nils-herrmann/clean_scirepeval huggingface dataset:
Multi-channel Weighted Nuclear Norm Minimization for Real Color Image Denoising

Most of the existing denoising algorithms are developed for grayscale images. It is not trivial to extend them for color image denoising since the noise statistics in R, G, and B channels can be very different for real noisy images. In this paper, we propose a multi-channel (MC) optimization model for real color image denoising under the weighted nuclear norm minimization (WNNM) framework. We concatenate the RGB patches to make use of the channel redundancy, and introduce a weight matrix to balance the data fidelity of the three channels in consideration of their different noise statistics. The proposed MC-WNNM model does not have an analytical solution. We reformulate it into a linear equality-constrained problem and solve it via alternating direction method of multipliers. Each alternative updating step has a closed-form solution and the convergence can be guaranteed. Experiments on both synthetic and real noisy image datasets demonstrate the superiority of the proposed MC-WNNM over state-of-the-art denoising methods.
A Probabilistic Collaborative Representation Based Approach for Pattern Classification

Conventional representation based classifiers, ranging from the classical nearest neighbor classifier and nearest subspace classifier to the recently developed sparse representation based classifier (SRC) and collaborative representation based classifier (CRC), are essentially distance based classifiers. Though SRC and CRC have shown interesting classification results, their intrinsic classification mechanism remains unclear. In this paper we propose a probabilistic collaborative representation framework, where the probability that a test sample belongs to the collaborative subspace of all classes can be well defined and computed. Consequently, we present a probabilistic collaborative representation based classifier (ProCRC), which jointly maximizes the likelihood that a test sample belongs to each of the multiple classes. The final classification is performed by checking which class has the maximum likelihood. The proposed ProCRC has a clear probabilistic interpretation, and it shows superior performance to many popular classifiers, including SRC, CRC and SVM. Coupled with the CNN features, it also leads to state-of-the-art classification results on a variety of challenging visual datasets.
Fractional-Order Anisotropic Diffusion for Image Denoising

This paper introduces a new class of fractional-order anisotropic diffusion equations for noise removal. These equations are Euler-Lagrange equations of a cost functional which is an increasing function of the absolute value of the fractional derivative of the image intensity function, so the proposed equations can be seen as generalizations of second-order and fourth-order anisotropic diffusion equations. We use the discrete Fourier transform to implement the numerical algorithm and give an iterative scheme in the frequency domain. It is one important aspect of the algorithm that it considers the input image as a periodic image. To overcome this problem, we use a folded algorithm by extending the image symmetrically about its borders. Finally, we list various numerical results on denoising real images. Experiments show that the proposed fractional-order anisotropic diffusion equations yield good visual effects and better signal-to-noise ratio.
Sparse representation or collaborative representation: Which helps face recognition?

As a recently proposed technique, sparse representation based classification (SRC) has been widely used for face recognition (FR). SRC first codes a testing sample as a sparse linear combination of all the training samples, and then classifies the testing sample by evaluating which class leads to the minimum representation error. While the importance of sparsity is much emphasized in SRC and many related works, the use of collaborative representation (CR) in SRC is ignored by most literature. However, is it really the l1-norm sparsity that improves the FR accuracy? This paper devotes to analyze the working mechanism of SRC, and indicates that it is the CR but not the l1-norm sparsity that makes SRC powerful for face classification. Consequently, we propose a very simple yet much more efficient face classification scheme, namely CR based classification with regularized least square (CRC_RLS). The extensive experiments clearly show that CRC_RLS has very competitive classification results, while it has significantly less complexity than SRC.
Subspace Segmentation by Correlation Adaptive Regression

Subspace segmentation aims to segment a given data set into clusters with each cluster corresponding to a subspace. Most recent works focus on subspace representation-based methods, which construct the affinity matrix based on the subspace representation of the data points. Ideally, the affinity matrix should be inter-cluster sparse and intra-cluster uniform. The inter-cluster sparsity guarantees segmenting data into different subspaces from which they are originally drawn and the intra-cluster uniformity encourages clustering highly correlated data together. Most previous methods partly satisfy these properties and cannot obtain ideal results. To satisfy both properties, we propose an explicit data correlation adaptive regression model for the subspace representation. The proposed model essentially uses <inline-formula> <tex-math notation="LaTeX">${l_{2}}$ </tex-math></inline-formula>-norm on the coefficients of highly correlated data points while <inline-formula> <tex-math notation="LaTeX">${l_{1}}$ </tex-math></inline-formula>-norm on that of less correlated data points. The <inline-formula> <tex-math notation="LaTeX">${l_{2}}$ </tex-math></inline-formula>-norm tends to enforce the coefficients corresponding to highly correlated data have the grouping effect, while the <inline-formula> <tex-math notation="LaTeX">${l_{1}}$ </tex-math></inline-formula>-norm tends to enforce the coefficients corresponding to uncorrelated data to be zero. So, the proposed model can ensure the affinity matrix have two attractive properties: inter-subspace sparsity and intra-cluster uniformity. Experimental results on several commonly used clustering data sets show that our method performs better than the state-of-the-art methods.
Learning smooth dictionary for image denoising

