Wen-Ze Shao

Bi-l0-l2-norm regularization for blind motion deblurring

A simple blur-kernel estimation method is developed for blind motion deblurring.The method is regularized by the newly proposed bi-l0-l2-norm regularization.The sharp image and the blur-kernel are estimated very efficiently using FFT.Leading performance is achieved in both terms of speed and output quality. In blind motion deblurring, leading methods today tend towards highly non-convex approximations of the l0-norm, especially in the image regularization term. In this paper, we propose a simple, effective and fast approach for the estimation of the motion blur-kernel, through a bi-l0-l2-norm regularization imposed on both the intermediate sharp image and the blur-kernel. Compared with existing methods, the proposed regularization is shown to be more effective and robust, leading to a more accurate motion blur-kernel and a better final restored image. A fast numerical scheme is deployed for alternatingly computing the sharp image and the blur-kernel, by coupling the operator splitting and augmented Lagrangian methods. Experimental results on both a benchmark image dataset and real-world motion blurred images show that the proposed approach is highly competitive with state-of-the-art methods in both deblurring effectiveness and computational efficiency.

A hybrid active contour model with structured feature for image segmentation

We propose a structural feature region-based active contour model based on the level set method for image segmentation. Firstly, an anisotropic data fitting term is proposed to adaptively detect the intensity both in terms of local direction and global region. Secondly, coupling with the duality theory and a structured gradient vector flow (SGVF) method, a new regularization term of the level set function is formulated to penalize the length of active contour. By this new regularization term, the structured information of images is utilized to improve the ability of preserving the elongated structures. The energy function of the proposed model is minimized by an efficient dual algorithm, avoiding the instability and the non-differentiability of traditional numerical solutions. We compare the proposed method to classical region-based active contour models and highlight its advantages through experiments on synthetic and medical images. A new regularization term is improved by a structured gradient vector flow method for extracting the elongated structures.The structured gradient vector flow method is improved by the structure tensor of intensity and dual variable.A new region is proposed to detect global and local intensity adaptively for efficiency of the curve evolution.

Structure-Based Low-Rank Model With Graph Nuclear Norm Regularization for Noise Removal

Nonlocal image representation methods, including group-based sparse coding and block-matching 3-D filtering, have shown their great performance in application to low-level tasks. The nonlocal prior is extracted from each group consisting of patches with similar intensities. Grouping patches based on intensity similarity, however, gives rise to disturbance and inaccuracy in estimation of the true images. To address this problem, we propose a structure-based low-rank model with graph nuclear norm regularization. We exploit the local manifold structure inside a patch and group the patches by the distance metric of manifold structure. With the manifold structure information, a graph nuclear norm regularization is established and incorporated into a low-rank approximation model. We then prove that the graph-based regularization is equivalent to a weighted nuclear norm and the proposed model can be solved by a weighted singular-value thresholding algorithm. Extensive experiments on additive white Gaussian noise removal and mixed noise removal demonstrate that the proposed method achieves a better performance than several state-of-the-art algorithms.

Multi-Parseval frame–based nonconvex sparse image deconvolution

Abstract. Image deconvolution is an ill-posed, low-level vision task, restoring a clear image from the blurred and noisy observation. From the perspective of statistics, previous work on image deconvolution has been formulated as a maximum a posteriori or a general Bayesian inference problem, with Gaussian or heavy-tailed non-Gaussian prior image models (e.g., a student’s t distribution). We propose a Parseval frame–based nonconvex image deconvolution strategy via penalizing the l0-norm of the coefficients of multiple different Parseval frames. With these frames, flexible filtering operators are provided to adaptively capture the point singularities, the curvilinear edges and the oscillating textures in natural images. The proposed optimization problem is implemented by borrowing the idea of recent penalty decomposition method, resulting in a simple and efficient iteration algorithm. Experimental results show that the proposed deconvolution scheme is highly competitive among state-of-the-art methods, in both the improvement of signal-to-noise ratio and visual perception.

A posterior mean approach for MRF-based spatially adaptive multi-frame image super-resolution

Multi-frame image super-resolution (SR) has been intensively studied in recent years, aiming at reconstructing high-resolution images from several degraded ones (e.g., shift, blurred, aliased, and noisy). In the literature, one of the most popular SR frameworks is the maximum a posteriori model, where a spatially homogeneous image prior and manually adjusted regularization parameter are commonly used for the entire high-resolution image, thus ignoring local spatially adaptive properties of natural images. In this paper, a posterior mean approach is proposed for spatially adaptive multi-frame image super-resolution. First, a flexible Laplacian prior is proposed incorporating both the gradient and Hessian information of images, not only able to better preserve image structures, e.g., edge, texture, but also to suppress staircase effects in the flat regions. In the subsequent, a fully Bayesian SR framework is formulated, wherein the variational Bayesian method is utilized to simultaneously estimate the high-resolution image and unknown hyper-parameters for the image prior and noise. The final experimental results show that the proposed approach is highly competitive against existing algorithms, producing a super-resolved image with higher peak signal-to-noise ratio and better visual perception.

