Zhi-Hui Wei

Adaptive Fractional-order Multi-scale Method for Image Denoising

The total variation model proposed by Rudin, Osher, and Fatemi performs very well for removing noise while preserving edges. However, it favors a piecewise constant solution in BV space which often leads to the staircase effect, and small details such as textures are often filtered out with noise in the process of denoising. In this paper, we propose a fractional-order multi-scale variational model which can better preserve the textural information and eliminate the staircase effect. This is accomplished by replacing the first-order derivative with the fractional-order derivative in the regularization term, and substituting a kind of multi-scale norm in negative Sobolev space for the L2 norm in the fidelity term of the ROF model. To improve the results, we propose an adaptive parameter selection method for the proposed model by using the local variance measures and the wavelet based estimation of the singularity. Using the operator splitting technique, we develop a simple alternating projection algorithm to solve the new model. Numerical results show that our method can not only remove noise and eliminate the staircase effect efficiently in the non-textured region, but also preserve the small details such as textures well in the textured region. It is for this reason that our adaptive method can improve the result both visually and in terms of the peak signal to noise ratio efficiently.

Regularized motion blur-kernel estimation with adaptive sparse image prior learning

This paper proposes a regularized negative log-marginal-likelihood minimization method for motion blur-kernel estimation, which is the core problem of blind motion deblurring. In contrast to existing approaches, the proposed method treats the blur-kernel as a deterministic parameter in a directed graphical model wherein, the sharp image is sparsely modeled by using a three-layer hierarchical Bayesian prior and the inverse noise variance is supposed distributed to the Gamma hyper-prior. By borrowing the ideas of mean filed approximation and iteratively reweighted least squares, the posterior distributions of the sharp image, the inverse noise variance and the hyper-parameters involved in the image prior, as well as the deterministic model parameters including the motion blur-kernel and those involved in the hyper-priors, are all estimated automatically for each blind motion deblurring problem. It is worthy to note that, the new approach relies on a strict minimization objective function, and learns a more adaptive sparse image prior while with considerably less implementation heuristics compared with existing motion blur-kernel estimation approaches. Experimental results on both benchmark and real-world motion blurred images demonstrate that the proposed method has achieved state-of-the-art or even better performance than the current blind motion deblurring approaches in terms of the image deblurring quality. The results also show that the proposed approach is robust to the size of the motion blur-kernel to a great extent. A new motion blur-kernel estimation method is proposed for blind image deblurring.The new method is formulated in a unified and rigorous optimization perspective.Sparse image priors are learned adaptively for each blind deblurring problem.The noise variance is automatically estimated unlike state-of-the art VB methods.The method achieves better performance in terms of deblurring effectiveness

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.

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.

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.

A relaxed split bregman iteration for total variation regularized image denoising

The split Bregman iteration is an efficient tool for solving the total variation regularized minimization problems and has received considerable attention in recent years. In denoising case, it can remove noise well, but fails to preserve textures efficiently. In this paper, we reinterpret the split Bregman iteration from the perspective of function matching, and reveal the reason why it can not preserve textures well. To improve the performance of texture preservation, we develop a relaxed split Bregman iteration for total variation regularized image denoising. Numerical results show that for partly textured images, the new method can remove noise in the non-textured region and preserve textures in the textured region adaptively, and therefore it can improve the result both visually and in terms of the peak signal to noise ratio efficiently.

Brain MR image segmentation and bias field correction using adaptive fuzzy C means model

The imperfections in the radio-frequency coils or problems associated with the acquisition sequences may cause MRI intensity inhomogeneities, which may mislead image segmentation. Comparing the tradition fuzzy C means model, this paper adds the bias field information in the objective function for simultaneous correction of the bias field and accurately segmentation. In adaptive model, the bias field is modeled as a linear combination of a set of basis functions to ensure the smoothness and slowly varying, and can be easy estimated by computing the coefficients of this basis functions in every iteration. Experimental results on both synthetic images and MR data are given to demonstrate the effectiveness and efficiency of the proposed algorithm.