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Image denoising is a challenging inverse problem due to complex scenes and information loss. Recently, various methods have been considered to solve this problem by building a well-designed convolutional neural network (CNN) or introducing some hand-designed image priors. Different from previous works, we investigate a new framework for image denoising, which integrates edge detection, edge guidance, and image denoising into an end-to-end CNN model. To achieve this goal, we propose a multilevel edge features guided network (MLEFGN). First, we build an edge reconstruction network (Edge-Net) to directly predict clear edges from the noisy image. Then, the Edge-Net is embedded as part of the model to provide edge priors, and a dual-path network is applied to extract the image and edge features, respectively. Finally, we introduce a multilevel edge features guidance mechanism for image denoising. To the best of our knowledge, the Edge-Net is the first CNN model specially designed to reconstruct image edges from the noisy image, which shows good accuracy and robustness on natural images. Extensive experiments clearly illustrate that our MLEFGN achieves favorable performance against other methods and plenty of ablation studies demonstrate the effectiveness of our proposed Edge-Net and MLEFGN. The code is available at https://github.com/MIVRC/MLEFGN-PyTorch .

Blind image deblurring is a conundrum because there are infinitely many pairs of latent image and blur kernel. To get a stable and reasonable deblurred image, proper prior knowledge of the latent image and the blur kernel is urgently required. Different from the recent works on the statistical observations of the difference between the blurred image and the clean one, our method is built on the surface-aware strategy arising from the intrinsic geometrical consideration. This approach facilitates the blur kernel estimation due to the preserved sharp edges in the intermediate latent image. Extensive experiments demonstrate that our method outperforms the state-of-the-art methods on deblurring the text and natural images. Moreover, our method can achieve attractive results in some challenging cases, such as low-illumination images with large saturated regions and impulse noise. A direct extension of our method to the non-uniform deblurring problem also validates the effectiveness of the surface-aware prior.

We present a probabilistic semi-supervised learning (SSL) framework based on sparse graph structure learning. Different from existing SSL methods with either a predefined weighted graph heuristically constructed from the input data or a learned graph based on the locally linear embedding assumption, the proposed SSL model is capable of learning a sparse weighted graph from the unlabeled high-dimensional data and a small amount of labeled data, as well as dealing with the noise of the input data. Our representation of the weighted graph is indirectly derived from a unified model of density estimation and pairwise distance preservation in terms of various distance measurements, where latent embeddings are assumed to be random variables following an unknown density function to be learned, and pairwise distances are then calculated as the expectations over the density for the model robustness to the data noise. Moreover, the labeled data based on the same distance representations are leveraged to guide the estimated density for better class separation and sparse graph structure learning. A simple inference approach for the embeddings of unlabeled data based on point estimation and kernel representation is presented. Extensive experiments on various data sets show promising results in the setting of SSL compared with many existing methods and significant improvements on small amounts of labeled data.

Morphology reconstruction of neurons from 3-D microscopic images is essential to neuroscience research. However, many reconstructions may contain errors and ambiguities because of the crossover neuronal fibers. In this article, an automatic algorithm is proposed for the detection and separation of crossover structures and is applied to neuron tracing for improving the neuron reconstruction results. First, a spherical-patches extraction (SPE)-Net is employed to detect the 3-D neuron crossover points and locate the crossover structures in neuron volumetric images. Second, a multiscale upgraded ray-shooting model (MSURS) is proposed to obtain robust results at different scales with high confidence and is employed to extract the crossover neuronal structure features. Then, a crossover structure separation (CSS) method is developed to eliminate the false connections of crossover structures and generate deformed separated neuronal fibers based on the extracted features to replace the original neurites signals. Experiments demonstrate that the SPE-Net for crossover point detection achieves average precision and recall rates of 73.89% and 79.66%, respectively, and demonstrate the proposed CSS method can improve 20.46% the performance of the reconstructions on average. The results confirm that the proposed method can effectively improve the neuron tracing results in volumetric images.