Priors play an important role for most of image denoising approaches under the Bayesian framework. Dictionary learning can capture the sparseness prior and has been widely used for various applications in recent years. In the other aspect, TGV (Total Generalized Variation) can reduce the staircasing effects and preserve the geometric structures by the smoothness prior. In this paper, a new dictionary learning model is proposed to combine the above two priors by adding a second order TGV regularizer on each atom of the dictionary. The proposed model is applied to image denoising, and experiments demonstrate its effectiveness.
Two-Direction Nonlocal Model for Image Denoising

Similarities inherent in natural images have been widely exploited for image denoising and other applications. In fact, if a cluster of similar image patches is rearranged into a matrix, similarities exist both between columns and rows. Using the similarities, we present a two-directional nonlocal (TDNL) variational model for image denoising. The solution of our model consists of three components: one component is a scaled version of the original observed image and the other two components are obtained by utilizing the similarities. Specifically, by using the similarity between columns, we get a nonlocal-means-like estimation of the patch with consideration to all similar patches, while the weights are not the pairwise similarities but a set of clusterwise coefficients. Moreover, by using the similarity between rows, we also get nonlocal-autoregression-like estimations for the center pixels of the similar patches. The TDNL model leads to an alternative minimization algorithm. Experiments indicate that the model can perform on par with or better than the state-of-the-art denoising methods.
Edge Strength Similarity for Image Quality Assessment

The objective image quality assessment aims to model the perceptual fidelity of semantic information between two images. In this letter, we assume that the semantic information of images is fully represented by edge-strength of each pixel and propose an edge-strength-similarity-based image quality metric (ESSIM). Through investigating the characteristics of the edge in images, we define the edge-strength to take both anisotropic regularity and irregularity of the edge into account. The proposed ESSIM is considerably simple, however, it can achieve slightly better performance than the state-of-the-art image quality metrics as evaluated on six subject-rated image databases.
A novel method for harmonic geometric transformation model based on wavelet collocation

Geometric distortion may occur in the data acquisition phase in information systems, and it can be characterized by some geometric transformation models. Once the distorted image is approximated by a certain geometric transformation model, we can apply its inverse transformation for the geometric restoration to remove the distortion. The harmonic model is a very important one, which can cover other linear and nonlinear geometric models. However, its implementation is very complicated, because it cannot be described by any fixed functions in mathematics. In fact, it is represented by a partial differential equation with a given boundary condition. In the paper a wavelet-based method is presented to handle the harmonic model. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performances are evaluated by experiments.
A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding

In many sparse coding based image restoration and image classification problems, using non-convex Ip-norm minimization (0 ≤ p <; 1) can often obtain better results than the convex l1-norm minimization. A number of algorithms, e.g., iteratively reweighted least squares (IRLS), iteratively thresholding method (ITM-Ip), and look-up table (LUT), have been proposed for non-convex Ip-norm sparse coding, while some analytic solutions have been suggested for some specific values of p. In this paper, by extending the popular soft-thresholding operator, we propose a generalized iterated shrinkage algorithm (GISA) for Ip-norm non-convex sparse coding. Unlike the analytic solutions, the proposed GISA algorithm is easy to implement, and can be adopted for solving non-convex sparse coding problems with arbitrary p values. Compared with LUT, GISA is more general and does not need to compute and store the look-up tables. Compared with IRLS and ITM-Ip, GISA is theoretically more solid and can achieve more accurate solutions. Experiments on image restoration and sparse coding based face recognition are conducted to validate the performance of GISA.
Perceptual Fidelity Aware Mean Squared Error

How to measure the perceptual quality of natural images is an important problem in low level vision. It is known that the Mean Squared Error (MSE) is not an effective index to describe the perceptual fidelity of images. Numerous perceptual fidelity indices have been developed, while the representatives include the Structural SIMilarity (SSIM) index and its variants. However, most of those perceptual measures are nonlinear, and they cannot be easily dopted as an objective function to minimize in various low level vision tasks. Can MSE be perceptual fidelity aware after some minor adaptation? In this paper we propose a simple framework to enhance the perceptual fidelity awareness of MSE by introducing an l2-norm structural error term to it. Such a Structural MSE (SMSE) can lead to very competitive image quality assessment (IQA) results. More surprisingly, we show that by using certain structure extractors, SMSE can be further turned into a Gaussian smoothed MSE (i.e., the Euclidean distance between the original and distorted images after Gaussian smooth filtering), which is much simpler to calculate but achieves rather better IQA performance than SSIM. The so called Perceptual-fidelity Aware MSE (PAMSE) can have great potentials in applications such as perceptual image coding and perceptual image restoration.
Fisher Discrimination Dictionary Learning for sparse representation

