Speckle Noise Reduction via Nonconvex High Total Variation Approach

We address the problem of speckle noise removal. The classical total variation is extensively used in this field to solve such problem, but this method suffers from the staircase-like artifacts and the loss of image details. In order to resolve these problems, a nonconvex total generalized variation (TGV) regularization is used to preserve both edges and details of the images. The TGV regularization which is able to remove the staircase effect has strong theoretical guarantee by means of its high order smooth feature. Our method combines the merits of both the TGV method and the nonconvex variational method and avoids their main drawbacks. Furthermore, we develop an efficient algorithm for solving the nonconvex TGV-based optimization problem. We experimentally demonstrate the excellent performance of the technique, both visually and quantitatively

Collaborative Representation based Classification for Face Recognition

By coding a query sample as a sparse linear combination of all training samples and then classifying it by evaluating which class leads to the minimal coding residual, sparse representation based classification (SRC) leads to interesting results for robust face recognition. It is widely believed that the l1- norm sparsity constraint on coding coefficients plays a key role in the success of SRC, while its use of all training samples to collaboratively represent the query sample is rather ignored. In this paper we discuss how SRC works, and show that the collaborative representation mechanism used in SRC is much more crucial to its success of face classification. The SRC is a special case of collaborative representation based classification (CRC), which has various instantiations by applying different norms to the coding residual and coding coefficient. More specifically, the l1 or l2 norm characterization of coding residual is related to the robustness of CRC to outlier facial pixels, while the l1 or l2 norm characterization of coding coefficient is related to the degree of discrimination of facial features. Extensive experiments were conducted to verify the face recognition accuracy and efficiency of CRC with different instantiations.Comment: It is a substantial revision of a previous conference paper (L. Zhang, M. Yang, et al. "Sparse Representation or Collaborative Representation: Which Helps Face Recognition?" in ICCV 2011

Image Denoising via Asymptotic Nonlocal Filtering

The nonlocal means algorithm is widely used in image denoising, but this algorithm does not work well for high-intensity noise. To overcome this shortcoming, we establish a coupled iterative nonlocal means model in this paper. Considering the computation complexity of the new model, we realize it by using multiscale wavelet transform and propose an asymptotic nonlocal filtering algorithm which can reduce the influence of noise on similarity estimation and computation complexity. Moreover, we build a new nonlocal weight function based on the structure similarity index. Simulation results indicate that the proposed approach cannot only remove the noise but also preserve the structure of image and has good visual effects, especially for highly degenerated images

Discontinuous Deformation Analysis Enriched by the Bonding Block Model

The discontinuous deformation analysis (DDA) has been extensively applied in geotechnical engineering owing to its salient merits in the modeling of discontinuities. However, this method assumes a constant stress field within every block and hence cannot provide reliable estimation for block deformations and stresses. This paper proposes a novel scheme to improve the accuracy of the DDA. In our method, advanced subdivision is introduced to represent a block as an assembly of triangular or quadrilateral elements, in which overlapped element edges are separated from each other and are glued together by bonding springs. The accuracy and the effectiveness of the proposed method are illustrated by three numerical experiments for both continuous and discontinuous problems

Accelerated Chambolle Projection Algorithms for Image Restoration

In this paper, the accelerated Chambolle projection algorithms based on Frank–Wolfe have been proposed. For solving the image restoration under the additive Gaussian noise, the Chambolle projection method (CP) is widely used. However, the projection operator has a large computational cost and complex form. By means of the Frank–Wolfe method, this projection operation can be greatly simplified. We propose two new algorithms, called Chambolle projection based on Frank–Wolfe (CP–FW) and Chambolle projection based on accelerated Frank–Wolfe (CP–AFW). They have a fast convergence rate and low computation cost. Furthermore, we extend the new algorithms to deal with the Poisson noise. The convergence of the new algorithms is discussed, and results of the experiment show their effectiveness and efficiency

Accelerated Chambolle Projection Algorithms for Image Restoration

In this paper, the accelerated Chambolle projection algorithms based on Frank–Wolfe have been proposed. For solving the image restoration under the additive Gaussian noise, the Chambolle projection method (CP) is widely used. However, the projection operator has a large computational cost and complex form. By means of the Frank–Wolfe method, this projection operation can be greatly simplified. We propose two new algorithms, called Chambolle projection based on Frank–Wolfe (CP–FW) and Chambolle projection based on accelerated Frank–Wolfe (CP–AFW). They have a fast convergence rate and low computation cost. Furthermore, we extend the new algorithms to deal with the Poisson noise. The convergence of the new algorithms is discussed, and results of the experiment show their effectiveness and efficiency

Learing Sampling and Reconstruction Using Bregman Iteration for CS-MRI

The purpose of compressed sensing magnetic resonance imaging (CS-MRI) is to reconstruct clear images using data from the Nyquist sampling space. By reducing the amount of sampling, MR imaging can be accelerated, thereby improving the efficiency of device data collection and increasing patient throughput. The two basic challenges in CS-MRI are designing sparse sampling masks and designing effective reconstruction algorithms. In order to be consistent with the analysis conclusion of CS theory, we propose a bi-level optimization model to optimize the sampling mask and the reconstruction network at the same time under the constraints of data terms. The proposed sampling sub-network is based on an additive gradient strategy. In our reconstructed subnet, we design a phase deep unfolding network based on the Bregman iterative algorithm to find the solution of constrained problems by solving a series of unconstrained problems. Experiments on two widely used MRI datasets show that our proposed model yields sub-sampling patterns and reconstruction models customized for training data, achieving state-of-the-art results in terms of quantitative metrics and visual quality

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