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k Block Sparse Vector Recovery via Block l1 - l2 Minimization

CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2023年第5期42卷 2897-2915页

作者： Xie, Shaohua Liang, Kaihao Sun Yat Sen Univ Sch Math 135 Xin Gang Xi Lu Guangzhou 510275 Guangdong Peoples R China Zhongkai Univ Agr & Engn Dept Math 501 Zhongkai Rd Guangzhou 510225 Guangdong Peoples R China

In this paper, k block sparse vectors are studied, and the block l(1) - l(2) model is adopted. It is proved theoretically that when the block sparsity satisfies some conditions, the k block sparse vector can be accurately recovered by the noise free block l(1) - l(2) model, and it can also be stably recovered by the noisy block l(1) - l(2) model. In the algorithm, we use the convex difference algorithm, and prove that the aggregation points of the sequence generated by the algorithm converge to the stable point of the objective function. We prove that when the parameter lambda > 0 is less than a certain number lambda(k), the aggregation points of the sequence generated by the algorithm are block sparse. Finally, we conduct data experiments. The experiments show that when the vector is block sparse, the block l(1) - l(2) model can recover the unknown vector better than the traditional l(1) - l(2) model.

关键词： Compressed sensing k block sparse vector Block l(1) - l(2) minimization dca algorithm ADMM algorithm

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Learning pairwise SVM on hierarchical deep features for ear recognition

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IET BIOMETRICS 2018年第6期7卷 557-566页

作者： Omara, Ibrahim Wu, Xiaohe Zhang, Hongzhi Du, Yong Zuo, Wangmeng Harbin Inst Technol Sch Comp Sci & Technol Harbin Heilongjiang Peoples R China Menoufia Univ Fac Sci Dept Math Shibin Al Kawm Egypt Northeast Agr Univ Dept Elect & Informat Engn Harbin Heilongjiang Peoples R China

Convolutional neural networks (CNNs)-based deep features have been demonstrated with remarkable performance in various vision tasks, such as image classification and face verification. Compared with the hand-crafted descriptors, deep features exhibit more powerful representation ability. Typically, higher layer features contain more semantic information, while lower layer features can provide more low-level description. In addition, it turns out that the fusion of different layer features will lead to superior performance. Here, we propose a novel approach for human ear identification by combining hierarchical deep features. First, hierarchical deep features are extracted from ear images using CNN pre-trained on large-scale data set. To enhance the feature representation and reduce the high dimension of deep features, the discriminant correlation analysis (dca) is adopted for fusing deep features from different layers for further improvement. Owing to the lack of ear images per person, the authors propose to transform the ear identification problem to the binary classification by composing pairwise samples and resolve it with the pairwise support vector machine (SVM). Experiments are conducted on four public databases: USTB I, USTB II, IIT Delhi I, and IIT Delhi II. The proposed method achieves promising recognition rate and exhibits decent performance compared with the state-of-the-art methods.

关键词： support vector machines feature extraction computer vision image representation ear face recognition learning (artificial intelligence) pattern classification image classification feedforward neural nets convolution hierarchical deep features ear images feature representation layer features CNN models convolutional neural networks pairwise support vector machine discriminant correlation analysis algorithm dca algorithm ear recognition learning pairwise SVM

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l ₁-l ₂ regularization of split feasibility problems

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NUMERICAL algorithmS 2018年第3期78卷 739-757页

作者： Moudafi, Abdellatif Gibali, Aviv Aix Marseille Univ CNRS LIS UMR F-13284 Marseille France Domaine Univ St Jerome Ave Escadrille Normandie Niemen F-13397 Marseille France ORT Braude Coll Dept Math IL-2161002 Karmiel Israel

Numerous problems in signal processing and imaging, statistical learning and data mining, or computer vision can be formulated as optimization problems which consist in minimizing a sum of convex functions, not necessarily differentiable, possibly composed with linear operators and that in turn can be transformed to split feasibility problems (SFP);see for example Censor and Elfving (Numer. algorithms 8, 221-239 1994). Each function is typically either a data fidelity term or a regularization term enforcing some properties on the solution;see for example Chaux et al. (SIAM J. Imag. Sci. 2, 730-762 2009) and references therein. In this paper, we are interested in split feasibility problems which can be seen as a general form of Q-Lasso introduced in Alghamdi et al. (2013) that extended the well-known Lasso of Tibshirani (J. R. Stat. Soc. Ser. B 58, 267-288 1996). Q is a closed convex subset of a Euclidean m-space, for some integer m >= 1, that can be interpreted as the set of errors within given tolerance level when linear measurements are taken to recover a signal/image via the Lasso. Inspired by recent works by Lou and Yan (2016), Xu (IEEE Trans. Neural Netw. Learn. Syst. 23, 1013-1027 2012), we are interested in a nonconvex regularization of SFP and propose three split algorithms for solving this general case. The first one is based on the DC (difference of convex) algorithm (dca) introduced by Pham Dinh Tao, the second one is nothing else than the celebrate forward-backward algorithm, and the third one uses a method introduced by Mine and Fukushima. It is worth mentioning that the SFP model a number of applied problems arising from signal/image processing and specially optimization problems for intensity-modulated radiation therapy (IMRT) treatment planning;see for example Censor et al. (Phys. Med. Biol. 51, 2353-2365, 2006).

