proposed JGRSC-CS, patch group is treated as the basic unit
of sparse coding and two dictionaries (namely internal and external
dictionaries) are applied to exploit the sparse representation of each group
simultaneously. The internal self-adaptive dictionary is used to remove
artifacts, and an external Gaussian Mixture Model (GMM) dictionary, learned
from clean training images, is used to enhance details and texture. To make the
proposed method effective and robust, the split Bregman method is adopted to
reconstruct the whole image. Experimental results manifest the proposed
JGRSC-CS algorithm outperforms existing state-of-the-art methods in both peak
signal to noise ratio (PSNR) and visual quality.Comment: 27 pages, 7 figure
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
A survey of sparse representation: algorithms and applications
Sparse representation has attracted much attention from researchers in fields
of signal processing, image processing, computer vision and pattern
recognition. Sparse representation also has a good reputation in both
theoretical research and practical applications. Many different algorithms have
been proposed for sparse representation. The main purpose of this article is to
provide a comprehensive study and an updated review on sparse representation
and to supply a guidance for researchers. The taxonomy of sparse representation
methods can be studied from various viewpoints. For example, in terms of
different norm minimizations used in sparsity constraints, the methods can be
roughly categorized into five groups: sparse representation with -norm
minimization, sparse representation with -norm (0p1) minimization,
sparse representation with -norm minimization and sparse representation
with -norm minimization. In this paper, a comprehensive overview of
sparse representation is provided. The available sparse representation
algorithms can also be empirically categorized into four groups: greedy
strategy approximation, constrained optimization, proximity algorithm-based
optimization, and homotopy algorithm-based sparse representation. The
rationales of different algorithms in each category are analyzed and a wide
range of sparse representation applications are summarized, which could
sufficiently reveal the potential nature of the sparse representation theory.
Specifically, an experimentally comparative study of these sparse
representation algorithms was presented. The Matlab code used in this paper can
be available at: http://www.yongxu.org/lunwen.html.Comment: Published on IEEE Access, Vol. 3, pp. 490-530, 201
Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration
Hyperspectral imaging, providing abundant spatial and spectral information
simultaneously, has attracted a lot of interest in recent years. Unfortunately,
due to the hardware limitations, the hyperspectral image (HSI) is vulnerable to
various degradations, such noises (random noise, HSI denoising), blurs
(Gaussian and uniform blur, HSI deblurring), and down-sampled (both spectral
and spatial downsample, HSI super-resolution). Previous HSI restoration methods
are designed for one specific task only. Besides, most of them start from the
1-D vector or 2-D matrix models and cannot fully exploit the structurally
spectral-spatial correlation in 3-D HSI. To overcome these limitations, in this
work, we propose a unified low-rank tensor recovery model for comprehensive HSI
restoration tasks, in which non-local similarity between spectral-spatial cubic
and spectral correlation are simultaneously captured by 3-order tensors.
Further, to improve the capability and flexibility, we formulate it as a
weighted low-rank tensor recovery (WLRTR) model by treating the singular values
differently, and study its analytical solution. We also consider the exclusive
stripe noise in HSI as the gross error by extending WLRTR to robust principal
component analysis (WLRTR-RPCA). Extensive experiments demonstrate the proposed
WLRTR models consistently outperform state-of-the-arts in typical low level
vision HSI tasks, including denoising, destriping, deblurring and
super-resolution.Comment: 22 pages, 22 figure
A Tale of Two Bases: Local-Nonlocal Regularization on Image Patches with Convolution Framelets
We propose an image representation scheme combining the local and nonlocal
characterization of patches in an image. Our representation scheme can be shown
to be equivalent to a tight frame constructed from convolving local bases (e.g.
wavelet frames, discrete cosine transforms, etc.) with nonlocal bases (e.g.