Imbalanced data classification, as a challenging task, has drawn a significant interest in numerous scientific areas. One popular strategy to balance the instance quantities between two classes is oversampling via generating synthetic instances. However, it still suffers from two key issues: where and how many synthetic instances should be generated. In this paper, we propose a Local distribution-based Adaptive Minority Oversampling method (LAMO) to deal with the imbalance classification problem. LAMO first identifies the informative borderline minority instances as sampling seeds according to their neighbors and the corresponding class distribution. Then, LAMO captures the local distribution of each seed according to its Euclidean distances from the nearest majority instance and nearest minority instance.Finally, LAMO generates synthetic instances around seeds via a Gaussian Mixture Model (GMM). For each component of GMM, the mixing coefficient and bandwidth are adaptively set with the aid of seeds’ local distribution. Extensive experiments have been conducted on both simulated and real data sets under varying the imbalance ratio and data size. By comparing with the state-of-the-art oversampling methods, the proposed LAMO obtains promising results in terms of several widely used evaluation metrics.

The digital reconstruction of neurons is essential to various neuroscientific studies. Due to the existence of gaps and ambiguities in neuron images, the neuron tracing results generated by most automatic reconstruction algorithms may be incomplete, resulting in false negatives (FNs), which need to be repaired in proof editing. However, the automatic proof-editing methods for repairing FN branches have rarely been explored. In this study, we propose a proof-editing algorithm for automatically detecting and repairing the FN branches of the initial reconstruction, which is based on a multiscale upgraded ray (MUR)-shooting model and an MOST-based repairer. The MUR detects the FN branch and the corresponding branch direction vector by analyzing the multiscale intensity distribution features around a topological feature point. The topological feature points contain the junction points detected from the neuron image and the tip nodes extracted from the initial reconstruction. The MOST-based repairer is proposed to prevent the redundant reconstructions by assigning the detected branch direction vector as the initial tracing direction, which rejects the nodes returning to the traced area. The experimental results demonstrate clearly that the proposed method can reduce 20% of the false-negative rate at most. The experimental results confirm that the proposed method is extremely helpful for generating faithful reconstructions.

Training deep neural networks can be difficult. For classical neural networks, the initialization method by Xavier and Yoshua which is later generalized by He, Zhang, Ren and Sun can facilitate stable training. However, with the recent development of new layer types, we find that the above mentioned initialization methods may fail to lead to successful training. Based on these two methods, we will propose a new initialization by studying the parameter space of a network. Our principal is to put constrains on the growth of parameters in different layers in a consistent way. In order to do so, we introduce a norm to the parameter space and use this norm to measure the growth of parameters. Our new method is suitable for a wide range of layer types, especially for layers with parameter-sharing weight matrices.

In this paper, we investigate the challenging task of removing haze from a single natural image. The analysis on the haze formation model shows that the atmospheric veil has much less relevance to chrominance than luminance, which motivates us to neglect the haze in the chrominance channel and concentrate on the luminance channel in the dehazing process. Besides, the experimental study illustrates that the YUV color space is most suitable for image dehazing. Accordingly, a variational model is proposed in the Y channel of the YUV color space by combining the reformulation of the haze model and the two effective priors. As we mainly focus on the Y channel, most of the chrominance information of the image is preserved after dehazing. The numerical procedure based on the alternating direction method of multipliers (ADMM) scheme is presented to obtain the optimal solution. Extensive experimental results on real-world hazy images and synthetic dataset demonstrate clearly that our method can unveil the details and recover vivid color information, which is competitive among many existing dehazing algorithms. Further experiments show that our model also can be applied for image enhancement.

The task of single image super-resolution (SISR) is a highly ill-posed inverse problem since reconstructing the high-frequency details from a low-resolution image is challenging. Most previous CNN-based super-resolution (SR) methods tend to directly learn the mapping from the low-resolution image to the high-resolution image through some complex convolutional neural networks. However, the method of blindly increasing the depth of the network is not the best choice because the performance improvement of such methods is marginal but the computational cost is huge. A more efficient method is to integrate the image prior knowledge into the model to assist the image reconstruction. Indeed, the soft-edge has been widely applied in many computer vision tasks as the role of an important image feature. In this paper, we propose a Soft-edge assisted Network (SeaNet) to reconstruct the high-quality SR image with the help of image soft-edge. The proposed SeaNet consists of three sub-nets: a rough image reconstruction network (RIRN), a soft-edge reconstruction network (Edge-Net), and an image refinement network (IRN). The complete reconstruction process consists of two stages. In Stage-I, the rough SR feature maps and the SR soft-edge are reconstructed by the RIRN and Edge-Net, respectively. In Stage-II, the outputs of the previous stages are fused and then fed to the IRN for high-quality SR image reconstruction. Extensive experiments show that our SeaNet converges rapidly and achieves excellent performance under the assistance of image soft-edge. The code is available at https://gitlab.com/junchenglee/seanet-pytorch .

