11 research outputs found
Improved Total Variation based Image Compressive Sensing Recovery by Nonlocal Regularization
Recently, total variation (TV) based minimization algorithms have achieved
great success in compressive sensing (CS) recovery for natural images due to
its virtue of preserving edges. However, the use of TV is not able to recover
the fine details and textures, and often suffers from undesirable staircase
artifact. To reduce these effects, this letter presents an improved TV based
image CS recovery algorithm by introducing a new nonlocal regularization
constraint into CS optimization problem. The nonlocal regularization is built
on the well known nonlocal means (NLM) filtering and takes advantage of
self-similarity in images, which helps to suppress the staircase effect and
restore the fine details. Furthermore, an efficient augmented Lagrangian based
algorithm is developed to solve the above combined TV and nonlocal
regularization constrained problem. Experimental results demonstrate that the
proposed algorithm achieves significant performance improvements over the
state-of-the-art TV based algorithm in both PSNR and visual perception.Comment: 4 Pages, 1 figures, 3 tables, to be published at IEEE Int. Symposium
of Circuits and Systems (ISCAS) 201
ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing
With the aim of developing a fast yet accurate algorithm for compressive
sensing (CS) reconstruction of natural images, we combine in this paper the
merits of two existing categories of CS methods: the structure insights of
traditional optimization-based methods and the speed of recent network-based
ones. Specifically, we propose a novel structured deep network, dubbed
ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm
(ISTA) for optimizing a general norm CS reconstruction model. To cast
ISTA into deep network form, we develop an effective strategy to solve the
proximal mapping associated with the sparsity-inducing regularizer using
nonlinear transforms. All the parameters in ISTA-Net (\eg nonlinear transforms,
shrinkage thresholds, step sizes, etc.) are learned end-to-end, rather than
being hand-crafted. Moreover, considering that the residuals of natural images
are more compressible, an enhanced version of ISTA-Net in the residual domain,
dubbed {ISTA-Net}, is derived to further improve CS reconstruction.
Extensive CS experiments demonstrate that the proposed ISTA-Nets outperform
existing state-of-the-art optimization-based and network-based CS methods by
large margins, while maintaining fast computational speed. Our source codes are
available: \textsl{http://jianzhang.tech/projects/ISTA-Net}.Comment: 10 pages, 6 figures, 4 Tables. To appear in CVPR 201
The Power of Triply Complementary Priors for Image Compressive Sensing
Recent works that utilized deep models have achieved superior results in
various image restoration applications. Such approach is typically supervised
which requires a corpus of training images with distribution similar to the
images to be recovered. On the other hand, the shallow methods which are
usually unsupervised remain promising performance in many inverse problems,
\eg, image compressive sensing (CS), as they can effectively leverage non-local
self-similarity priors of natural images. However, most of such methods are
patch-based leading to the restored images with various ringing artifacts due
to naive patch aggregation. Using either approach alone usually limits
performance and generalizability in image restoration tasks. In this paper, we
propose a joint low-rank and deep (LRD) image model, which contains a pair of
triply complementary priors, namely \textit{external} and \textit{internal},
\textit{deep} and \textit{shallow}, and \textit{local} and \textit{non-local}
priors. We then propose a novel hybrid plug-and-play (H-PnP) framework based on
the LRD model for image CS. To make the optimization tractable, a simple yet
effective algorithm is proposed to solve the proposed H-PnP based image CS
problem. Extensive experimental results demonstrate that the proposed H-PnP
algorithm significantly outperforms the state-of-the-art techniques for image
CS recovery such as SCSNet and WNNM
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
Natural image restoration based on multi-scale group sparsity residual constraints
The Group Sparse Representation (GSR) model shows excellent potential in various image restoration tasks. In this study, we propose a novel Multi-Scale Group Sparse Residual Constraint Model (MS-GSRC) which can be applied to various inverse problems, including denoising, inpainting, and compressed sensing (CS). Our new method involves the following three steps: (1) finding similar patches with an overlapping scheme for the input degraded image using a multi-scale strategy, (2) performing a group sparse coding on these patches with low-rank constraints to get an initial representation vector, and (3) under the Bayesian maximum a posteriori (MAP) restoration framework, we adopt an alternating minimization scheme to solve the corresponding equation and reconstruct the target image finally. Simulation experiments demonstrate that our proposed model outperforms in terms of both objective image quality and subjective visual quality compared to several state-of-the-art methods