spectral basis induced by nonlinear dimension reduction on patches), and we
call the resulting frame elements {\it convolution framelets}. Insight gained
from analyzing the proposed representation leads to a novel interpretation of a
recent high-performance patch-based image inpainting algorithm using Point
Integral Method (PIM) and Low Dimension Manifold Model (LDMM) [Osher, Shi and
Zhu, 2016]. In particular, we show that LDMM is a weighted
-regularization on the coefficients obtained by decomposing images into
linear combinations of convolution framelets; based on this understanding, we
extend the original LDMM to a reweighted version that yields further improved
inpainting results. In addition, we establish the energy concentration property
of convolution framelet coefficients for the setting where the local basis is
constructed from a given nonlocal basis via a linear reconstruction framework;
a generalization of this framework to unions of local embeddings can provide a
natural setting for interpreting BM3D, one of the state-of-the-art image
denoising algorithms
Nonconvex Nonsmooth Low-Rank Minimization for Generalized Image Compressed Sensing via Group Sparse Representation
Group sparse representation (GSR) based method has led to great successes in
various image recovery tasks, which can be converted into a low-rank matrix
minimization problem. As a widely used surrogate function of low-rank, the
nuclear norm based convex surrogate usually leads to over-shrinking problem,
since the standard soft-thresholding operator shrinks all singular values
equally. To improve traditional sparse representation based image compressive
sensing (CS) performance, we propose a generalized CS framework based on GSR
model, which leads to a nonconvex nonsmooth low-rank minimization problem. The
popular L_2-norm and M-estimator are employed for standard image CS and robust
CS problem to fit the data respectively. For the better approximation of the
rank of group-matrix, a family of nuclear norms are employed to address the
over-shrinking problem. Moreover, we also propose a flexible and effective
iteratively-weighting strategy to control the weighting and contribution of
each singular value. Then we develop an iteratively reweighted nuclear norm
algorithm for our generalized framework via an alternating direction method of
multipliers framework, namely, GSR-AIR. Experimental results demonstrate that
our proposed CS framework can achieve favorable reconstruction performance
compared with current state-of-the-art methods and the robust CS framework can
suppress the outliers effectively.Comment: This paper has been submitted to the Journal of the Franklin
Institute. arXiv admin note: substantial text overlap with arXiv:1903.0978
A Critical Analysis of Patch Similarity Based Image Denoising Algorithms
Image denoising is a classical signal processing problem that has received
significant interest within the image processing community during the past two
decades. Most of the algorithms for image denoising has focused on the paradigm
of non-local similarity, where image blocks in the neighborhood that are
similar, are collected to build a basis for reconstruction. Through rigorous
experimentation, this paper reviews multiple aspects of image denoising
algorithm development based on non-local similarity. Firstly, the concept of
non-local similarity as a foundational quality that exists in natural images
has not received adequate attention. Secondly, the image denoising algorithms
that are developed are a combination of multiple building blocks, making
comparison among them a tedious task. Finally, most of the work surrounding
image denoising presents performance results based on Peak-Signal-to-Noise
Ratio (PSNR) between a denoised image and a reference image (which is perturbed
with Additive White Gaussian Noise). This paper starts with a statistical
analysis on non-local similarity and its effectiveness under various noise
levels, followed by a theoretical comparison of different state-of-the-art
image denoising algorithms. Finally, we argue for a methodological overhaul to
incorporate no-reference image quality measures and unprocessed images (raw)
during performance evaluation of image denoising algorithms
Collaborative Total Variation: A General Framework for Vectorial TV Models
Even after over two decades, the total variation (TV) remains one of the most
popular regularizations for image processing problems and has sparked a
tremendous amount of research, particularly to move from scalar to
vector-valued functions. In this paper, we consider the gradient of a color
image as a three dimensional matrix or tensor with dimensions corresponding to
the spatial extend, the differences to other pixels, and the spectral channels.
The smoothness of this tensor is then measured by taking different norms along
the different dimensions. Depending on the type of these norms one obtains very
different properties of the regularization, leading to novel models for color
images. We call this class of regularizations collaborative total variation
(CTV). On the theoretical side, we characterize the dual norm, the
subdifferential and the proximal mapping of the proposed regularizers. We
further prove, with the help of the generalized concept of singular vectors,
that an channel coupling makes the most prior assumptions and
has the greatest potential to reduce color artifacts. Our practical
contributions consist of an extensive experimental section where we compare the
performance of a large number of collaborative TV methods for inverse problems
like denoising, deblurring and inpainting
Single image super resolution based on multi-scale structure and non-local smoothing
In this paper, we propose a hybrid super-resolution method by combining global and local dictionary training in the sparse domain. In order to present and differentiate the feature mapping in different scales, a global dictionary set is trained in multiple structure scales, and a non-linear function is used to choose the appropriate dictionary to initially reconstruct the HR image. In addition, we introduce the Gaussian blur to the LR images to eliminate a widely used but inappropriate assumption that the low resolution (LR) images are generated by bicubic interpolation from high-resolution (HR) images. In order to deal with Gaussian blur, a local dictionary is generated and iteratively updated by K-means principal component analysis (K-PCA) and gradient decent (GD) to model the blur effect during the down-sampling. Compared with the state-of-the-art SR algorithms, the experimental results reveal that the proposed method can produce sharper boundaries and suppress undesired artifacts with the present of Gaussian blur. It implies that our method could be more effect in real applications and that the HR-LR mapping relation is more complicated than bicubic interpolation
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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