Cauchy noise, as a typical non-Gaussian noise, appears frequently in many important fields, such as radar, medical, and biomedical imaging. In this letter, we focus on image recovery under Cauchy noise. Instead of the celebrated total variation or low-rank prior, we adopt a novel deep-learning-based image denoiser prior to effectively remove Cauchy noise with blur. To preserve more detailed texture and better balance between the receptive field size and the computational cost, we apply the multi-level wavelet convolutional neural network (MWCNN) to train this denoiser. We use the forward-backward splitting (FBS) method to handle the proposed model, which can be implemented efficiently without introducing auxiliary variables. Moreover, the multi-noise-levels strategy is employed to train a series of denoisers to restore the image corrupted by Cauchy noise and blur. Numerical experiments demonstrate clearly that our method has better performance than the existing image restoration methods for removing Cauchy noise in terms of the quantitative index and visual quality.

In this paper, we propose a new three-stage segmentation framework based on a convex variant of the Mumford--Shah model and the intensity inhomogeneity information of an image. The first stage in o...

A natural image u is often sparse under a given transformation W, one can use $$L_0$$ norm of Wu as a regularisation term in image reconstructions. Since minimizing the $$L_0$$ norm is a NP hard problem, the $$L_1$$ norm is widely used as an replacement. However, recent studies show that nonconvex penalties, e.g., MCP, enjoy better performance for sparse signal recovery. In this paper, we propose a nonconvex model for image restoration with a minimax concave penalty (MCP). First we establish the existence of a global minimizer for the nonconvex model. Then we solve this model by using the alternating direction method of multipliers algorithm. The convergence of the proposed algorithm is analysed with properly chosen parameters. Numerical experiments show that the MCP model outperforms TV model in terms of efficiency and accuracy.

Selective image segmentation is an important topic in medical imaging and real applications. In this paper, we propose a weighted variational selective image segmentation model which contains two steps. The first stage is to obtain a smooth approximation related to Mumford-Shah model to the target region in the input image. Using weighted function, the approximation provides a larger value for the target region and smaller values for other regions. In the second stage, we make use of this approximation and perform a thresholding procedure to obtain the object of interest. The approximation can be obtained by the alternating direction method of multipliers and the convergence analysis of the method can be established. Experimental results for medical image selective segmentation are given to demonstrate the usefulness of the proposed method. We also do some comparisons and show that the performance of the proposed method is more competitive than other testing methods.

We reformulate the original phase retrieval problem into two variational models (with and without regularization), both containing a globally Lipschitz differentiable term. These two models can be efficiently solved via the proposed Partially Preconditioned Proximal Alternating Linearized Minimization (P${}^3$ALM) for masked Fourier measurements. Thanks to the Lipschitz differentiable term, we prove the global convergence of P${}^3$ALM for solving the nonconvex phase retrieval problems. Extensive experiments are conducted to show the effectiveness of the proposed methods.

Imbalance classification is a challenging research topic in the community of machine learning, in which it is difficult to acquire the discriminative features. To date, a series of methods have been proposed but they still suffer from the following issues. The first issue is caused by the underrepresented data where the boundaries between classes are not clear. The second one is the complex structure in majority classes. To address these two issues, a Smooth Soft-Balance Discriminative Analysis method (S2BDA) is proposed to deal with imbalanced data. Among it, the underrepresented data is preprocessed via a smoothing technique so that the compact representation of each class can be obtained to make the boundaries between classes more explicit. To mine the structure of majority classes meanwhile keep the pattern hidden in the minority class, a soft-balance clustering model is designed to determine the subclasses from the majority class. Based on the balanced subclasses, S2BDA takes advantage of subclass-aware discriminant analysis to extract the discriminative features for imbalanced data classification. Extensive experiments are conducted on two synthetic data sets and sixteen real-world data sets with various imbalance ratios (from 4 to 39.18), data sizes (from 132 to 20000), number of categories (from 2 to 9) and dimensionalities (from 4 to 178). The experimental results have demonstrated that S2BDA outperforms the state-of-the-art methods in terms of the widely used evaluation metrics.

