The deep unfolding network (DUN) provides an efficient framework for image restoration. It consists of a regularization module and a data fitting module. In existing DUN models, it is common to directly use a deep convolution neural network (DCNN) as the regularization module, and perform data fitting before regularization in each iteration/stage. In this work, we present a DUN by incorporating a new regularization module, and putting the regularization module before the data fitting module. The proposed regularization model is deducted by using the regularization by denoing (RED) and plugging in it a newly designed DCNN. For the data fitting module, we use the closed-form solution with Faster Fourier Transform (FFT). The resulted DRED-DUN model has some major advantages. First, the regularization model inherits the flexibility of learned image-adaptive and interpretability of RED. Second, the DRED-DUN model is an end-to-end trainable DUN, which learns the regularization network and other parameters jointly, thus leads to better restoration performance than the plug-and-play framework. Third, extensive experiments show that, our proposed model significantly outperforms the-state-of-the-art model-based methods and learning based methods in terms of PSNR indexes as well as the visual effects. In particular, our method has much better capability in recovering salient image components such as edges and small scale textures.

Spectral regularization is a widely used approach for low-rank matrix recovery (LRMR) by regularizing matrix singular values. Most of the existing LRMR solvers iteratively compute the singular values via applying singular value decomposition (SVD) on a dense matrix, which is computationally expensive and severely limits their applications to large-scale problems. To address this issue, we present a generalized unitarily invariant gauge (GUIG) function for LRMR. The proposed GUIG function does not act on the singular values; however, we show that it generalizes the well-known spectral functions, including the rank function, the Schatten- p quasi-norm, and logsum of singular values. The proposed GUIG regularization model can be formulated as a bilinear variational problem, which can be efficiently solved without computing SVD. Such a property makes it well suited for large-scale LRMR problems. We apply the proposed GUIG model to matrix completion and robust principal component analysis and prove the convergence of the algorithms. Experimental results demonstrate that the proposed GUIG method is not only more accurate but also much faster than the state-of-the-art algorithms, especially on large-scale problems.

We consider the problem of millimeter-wave (MMW) imaging for concealed objects using a transceiver antenna array. In practical implementations, larger array element spacing leads to aliasing in the spectrum of the received echo signals. In this paper, we propose a new imaging method by de-aliasing. Numerical simulation results show that in the case of aliasing, our proposed de-aliasing method outperforms the traditional method in both of resolution and clarity.

Sparse representation (SR) and dictionary learning (DL) have been widely used to encode the feature data and facilitate pattern classification. Existing methods generally use l0/l1norm or class-specific dictionary to enforce the class discriminative ability of the SR. The resulted class discriminative ability is limited. In this work, we propose to use the training set as the synthesis dictionary for SR of the training samples because it provides the most natural class-specific dictionary. The class information of the training set can be used to enhance an ideal discriminative property of the SR: exact block diagonal structure, meaning that each data can be represented only by data-in-class. To make the test stage easy, an analysis dictionary and a linear classifier are learnt under the supervision of the discriminative SR of the training set. Once the analysis dictionary and the classifier are learnt, the test stage is very simple and computation efficient. We call our method Discriminative Analysis Dictionary and Classifier Learning (DADCL). Extensive experiments show that our method outperforms some existing state-of-the-art methods.

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 l2-norm on the coefficients of highly correlated data points while l1-norm on that of less correlated data points. The l2-norm tends to enforce the coefficients corresponding to highly correlated data have the grouping effect, while the l1-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.

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 work, 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.

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.

In this study, the authors propose a new image representation model that fully exploits the similarity inherent in natural images. The idea is based on an observation of similar patches. For a clean image, when a cluster of similar patches are collected to form the similar patch matrix (SPM), there exists high correlation among columns/rows of the SPM. This implies that, when the column/row vectors are linearly expressed by a dictionary, their coefficients of columns/rows should have high correlation, which leads to the coefficient matrixes of column/row representation are low‐ranked. This observation inspires them to propose a novel image denoising model named bidirectional low rank representation (BiLRR) with cluster adaptive dictionary. Specifically, they use low rank penalties simultaneously on the coefficient matrixes of column and row representations to recover the correlation structure of the SPM. Meanwhile, a cluster adaptive dictionary is learned to represent each SPM so as to well preserve the fine structure of image. By applying variable splitting and penalty technique, they present an efficient alternative minimisation algorithm to solve the proposed BiLRR model. Experimental results indicate the authors’ method achieves a competitive denoising performance in comparison with state‐of‐the‐art algorithms in terms of subjective and objective qualities.

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.

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.

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.

The Chan-Vese model is very efficient in segmenting images. However, the algorithm given by Chan and Vese is sensitive to the initial level set function and the regularization parameter. It is difficult to get a right segmentation if the initial level set function and the regularization parameter are not chosen properly. In this paper, we aim to automatically and accurately segment binary images . We propose a two-stage segmentation algorithm and an adaptive parameter estimation method for the regularization parameter. Experiments on some synthetic images and real images show that the proposed algorithm is very efficient.