Learning low-rank and discriminative dictionary for image classification

Dictionary learning plays a crucial role in sparse representation based image classification. In this paper, we propose a novel approach to learn a discriminative dictionary with low-rank regularization on the dictionary. Specifically, we apply Fisher discriminant function to the coding coefficients to make the dictionary more discerning, that is, a small ratio of the within-class scatter to between-class scatter. In practice, noisy information in the training samples will undermine the discriminative ability of the dictionary. Inspired by the recent advances in low-rank matrix recovery theory, we apply low-rank regularization on the dictionary to tackle this problem. The iterative projection method (IPM) and inexact augmented Lagrange multiplier (ALM) algorithm are adopted to solve our objective function. The proposed discriminative dictionary learning with low-rank regularization (D²L²R²) approach is evaluated on four face and digit image datasets in comparison with existing representative dictionary learning and classification algorithms. The experimental results demonstrate the superiority of our approach.     

Sparse coding and dictionary learning with class-specific group sparsity

In recent years, sparse coding via dictionary learning has been widely used in many applications for exploiting sparsity patterns of data. For classification, useful sparsity patterns should have discrimination, which cannot be well achieved by standard sparse coding techniques. In this paper, we investigate structured sparse coding for obtaining discriminative class-specific group sparsity patterns in the context of classification. A structured dictionary learning approach for sparse coding is proposed by considering the \(\ell _{2,0}\) norm on each class of data. An efficient numerical algorithm with global convergence is developed for solving the related challenging \(\ell _{2,0}\) minimization problem. The learned dictionary is decomposed into class-specific dictionaries for the classification that is done according to the minimum reconstruction error among all the classes. For evaluation, the proposed method was applied to classifying both the synthetic data and real-world data. The experiments show the competitive performance of the proposed method in comparison with several existing discriminative sparse coding methods.

     

Synthesis K-SVD based analysis dictionary learning for pattern classification

In the fields of computer vision and pattern recognition, dictionary learning techniques have been widely applied. In classification tasks, synthesis dictionary learning is usually time-consuming during the classification stage because of the sparse reconstruction procedure. Analysis dictionary learning, which is another research line, is more favorable due to its flexible representative ability and low classification complexity. In this paper, we propose a novel discriminative analysis dictionary learning method to enhance classification performance. Particularly, we incorporate a linear classifier and the supervised information into the traditional analysis dictionary learning framework by adding a discrimination error term. A synthesis K-SVD based algorithm which can effectively constrain the sparsity is presented to solve the proposed model. Extensive comparison experiments on benchmark databases validate the satisfactory performance of our method.

     

Learning group-based dictionaries for discriminative image representation

Dictionary learning is a critical issue for achieving discriminative image representation in many computer vision tasks such as object detection and image classification. In this paper, a new algorithm is developed for learning discriminative group-based dictionaries, where the inter-concept (category) visual correlations are leveraged to enhance both the reconstruction quality and the discrimination power of the group-based discriminative dictionaries. A visual concept network is first constructed for determining the groups of visually similar object classes and image concepts automatically. For each group of such visually similar object classes and image concepts, a group-based dictionary is learned for achieving discriminative image representation. A structural learning approach is developed to take advantage of our group-based discriminative dictionaries for classifier training and image classification. The effectiveness and the discrimination power of our group-based discriminative dictionaries have been evaluated on multiple popular visual benchmarks.     

基于层次结构化字典学习的人脸表情识别*

针对传统稀疏表示方法构建的字典不具备判别性的问题,以K-SVD算法为基础,对判别字典的构建和分类求解进行了研究,提出一种基于层次结构化字典学习的表情识别方法。先将训练样本切割出眼眉、脸颊和嘴三部分,对分割的各部分利用K-SVD算法得到块字典向量,再用层次分析法的权重赋值方法求块字典向量的权重值,构成各类子字典。将所有的子字典进行联合,用结构化字典学习算法求解。测试样本的归类取决于求解结果重构的效果。在JAFFE和CK表情库上的实验表明,该算法在保证了字典判别性的同时,也达到了较高的识别率。     