To improve the image segmentation quality, it is important to adequately describe the local features of targets in images. In this paper, we develop a novel adaptive total variation based two-stage segmentation approach to restore and segment images under complex degradations. To find a smooth approximation solution in the first stage, we introduce an effective regularization term that combines an adaptive weighted matrix with the gradient operator. The adaptive weighted matrix gives different penalties in the axis directions to enhance the diffusion along the tangent direction of the edge. It can filter out the details far away from the edge and preserve the main structure of targets. For the convex objective function in the first stage, a semi-proximal alternating direction method of multipliers (sPADMM) with guaranteed convergence is successfully employed. We utilize the K-means method to select thresholds automatically and complete the segmentation by thresholding the image into different regions in the second stage. Extensive experimental comparisons between our method and some state-of-the-art methods including a deep learning approach are provided. All numerical results illustrate clearly that our method has better performance for different kinds of segmentation and restoration tasks.

The hybrid variational model for restoration of texture images corrupted by blur and Gaussian noise we consider combines total variation regularisation and a fractional-order regularisation, and is solved by an alternating minimisation direction algorithm. Numerical experiments demonstrate the advantage of this model over the adaptive fractional-order variational model in image quality and computational time.

Multiplicative noise removal is a challenging problem in image restoration. In this paper, by applying Box-Cox transformation, we convert the multiplicative noise removal problem into the additive noise removal problem and the block matching three dimensional (BM3D) method is applied to get the final recovered image. Indeed, BM3D is an effective method to remove additive Gaussian white noise in images. A maximum likelihood method is designed to determine the parameter in the Box-Cox transformation. We also present the unbiased inverse transform for the Box-Cox transformation which is important. Both theoretical analysis and experimental results illustrate clearly that the proposed method can remove multiplicative noise very well especially when multiplicative noise is heavy. The proposed method is superior to the existing methods for multiplicative noise removal in the literature.

International audience; In the usual non-local variational models, such as the non-local total variations (NLTV), the image is regularized by minimizing an energy term that penalizes gray-levels discrepancy between some specified pairs of pixels, a weight value is computed between these two pixels to penalize their dissimilarity. In this paper, we impose some regularity to those weight values. More precisely, we minimize a function involving a regularization term, analogous to an $H^1$ term, on weights. Doing so, the finite differences defining the image regularity depend on their environment. When the weights are difficult to define, they can be restored by the proposed stable regularization scheme.We provide all the details necessary for the implementation of a PALM algorithm with proved convergence. We illustrate the ability of the model to restore relevant unknown edges from the neighboring edges on an image inpainting problem. We also argue on inpainting, zooming and denoising problems that the model better recovers thin structures.

In this paper, we propose a SLaT (Smoothing, Lifting and Thresholding) method with three stages for multiphase segmentation of color images corrupted by different degradations: noise, information loss, and blur. At the first stage, a convex variant of the Mumford-Shah model is applied to each channel to obtain a smooth image. We show that the model has unique solution under the different degradations. In order to properly handle the color information, the second stage is dimension lifting where we consider a new vector-valued image composed of the restored image and its transform in the secondary color space with additional information. This ensures that even if the first color space has highly correlated channels, we can still have enough information to give good segmentation results. In the last stage, we apply multichannel thresholding to the combined vector-valued image to find the segmentation. The number of phases is only required in the last stage, so users can choose or change it all without the need of solving the previous stages again. Experiments demonstrate that our SLaT method gives excellent results in terms of segmentation quality and CPU time in comparison with other state-of-the-art segmentation methods., 19 pages

In this paper, we focus on the challenging problem of removing the spatially varying out-of-focus blur from a single natural image. We first propose an effective method to estimate the blur map by the total variation refinement on Holder coefficient, then discuss the properties of the corresponding kernel matrix. A tight-frame based energy functional, whose minimizer is related to the optimal defocus result, is thus built. For tackling functional more efficiently, we describe the numerical procedure based on an accelerated primal-dual scheme. To verify the effectiveness of our method, we compare it with some state-of-the-art schemes using both synthesized and natural images. Experimental results demonstrate that the proposed method performs better than the compared methods.