Sparse representation based classification has led to interesting image recognition results, while the dictionary used for sparse coding plays a key role in it. This paper presents a novel dictionary learning (DL) method to improve the pattern classification performance. Based on the Fisher discrimination criterion, a structured dictionary, whose dictionary atoms have correspondence to the class labels, is learned so that the reconstruction error after sparse coding can be used for pattern classification. Meanwhile, the Fisher discrimination criterion is imposed on the coding coefficients so that they have small within-class scatter but big between-class scatter. A new classification scheme associated with the proposed Fisher discrimination DL (FDDL) method is then presented by using both the discriminative information in the reconstruction error and sparse coding coefficients. The proposed FDDL is extensively evaluated on benchmark image databases in comparison with existing sparse representation and DL based classification methods.
An image denoising method based on Markov-Chain Monte Carlo sampling with alterable direction and low rank approximation

The proposed image denoising method investigates a novel similar block searching strategy based on non-local Markov-Chain Monte Carlo (MCMC) sampling with alterable direction. Firstly, observed image is decomposed with 2-D wavelet transform to obtain a series sub-band images in spatial Following, the similar matching block clusters of each sub-band image in spatial are obtained by taking the different sampling which obey different directional elliptical Gaussian distributions. The matrix of similar patches cluster is decomposed by singular value decomposition method, and the image noise is suppressed by applying the low rank structure from decomposing. The simulation results show that the proposed method outperforms the Block Method of 3-Dimension (BM3DJ and the Non-Local Means (NLM) methods in computational-complexity. The proposed method has a better performance in protecting image details compared with the NLM method, and has some advantages over the BM3D method in terms of visual quality.
Change Field: A New Change Measure for VHR Images

Due to the complexity of very high resolution (VHR) images and the inaccurate correspondence, change feature extraction is the key difficulty of VHR image change detection. In this letter, change field is proposed to represent the complex changes between VHR images. Change field measures the complex changes based on the displacements and the compensated distance. Based on change field, a novel change detection approach is proposed, where the inter-class variability is improved and the changed class and the unchanged class can be separated effectively. Experiments demonstrate the effectiveness of the proposed approach.
Solving a New Class of Variational Models for Image Decomposition via Projection

In this paper, we propose a new class of variational models for image decomposition into structure and texture or noise, which is based on Besov spaces. They can be seen as generalizations of Daubechies-Teschke's work. And we, inspired by Lorenz, give proof for the general characterization of the solution of these models based on the orthogonal projections onto the convex set, as well as some material examples of the proposed models. Finally, we present numerical examples on denoising and decompositions of images
Subspace clustering by weighted correlation adaptive regression

Subspace clustering aims to reveal the latent subspace structure underlying high dimensional data by segmenting the data into corresponding subspaces. It has found wide applications in machine learning and computer vision. Most recent works on subspace segmentation focus on subspace representation based methods, which constructs the affinity matrix from the subspace representation of data points. In this work, we propose an explicit data-correlation-adaptive penalty on representation coefficients. Specifically, we define a data-correlation-adaptive penalty by a weighted combination of the l1-norm and l2-norm, and formulate the subspace representation as a weighted correlation adaptive regression (WCAR) problem. It can be regarded as a method which interpolates SSC and LSR adaptively depending on the correlation among data samples. It shows good subspace selection ability for uncorrelated data as well as grouping ability for highly correlated data. Experimental results on several commonly used clustering datasets show that our method performs better than the state-of-the-art methods.
Texture preserving Perona-Malik model

The Perona-Malik (PM) model, an effective anisotropic diffusion, can preserve edges while removing the noise. However, the disadvantage of the PM model is tending to impair textures and details so that denoising is not sufficient in the whole process. For this reason, we present a novel texture preserving Perona-Malik (TPPM) models based on the local directional variance. In the TPPM model, the diffusion coefficient of the PM model is adaptively determined to be low diffusion in large variance domain and be high diffusion in low variance domain. The related parameters are studied. Comparative results on real image denoising demonstrate that our model outforms the PM model, classical total variational (TV) method, a wavelet-based method and a nonlocal means filter in signal-to-noise ratio. The proposed model is also competitive with other methods visually. Furthermore, the execution times are very fast.
Multiscale nonlocal means for image denoising

