Liang-Jian Deng

Single image super-resolution by approximated Heaviside functions

Image super-resolution is a process to enhance image resolution. It is widely used in medical imaging, satellite imaging, target recognition, etc. In this paper, we conduct continuous modeling and assume that the unknown image intensity function is defined on a continuous domain and belongs to a space with a redundant basis. We propose a new iterative model for single image super-resolution based on an observation: an image is consisted of smooth components and non-smooth components, and we use two classes of approximated Heaviside functions (AHFs) to represent them respectively. Due to sparsity of the non-smooth components, a

Single-Image Super-Resolution via an Iterative Reproducing Kernel Hilbert Space Method

L_{1}

A fast image recovery algorithm based on splitting deblurring and denoising

model is employed. In addition, we apply the proposed iterative model to image patches to reduce computation and storage. Comparisons with some existing competitive methods show the effectiveness of the proposed method.

Stripe noise removal of remote sensing images by total variation regularization and group sparsity constraint

Image super-resolution (SR), a process to enhance image resolution, has important applications in satellite imaging, high-definition television, medical imaging, and so on. Many existing approaches use multiple low-resolution (LR) images to recover one high-resolution (HR) image. In this paper, we present an iterative scheme to solve single-image SR problems. It recovers a high-quality HR image from solely one LR image without using a training data set. We solve the problem from image intensity function estimation perspective and assume that the image contains smooth and edge components. We model the smooth components of an image using a thin-plate reproducing kernel Hilbert space and the edges using approximated Heaviside functions. The proposed method is applied to image patches, aiming to reduce computation and storage. Visual and quantitative comparisons with some competitive approaches show the effectiveness of the proposed method.

Group sparsity based regularization model for remote sensing image stripe noise removal

In this paper, we employ a popular splitting strategy to design a fast iterative algorithm for image restoration. We divide the algorithm into two steps, i.e., deblurring step and denoising step. In the deblurring step, Fourier transform is employed for image deblurring under the periodic boundary condition. In the denoising step, we use a simple and fast method, called fast iterative shrinkage/thresholding algorithm (FISTA), to reduce image noise. In addition, we also give the convergence analysis for the proposed method. Visual and quantitative results demonstrate the proposed algorithm, applied to l 1 regularization model and total-variation (TV) regularization model, is a faster algorithm and keeps image details well.

A generalized product-type BiCOR method and its application in signal deconvolution

Remote sensing images have been used in many fields, such as urban planning, military, and environment monitoring, but corruption by stripe noise limits its subsequent applications. Most existing stripe noise removal (destriping) methods aim to directly estimate the clear images from the stripe images without considering the intrinsic properties of stripe noise, which causes the image structure destroyed. In this paper, we propose a new destriping method from the perspective of image decomposition, which takes the intrinsic properties of stripe noise and image characteristics into full consideration. The proposed method integrates the unidirectional total variation (TV) regularization, group sparsity regularization, and TV regularization together in an image decomposition framework. The first two terms are utilized to exploit the stripe noise properties by implementing statistical analysis, and the TV regularization is adopted to explore the spatial piecewise smooth structure of stripe-free image. Moreover, an efficient alternating minimization scheme is designed to solve the proposed model. Extensive experiments on simulated and real data demonstrate that our method outperforms several existing state-of-the-art destriping methods in terms of both quantitative and qualitative assessments.

Exemplar-Based Image Inpainting Using a Modified Priority Definition

Abstract Stripe noise degradation is a common phenomenon in remote sensing image, which largely affects the visual quality and brings great difficulty for subsequent processing. In contrast to existing stripe noise removal (destriping) models in which the reconstruction is performed to directly estimate the clean image from the striped one, the proposed model achieves the destriping by estimating the stripe component firstly. Since the stripe component possesses column sparse structure, the group sparsity is employed in this study. In addition, difference-based constraints are used to describe the direction information of the stripes. Then, we build a novel convex optimization model which consists of a unidirectional total variation term, a group sparsity term and a gradient domain fidelity term solved by an efficient alternating direction method of multiplier. Compared with the state-of-the-art methods, experiment results on simulated and real data are reported to demonstrate the effectiveness of the proposed method.

A Novel Tensor-Based Video Rain Streaks Removal Approach via Utilizing Discriminatively Intrinsic Priors

For solving nonsymmetric linear systems, we attempt to establish symmetric structures in nonsymmetric systems and handle them through the methods devised for symmetric cases. A Biconjugate A-Orthogonal Residual method based on Biconjugate A-Orthonormalization Procedure has been proposed and nominated as BiCOR in [Y.-F. Jing, T.-Z. Huang, Y. Zhang, L. Li, G.-H. Cheng, Z.-G. Ren, Y. Duan, T. Sogabe, B. Carpentieri, Lanczos-type variants of the COCR method for complex nonsymmetric linear systems, J. Comput. Phys. 228 (2009) 6376-6394.]. As many similar characteristics exist between BiCOR and BiCG, the strategies of improved variants of BiCG, such as CGS and BiCGSTAB, can be utilized to enhance the algorithm for BiCOR. Making use of the product of residual polynomials of BiCOR and other polynomials, CORS and BiCORSTAB have been proposed along the same ideas of CGS and BiCGSTAB, respectively in the above-mentioned paper. In this paper, a unified generalized framework of product-type BiCOR, which is epitomized by the product of residual polynomials and other polynomials, is proposed. Numerical examples are selected from the blurring signal cases and the effect of the generalized product-type BiCOR method is prominent in signal deconvolution.

Two New Efficient Iterative Regularization Methods for Image Restoration Problems

Exemplar-based algorithms are a popular technique for image inpainting. They mainly have two important phases: deciding the filling-in order and selecting good exemplars. Traditional exemplar-based algorithms are to search suitable patches from source regions to fill in the missing parts, but they have to face a problem: improper selection of exemplars. To improve the problem, we introduce an independent strategy through investigating the process of patches propagation in this paper. We first define a new separated priority definition to propagate geometry and then synthesize image textures, aiming to well recover image geometry and textures. In addition, an automatic algorithm is designed to estimate steps for the new separated priority definition. Comparing with some competitive approaches, the new priority definition can recover image geometry and textures well.

Matrix factorization for low-rank tensor completion using framelet prior

Rain streaks removal is an important issue of the outdoor vision system and has been recently investigated extensively. In this paper, we propose a novel tensor based video rain streaks removal approach by fully considering the discriminatively intrinsic characteristics of rain streaks and clean videos, which needs neither rain detection nor time-consuming dictionary learning stage. In specific, on the one hand, rain streaks are sparse and smooth along the raindrops direction, and on the other hand, the clean videos possess smoothness along the rain-perpendicular direction and global and local correlation along time direction. We use the l1 norm to enhance the sparsity of the underlying rain, two unidirectional Total Variation (TV) regularizers to guarantee the different discriminative smoothness, and a tensor nuclear norm and a time directional difference operator to characterize the exclusive correlation of the clean video along time. Alternation direction method of multipliers (ADMM) is employed to solve the proposed concise tensor based convex model. Experiments implemented on synthetic and real data substantiate the effectiveness and efficiency of the proposed method. Under comprehensive quantitative performance measures, our approach outperforms other state-of-the-art methods.