Image smoothing is a very important topic in image processing. Among these image smoothing methods, the L0 gradient minimization method is one of the most popular ones. However, the L0 gradient minimization method suffers from the staircasing effect and over-sharpening issue, which highly degrade the quality of the smoothed image. To overcome these issues, we use not only the L0 gradient term for finding edges, but also a surface area based term for the purpose of smoothing the inside of each region. An alternating minimization algorithm is suggested to efficiently solve the proposed model, where each subproblem has a closed-form solution. Leveraging the introduced surface area term, the proposed method can effectively alleviate the staircasing effect and the over-sharpening issue. The superiority of our method over the state-of-the-art methods is demonstrated by a series of experiments.

Image colorization refers to a computer-assisted process that adds colors to grayscale images. It is a challenging task since there is usually no one-to-one correspondence between color and local texture. In this paper, we tackle this issue by exploiting weighted nonlocal self-similarity and local consistency constraints at the resolution of superpixels. Given a grayscale target image, we first select a color source image containing similar segments to target image and extract multi-level features of each superpixel in both images after superpixel segmentation. Then a set of color candidates for each target superpixel is selected by adopting a top-down feature matching scheme with confidence assignment. Finally, we propose a variational approach to determine the most appropriate color for each target superpixel from color candidates. Experiments demonstrate the effectiveness of the proposed method and show its superiority to other state-of-the-art methods. Furthermore, our method can be easily extended to color transfer between two color images.

This paper is concerned with the monotone inclusion involving the sum of a finite number of maximally monotone operators and the parallel sum of two maximally monotone operators with bounded linear operators. To solve this monotone inclusion, we first transform it into the formulation of the sum of three maximally monotone operators in a proper product space. Then we derive two efficient iterative algorithms, which combine the partial inverse method with the preconditioned Douglas-Rachford splitting algorithm and the preconditioned proximal point algorithm. Furthermore, we develop an iterative algorithm, which relies on the preconditioned Douglas-Rachford splitting algorithm without using the partial inverse method. We carefully analyze the theoretical convergence of the proposed algorithms. Finally, in order to demonstrate the effectiveness and efficiency of these algorithms, we conduct numerical experiments on a novel image denoising model for salt-and-pepper noise removal. Numerical results show the good performance of the proposed algorithms.

Image restoration is an important technique to deal with the degradation of the image. This paper presents an efficient and trusty denoising scheme, which combines the convolutional neural network (CNN) technique with the traditional variational model, to offer interpretable and high quality reconstructions. In this scheme, CNN, which has proven effectiveness in feature extraction tasks, is adopted to obtain the designed edge features from the noisy images, to be the prior of the reconstruction through an edge regularization. In the proposed denoising model, the total variation (TV) regularization is also adopted for its superior performance in allowing the sharp edges. The solution of the proposed model is obtained by using the Bregman splitting method, with the existence and the uniqueness of the solution also analyzed in this paper. Extensive experiments show that the two regularizations combined in the proposed model are able to fix the staircasing defects effectively and retrieve the fine textures in the recovered images as well, which outperforms the state-of-the-art interpretable denoising methods. Moreover, the proposed edge regularization can be easily extended into other kinds of noise or other restoration tasks, which implies the strong adaptivity of the proposed scheme.

Recently, deep convolutional neural networks have demonstrated high-quality reconstruction for single image super-resolution. In this study, we present a network by using residual blocks with cascading simple blocks to improve the image resolution. Cascading simple blocks with a multi-layer perceptron are conducive to extract features and approximate a complex mapping with fewer parameters. Skip connections can help to alleviate the vanishing-gradient problem of deep networks. In addition, our network contains two pathways. One is to predict the high frequency information of the high resolution image and the other is to predict the low frequency information of the high resolution image. Then the information of two pathways is fused, and pixel-shuffle is used for upsampling. Moreover, to capture texture details of images, we introduce a novel loss function called detail perception loss, which is used to measure the difference of the wavelet coefficients from the reconstructed image and ground truth. By reducing detail perception loss, texture details of the reconstructed image are becoming more similar with texture details of ground truth. Extensive quantitative and qualitative experiments on four benchmark datasets show that our method achieves superior performance over typical single image super-resolution methods.