The non-local means method (NLM) is widely used in image denoising. However, the performance of this method heavily depends on the choice of smoothness parameters. In this paper, we present a novel multi-scale non-local means method (MNLM) for image denoising. By introducing the multi-scale decomposition of images, our method can avoid the difficulty of choosing the smoothness parameters. Compared with the classical NLM method, MNLM not only improves the accuracy of the measurement of similarity, but also generates better denoising results.
Variational Models for Fusion and Denoising of Multifocus Images

In this letter, variational models in pixel domain and wavelet domain are presented for fusion and denoising of noisy multifocus images. In pixel domain, the problem is formulized as minimizing a weighted energy functional, where the total variation (TV) is used as regularity constraint for noise reduction. A new family of weight functions for fusion is proposed that are based on the local average modulus of gradients and the power transform. In wavelet domain, the problem is formulized as shrinkage of the weighted wavelet coefficients of source images, where weight functions are based on the local average modulus of intra- and inter-scale wavelet coefficients and the power transform. The experiments are made to verify the effectiveness of the proposed methods.
Image Segmentation by Active Contour Model with a New Data Fidelity

Image intensity inhomogeneity and low contrast aretwo substantial challengesfor image segmentation. In this work, we propose a new active contour method forsegmenting images with inhomogeneous intensity and low contrast. To deal with the intensity inhomogeneity, we use a local image fitting term. To deal with low contrast, we use a strictly convex and differential function as the data fidelity measure. It has several advantages over the L2 norm and the L1 norm. First, it can well approximate the L1 norm, thus is robust to low contrast and outliers. Second, it possesses the convexity and differentiability of the L2 norm, thus the minimization problem has a global optimal solution and the problem can be easily solved by using the gradient descent method. The experimental results show that the proposed method is robust to intensity inhomogeneity, low contrast and outliers.
Unified Discriminative and Coherent Semi-Supervised Subspace Clustering

The ubiquitous large, complex, and high dimensional datasets in computer vision and machine learning generates the problem of subspace clustering, which aims to partition the data into several low dimensional subspaces. By utilizing relatively limited labeled data and sufficient unlabeled data, the semi-supervised subspace clustering is more effective, practical, and become more popular. In this paper, we present a new regularity combing the labels and the affinity to ensure the coherence of the affinity between data points from the same subspace as well as the discrimination of cluster labels for data points from different subspaces. We combine it with the manifold smoothing term of the existing methods and the Gaussian fields and harmonic functions method to give a new unified optimization framework for semi-supervised subspace clustering. Analysis shows the proposed model fully combines the affinity and the labels to guide each other so that both are discriminative between clusters and coherent within clusters. Extensive experiments show that our method outperforms the existing state-of-the-art methods, thus suggests that the property of discriminative between clusters and coherent within clusters of our method is advantageous to semi-supervised subspace clustering.
Distorted pattern fusion using wavelet transform

An effective pattern fusion method based on wavelet transform is proposed. After geometric change, corrupt pattern images are obtained from distorted pictures. Considering the special characters of the pattern or text, a novel fusion scheme is then developed to de-noise, register and fuse in order to get a lucid one for further discrimination. The scheme is based on wavelet transform. The efficiency of this new method is verified by experimental results. To our knowledge, it is the first attempt to consider the pattern registration and fusion.
Adaptive regularizer learning for low rank approximation with application to image denoising

In this paper, we propose an adaptive regularizer learning method in the framework of MAP for low rank approximation (ARLLR). We assume that the prior distribution of the singular values is Laplacian with varying scale parameters. By using a full maximize a posterior (MAP) we learn the optimal scale parameters iteratively. We indicate that ARLLR is equivalent to low rank approximation regularized by Logarithm on singular values. In theory, we prove that ARLLR (Logarithm regularization) although being non-convex can be solved in closed form, and we further prove that local minimum can be easily obtained. Finally, ARLLR is applied to image de-noising. Experimental results show that the proposed method enhances image denoising compared with state-of-the-art image denoising algorithms(especially for BM3D, SAIST and WNNM) in both quantity value (PSNR) and visual quality.
Image decomposition using nonconvex functional

This paper proposes a new model for image decomposition by nonconvex functional minimization. Instead of using the Banach norm as the fidelity term, we use the integral of the square of residual component divided by its gradient as the fidelity term. This nonconvex fidelity term has very low value for the texture image and high value for the geometric image, so it is appropriate for image decomposition. The gradient descent procedure is used to solve the proposed minimization problem, which leads to evolve a new nonlinear second-order partial differential equation to steady state. The experimental results demonstrate the proposed model makes visual improvements compared with the classical OSV model, which includes that the cartoon component has less texture and the texture component has less cartoon information.