Simple, Accurate, and Robust Nonparametric Blind Super-Resolution

This paper proposes a simple, accurate, and robust approach to single image blind super-resolution (SR). This task is formulated as a functional to be minimized with respect to both an intermediate super-resolved image and a non- parametric blur-kernel. The proposed method includes a convolution consistency constraint which uses a non-blind learning-based SR result to better guide the estimation process. Another key component is the bi-l0-l2-norm regularization placed on the super-resolved, sharp image and the blur-kernel, which is shown to be quite beneficial for accurate blur-kernel estimation. The numerical optimization is implemented by coupling the splitting augmented Lagrangian and the conjugate gradient. With the pre-estimated blur-kernel, the final SR image is reconstructed using a simple TV-based non-blind SR method. The new method is demonstrated to achieve better performance than Michaeli and Irani [2] in both terms of the kernel estimation accuracy and image SR quality.

Motion Deblurring Using Non-stationary Image Modeling

It is well-known that shaken cameras or mobile phones during exposure usually lead to motion blurry photographs. Therefore, camera shake deblurring or motion deblurring is required and requested in many practical scenarios. The contribution of this paper is the proposal of a simple yet effective approach for motion blur kernel estimation, i.e., blind motion deblurring. Though there have been proposed several methods for motion blur kernel estimation in the literature, we impose a type of non-stationary Gaussian prior on the gradient fields of sharp images, in order to automatically detect and purse the salient edges of images as the important clues to blur kernel estimation. On one hand, the prior is able to promote sparsity inherited in the non-stationarity of the precision parameters (inverse of variances). On the other hand, since the prior is in a Gaussian form, there exists a great possibility of deducing a conceptually simple and computationally tractable inference scheme. Specifically, the well-known expectation–maximization algorithm is used to alternatingly estimate the motion blur kernels, the salient edges of images as well as the precision parameters in the image prior. In difference from many existing methods, no hyperpriors are imposed on any parameters in this paper; there are not any pre-processing steps involved in the proposed method, either, such as explicit suppression of random noise or prediction of salient edge structures. With estimated motion blur kernels, the deblurred images are finally generated using an off-the-shelf non-blind deconvolution method proposed by Krishnan and Fergus (Adv Neural Inf Process Syst 22:1033–1041, 2009). The rationality and effectiveness of our proposed method have been well demonstrated by the experimental results on both synthetic and realistic motion blurry images, showing state-of-the-art blind motion deblurring performance of the proposed approach in the term of quantitative metric as well as visual perception.

The magic of split augmented Lagrangians applied to K-frame-based l0–l2 minimization image restoration

We propose a simple, yet efficient image deconvolution approach, which is formulated as a complementary K-frame-based l0–l2 minimization problem, aiming at benefiting from the advantages of each frame. The problem is solved by borrowing the idea of alternating split augmented Lagrangians. The experimental results demonstrate that our approach has achieved competitive performance among state-of-the-art methods.

A Generalized Robust Minimization Framework for Low-Rank Matrix Recovery

This paper considers the problem of recovering low-rank matrices which are heavily corrupted by outliers or large errors. To improve the robustness of existing recovery methods, the problem is solved by formulating it as a generalized nonsmooth nonconvex minimization functional via exploiting the Schatten -norm and seminorm. Two numerical algorithms are provided based on the augmented Lagrange multiplier (ALM) and accelerated proximal gradient (APG) methods as well as efficient root-finder strategies. Experimental results demonstrate that the proposed generalized approach is more inclusive and effective compared with state-of-the-art methods, either convex or nonconvex.

Kullback---Leibler Divergence Based Composite Prior Modeling for Bayesian Super-Resolution

This paper proposes to adaptively combine the known total variation model and more recent Frobenius norm regularization for multi-frame image super-resolution (SR). In contrast to existing literature, in this paper both the composite prior modeling and posterior variational optimization are achieved in the Bayesian framework by utilizing the Kullback–Leibler divergence, and hyper-parameters related to the composite prior and noise statistics are all determined automatically, resulting in a spatially adaptive SR reconstruction method. Experimental results demonstrate that the new approach can generate a super-resolved image with higher signal-to-noise ratio and better visual perception, not only image details better preserved but also staircase effects better suppressed.