The similar image patches should have similar underlying structures. Thus the matrix constructed from stacking the similar patches together has low rank. Based on this fact, the nuclear norm minimization, which is the convex relaxation of low rank minimization, leads to good denoising results. Recently, the weighted nuclear norm minimization has been applied to image denoising. This approach presents state-of-the-art result for image denoising. In this paper, we further study the weighted nuclear norm minimization problem for general image recovery task. For the weights being in arbitrary order, we prove that such minimization problem has a unique global optimal solution in the closed form. Incorporating this idea with the celebrated total variation regularization, we then investigate the image deblurring problem. Numerical experimental results illustratively clearly that the proposed algorithms achieve competitive performance.

This paper introduces a two-stage model for multi-channel image segmentation, which is motivated by minimal surface theory. Indeed, in the first stage, we acquire a smooth solutionufrom a convex variational model related to minimal surface property and different data fidelity terms are considered. This minimization problem is solved efficiently by the classical primal-dual approach. In the second stage, we adopt thresholding to segment the smoothed imageu. Here, instead of using K-means to determine the thresholds, we propose a more stable hill-climbing procedure to locate the peaks on the 3D histogram ofuas thresholds, in the meantime, this algorithm can also detect the number of segments. Finally, numerical results demonstrate that the proposed method is very robust against noise and superior to other image segmentation approaches.

This paper proposes a difference of convex algorithm (DCA) to deal with a non-convex data fidelity term, proposed by Aubert and Aujol referred to as the AA model. The AA model was adopted in many subsequent works for multiplicative noise removal, most of which focused on convex approximation so that numerical algorithms with guaranteed convergence can be designed. Noting that the AA model can be naturally split into a difference of two convex functions, we apply the DCA to solve the original AA model. Compared to the gradient projection algorithm considered by Aubert and Aujol, the DCA often converges faster and leads to a better solution. We prove that the DCA sequence converges to a stationary point, which satisfies the first order optimality condition. In the experiments, we consider two applications, image denoising and deblurring, both of which involve multiplicative Gamma noise. Numerical results demonstrate that the proposed algorithm outperforms the state-of-the-art methods for multiplicative noise removal.

In this paper, we focus on variational approaches for image inpainting in transform domain and propose two new algorithms, iterative coupled transform domain inpainting (ICTDI) and iterative decoupled transform domain inpainting. In the derivation of ICTDI, we use operator splitting and the quadratic penalty technique to get a new approximate problem of the basic model. By the alternating minimization method, the approximate problem can be decomposed as three relatively simple subproblems with closed-form solutions. However, ICTDI is not efficient when some adaptive regularization operator is used, such as the learned BM3D frame. To overcome this drawback, with some modifications, we decouple our framework into three relatively independent parts: denoising, linear combination in the transform domain, and linear combination in the image domain. Therefore, we can use any existing denoising method in the denoising step. We consider three choices for regularization operators in our approach: gradient operator...

The phase retrieval problem has drawn considerable attention, as many optical detection devices can only measure magnitudes of the Fourier transform of the underlying object (signal or image). This paper addresses the phase retrieval problem from incomplete data, where only partial magnitudes of Fourier transform are obtained. In particular, we consider structured illuminated patterns in holography and find that noninteger values used in designing such patterns often yield better reconstruction than the conventional integer-valued ones. Furthermore, we demonstrate theoretically and numerically that three diffracted sets of (complete) magnitude data are sufficient to recover the object. To compensate for incomplete information, we incorporate a total variation regularization a priori to guarantee that the reconstructed image satisfies some desirable properties. The proposed model can be solved efficiently by an alternative directional multiplier method with provable convergence. Numerical experiments valid...

We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler (KL)-divergence term for the Poisson noise and a total variation (TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers (ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pocks first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.

