Xiangchu Feng

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.

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.

Weighted Nuclear Norm Minimization with Application to Image Denoising

As a convex relaxation of the low rank matrix factorization problem, the nuclear norm minimization has been attracting significant research interest in recent years. The standard nuclear norm minimization regularizes each singular value equally to pursue the convexity of the objective function. However, this greatly restricts its capability and flexibility in dealing with many practical problems (e.g., denoising), where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, where the singular values are assigned different weights. The solutions of the WNNM problem are analyzed under different weighting conditions. We then apply the proposed WNNM algorithm to image denoising by exploiting the image nonlocal self-similarity. Experimental results clearly show that the proposed WNNM algorithm outperforms many state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measure and visual perception quality.

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 Based Fisher Discrimination Dictionary Learning for Image Classification

The employed dictionary plays an important role in sparse representation or sparse coding based image reconstruction and classification, while learning dictionaries from the training data has led to state-of-the-art results in image classification tasks. However, many dictionary learning models exploit only the discriminative information in either the representation coefficients or the representation residual, which limits their performance. In this paper we present a novel dictionary learning method based on the Fisher discrimination criterion. A structured dictionary, whose atoms have correspondences to the subject class labels, is learned, with which not only the representation residual can be used to distinguish different classes, but also the representation coefficients have small within-class scatter and big between-class scatter. The classification scheme associated with the proposed Fisher discrimination dictionary learning (FDDL) model is consequently presented by exploiting the discriminative information in both the representation residual and the representation coefficients. The proposed FDDL model is extensively evaluated on various image datasets, and it shows superior performance to many state-of-the-art dictionary learning methods in a variety of classification tasks.

Blind image quality assessment using joint statistics of gradient magnitude and laplacian features

Blind image quality assessment (BIQA) aims to evaluate the perceptual quality of a distorted image without information regarding its reference image. Existing BIQA models usually predict the image quality by analyzing the image statistics in some transformed domain, e.g., in the discrete cosine transform domain or wavelet domain. Though great progress has been made in recent years, BIQA is still a very challenging task due to the lack of a reference image. Considering that image local contrast features convey important structural information that is closely related to image perceptual quality, we propose a novel BIQA model that utilizes the joint statistics of two types of commonly used local contrast features: 1) the gradient magnitude (GM) map and 2) the Laplacian of Gaussian (LOG) response. We employ an adaptive procedure to jointly normalize the GM and LOG features, and show that the joint statistics of normalized GM and LOG features have desirable properties for the BIQA task. The proposed model is extensively evaluated on three large-scale benchmark databases, and shown to deliver highly competitive performance with state-of-the-art BIQA models, as well as with some well-known full reference image quality assessment models.

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.

Convolutional Sparse Coding for Image Super-Resolution

Most of the previous sparse coding (SC) based super resolution (SR) methods partition the image into overlapped patches, and process each patch separately. These methods, however, ignore the consistency of pixels in overlapped patches, which is a strong constraint for image reconstruction. In this paper, we propose a convolutional sparse coding (CSC) based SR (CSC-SR) method to address the consistency issue. Our CSC-SR involves three groups of parameters to be learned: (i) a set of filters to decompose the low resolution (LR) image into LR sparse feature maps, (ii) a mapping function to predict the high resolution (HR) feature maps from the LR ones, and (iii) a set of filters to reconstruct the HR images from the predicted HR feature maps via simple convolution operations. By working directly on the whole image, the proposed CSC-SR algorithm does not need to divide the image into overlapped patches, and can exploit the image global correlation to produce more robust reconstruction of image local structures. Experimental results clearly validate the advantages of CSC over patch based SC in SR application. Compared with state-of-the-art SR methods, the proposed CSC-SR method achieves highly competitive PSNR results, while demonstrating better edge and texture preservation performance.

Support Vector Guided Dictionary Learning

Discriminative dictionary learning aims to learn a dictionary from training samples to enhance the discriminative capability of their coding vectors. Several discrimination terms have been proposed by assessing the prediction loss (e.g., logistic regression) or class separation criterion (e.g., Fisher discrimination criterion) on the coding vectors. In this paper, we provide a new insight on discriminative dictionary learning. Specifically, we formulate the discrimination term as the weighted summation of the squared distances between all pairs of coding vectors. The discrimination term in the state-of-the-art Fisher discrimination dictionary learning (FDDL) method can be explained as a special case of our model, where the weights are simply determined by the numbers of samples of each class. We then propose a parameterization method to adaptively determine the weight of each coding vector pair, which leads to a support vector guided dictionary learning (SVGDL) model. Compared with FDDL, SVGDL can adaptively assign different weights to different pairs of coding vectors. More importantly, SVGDL automatically selects only a few critical pairs to assign non-zero weights, resulting in better generalization ability for pattern recognition tasks. The experimental results on a series of benchmark databases show that SVGDL outperforms many state-of-the-art discriminative dictionary learning methods.

Patch Group Based Nonlocal Self-Similarity Prior Learning for Image Denoising

Patch based image modeling has achieved a great success in low level vision such as image denoising. In particular, the use of image nonlocal self-similarity (NSS) prior, which refers to the fact that a local patch often has many nonlocal similar patches to it across the image, has significantly enhanced the denoising performance. However, in most existing methods only the NSS of input degraded image is exploited, while how to utilize the NSS of clean natural images is still an open problem. In this paper, we propose a patch group (PG) based NSS prior learning scheme to learn explicit NSS models from natural images for high performance denoising. PGs are extracted from training images by putting nonlocal similar patches into groups, and a PG based Gaussian Mixture Model (PG-GMM) learning algorithm is developed to learn the NSS prior. We demonstrate that, owe to the learned PG-GMM, a simple weighted sparse coding model, which has a closed-form solution, can be used to perform image denoising effectively, resulting in high PSNR measure, fast speed, and particularly the best visual quality among all competing methods.