关键词： Q-Lasso Split feasibility Soft-thresholding Regularization dca algorithm Forward-backward iterations Mine-Fukushima algorithm Douglas-Rachford algorithm

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Discriminative Local Feature Fusion for Ear Recognition Problem 2018

Discriminative Local Feature Fusion for Ear Recognition Prob...

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8th International Conference on Bioscience, Biochemistry and Bioinformatics (ICBBB)

作者： Omara, Ibrahim Li, Xiaoming Xiao, Gang Adil, Khan Zuo, Wangmeng Harbin Inst Technol Sch Comp Sci & Technol Harbin Peoples R China Menoufia Univ Fac Sci Dept Math Al Menoufia Egypt 211 Hosp PLA Harbin Peoples R China

ISBN: (纸本)9781450353410

Ear recognition problem is known as selecting whether two ear images belong to the same person or not, this consider as a challenge due to variation in lighting, background, pose, scale, and occlusion. This paper presents an improvement method for unconstrained ear recognition problem based on local feature fusion, and further analyzes the performance and efficiency of discriminative local feature fusion for aligned and non-aligned ear images. Firstly, local discriminative features such as LPQ, HOG, LBP, POEM, BSIF and Gabor features are extracted from the ear images. Then, Discriminant Correlation Analysis (dca) is exploited for fusion and reduction dimension. Finally, support vector machine (SVM) is adopted for classification. Experiments are conducted on popular ear databases, USTB I, USTB II, and IIT Delhi II. Furthermore, we report an encouraging result on a difficult and challenging ear database called annotated web ear (AWE) that is collected from the wild. The experimental results show superior of proposed approach that can achieve a high performance for non-aligned images (AWE and USTB II datasets), on the other hand, unique local features can achieve promising recognition rates for aligned images, USTB I and IIT Delhi II datasets.

关键词： Biometrics ear recognition local features features level fusion dca algorithm

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Difference of two norms-regularizations for Q-Lasso

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APPLIED COMPUTING AND INFORMATICS 2021年第1期17卷 79-89页

作者： Moudafi, Abdellatif Aix Marseille Univ LIS UMR CNRS 7020 Domaine Univ St Jerome Marseille France

The focus of this paper is in Q-Lasso introduced in Alghamdi et al. (2013) which extended the Lasso by Tibshirani (1996). The closed convex subset Q belonging in a Euclidean m-space, for m is an element of IN, is the set of errors when linear measurements are taken to recover a signal/image via the Lasso. Based on a recent work by Wang (2013), we are interested in two new penalty methods for Q-Lasso relying on two types of difference of convex functions (DC for short) programming where the DC objective functions are the difference of l1 and l sigma q norms and the difference of l(1) and l(r) norms with r>1. By means of a generalized q-term shrinkage operator upon the special structure of l(sigma q) norm, we design a proximal gradient algorithm for handling the DC l(1)-l(sigma q) model. Then, based on the majorization scheme, we develop a majorized penalty algorithm for the DC l(1)-l(r) model. The convergence results of our new algorithms are presented as well. We would like to emphasize that extensive simulation results in the case Q={b} show that these two new algorithms offer improved signal recovery performance and require reduced computational effort relative to state-of-the-art l(1) and l(p) (p is an element of(0,1)) models, see Wang (2013). We also devise two DC algorithms on the spirit of a paper where exact DC representation of the cardinality constraint is investigated and which also used the largest-q norm of l(sigma q) and presented numerical results that show the efficiency of our DC algorithm in comparison with other methods using other penalty terms in the context of quadratic programing, see Jun-ya et al. (2017).

关键词： Q-Lasso Split feasibility Soft-thresholding DC-regularization Proximal gradient algorithm Majorized penalty algorithm Shrinkage dca algorithm

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