Natural images are usually composed of multiple objects at different scales in flat and slanted regions. Traditional labeling/segmentation approaches based on total variation minimization may produce staircase results with discontinuities and rough boundaries. In this paper, we propose a novel weighted variational model for image labeling/segmentation in the space of functions of bounded Hessian, the weights of which are automatically estimated based on edge information of the observed images. Especially, by minimizing the combined first and second-order regularizer, our model can overcome the shortage of total variation and provide more meaningful results. The efficient alternating direction method of multipliers based algorithm is established, all subproblems of which can be solved by either the fast Fourier transform or closed-form solution. We further introduce the weighted bounded Hessian regularizer into the two-stage segmentation framework for dealing with noisy and blurry image segmentation problems. Numerous experiments are conducted on both two-phase and multi-phase labeling/segmentation problems. By comparing with several state-of-the-art methods both qualitatively and quantitatively, it demonstrates that the proposed models can prominently improve the accuracy of image labeling and segmentation.

Image denoising problem still remains an active research field in the image processing. To improve the denoising quality, it is very important to describe the local structure of the image in the proposed model. This fact motivates us to introduce an adaptive weighted TVp regularization-based denoising model, where the rotation matrix and the weighted matrix depend on the local structure of the image. Specially, these two matrices can enhance the diffusion of the responding Euler-Lagrangian equation along with the tangential direction of the edge. This procedure offers more control over the regularization and then allows more denoising in smooth regions and less denoising when processing edge regions. In addition, since the proposed model is nonsmooth and non-Lipschitz, we employ the alternating direction method of multipliers (ADMM) to solve it with the help of using the half-quadratic scheme to solve the related l 2 − l p subproblem. In particular, we also provide the convergence analysis of the used numerical methods. Some numerical comparisons show that the proposed model leads to considerable performance gains when tested on several denoising tasks.

In this paper, we study the image deblurring problem based on sparse representation over learned dictionary which leads to promising performance in image restoration in recent years. However, the commonly used overcomplete dictionary is not well structured. This shortcoming makes the approximation be unstable and demand much computational time. To overcome this, the structured sparse model selection (SSMS) over a family of learned orthogonal bases was proposed recently. In this paper, We further analyze the properties of SSMS and propose a model for deblurring under Gaussian noise. Numerical experimental results show that the proposed algorithm achieves competitive performance. As a generalization, we give a modified model for deblurring under salt-and-pepper noise. The resulting algorithm also has a good performance.

International audience; Image restoration plays an important role in image processing, and numerous approaches have been proposed to tackle this problem. This paper presents a modified model for image restoration, that is based on a combination of Total Variation (TV) and Dictionary approaches. Since the well-known TV regularization is non-differentiable, the proposed method utilizes its dual formulation instead of its approximation in order to exactly preserve its properties. The data-fidelity term combines the one commonly used in image restoration and a wavelet thresholding based term. Then, the resulting optimization problem is solved via a first-order primal-dual algorithm. Numerical experiments demonstrate the good performance of the proposed model. In a last variant, we replace the classical TV by the nonlocal TV regularization, which results in a much higher quality of restoration.

In this paper, a new variational model for restoring blurred images with multiplicative noise is proposed. Based on the statistical property of the noise, a quadratic penalty function technique is utilized in order to obtain a strictly convex model under a mild condition, which guarantees the uniqueness of the solution and the stabilization of the algorithm. For solving the new convex variational model, a primal-dual algorithm is proposed, and its convergence is studied. The paper ends with a report on numerical tests for the simultaneous deblurring and denoising of images subject to multiplicative noise. A comparison with other methods is provided as well.

International audience; In this paper, we study a variant of the Matching Pursuit named Matching Pursuit Shrinkage. Similarly to the Matching Pursuit it seeks for an approximation of a datum living in a Hilbert space by a sparse linear expansion in an enumerable set of atoms. The difference with the usual Matching Pursuit is that, once an atom has been selected, we do not erase all the information along the direction of this atom. Doing so, we can evolve slowly along that direction. The goal is to attenuate the negative impact of bad atom selections. We analyse the link between the shrinkage function used by the algorithm and the fact that the result belongs to an lp space.

The piecewise constant Mumford--Shah (PCMS) model and the Rudin--Osher--Fatemi (ROF) model are two important variational models in image segmentation and image restoration, respectively. In this pa...