A classification-oriented dictionary learning model: Explicitly learning the particularity and commonality across categories

Empirically, we find that despite the most exclusively discriminative features owned by one specific object category, the various classes of objects usually share some common patterns, which do not contribute to the discrimination of them. Concentrating on this observation and motivated by the success of dictionary learning (DL) framework, in this paper, we propose to explicitly learn a class-specific dictionary (called particularity) for each category that captures the most discriminative features of this category, and simultaneously learn a common pattern pool (called commonality), whose atoms are shared by all the categories and only contribute to representation of the data rather than discrimination. In this way, the particularity differentiates the categories while the commonality provides the essential reconstruction for the objects. Thus, we can simply adopt a reconstruction-based scheme for classification. By reviewing the existing DL-based classification methods, we can see that our approach simultaneously learns a classification-oriented dictionary and drives the sparse coefficients as discriminative as possible. In this way, the proposed method will achieve better classification performance. To evaluate our method, we extensively conduct experiments both on synthetic data and real-world benchmarks in comparison with the existing DL-based classification algorithms, and the experimental results demonstrate the effectiveness of our method.     

Soft-competitive learning of sparse codes and its application to image reconstruction

We propose a new algorithm for the design of overcomplete dictionaries for sparse coding, neural gas for dictionary learning (NGDL), which uses a set of solutions for the sparse coefficients in each update step of the dictionary. In order to obtain such a set of solutions, we additionally propose the bag of pursuits (BOP) method for sparse approximation. Using BOP in order to determine the coefficients of the dictionary, we show in an image encoding experiment that in case of limited training data and limited computation time the NGDL update of the dictionary performs better than the standard gradient approach that is used for instance in the Sparsenet algorithm, or other state-of-the-art methods for dictionary learning such as the method of optimal directions (MOD) or the widely used K-SVD algorithm. In an application to image reconstruction, dictionaries trained with this algorithm outperform not only overcomplete Haar-wavelets and overcomplete discrete cosine transformations, but also dictionaries obtained with widely used algorithms like K-SVD.     

基于块分类和字典优化的K-SVD图像去噪研究

基于K-奇异值分解（K-SVD）的图像去噪方法使用K-SVD算法训练得到的过完备字典对图像进行稀疏表示去噪,能够在去除噪声的同时较好地保持原始图像信息。但该方法缺少对图像结构特征的考虑;此外,K-SVD算法训练得到的字典中往往含有噪声原子,从而导致该方法在强噪声下去噪性能欠佳。针对这些局限性,提出一种新的去噪方法：基于块分类和字典优化的K-SVD去噪方法。首先通过图像块的分类训练得到与图像结构相适应的字典,能够更为稀疏地表示图像;然后通过噪声原子检测将字典原子分为噪声原子和非噪声原子,并对噪声原子进行替换,减弱噪声原子对去噪性能的影响,得到优化字典;利用优化字典对图像进行稀疏表示去噪。仿真实验表明,与非局部均值去噪、曲波去噪以及经典K-SVD去噪等算法相比,新方法能够取得更好的去噪结果。     

稀疏表示在入侵检测中的应用

提出一种基于稀疏表示的入侵检测算法。将稀疏性约束引入过完备词典学习和编码过程中,使学习得到的稀疏系数可以保持较好的重构性,同时增强判别力。利用判别式K-SVD算法优化过完备词典和线性判别函数,将提取的稀疏特征作为线性分类器的输入,实现入侵检测。实验结果表明,该算法可以获得较低的误报率和较高的检测率,分类性能较好。     

Bilinear discriminative dictionary learning for face recognition

This work presents a novel dictionary learning method based on the _l2$l_2$-norm regularization to learn a dictionary more suitable for face recognition. By optimizing the reconstruction error for each class using the dictionary atoms associated with that class, we learn a structured dictionary which is able to make the reconstruction error for each class more discriminative for classification. Moreover, to make the coding coefficients of samples coded over the learned dictionary discriminative, a discriminative term bilinear to the training samples and the coding coefficients is incorporated in our dictionary learning model. The bilinear discriminative term essentially resolves a linear regression problem for patterns concatenated by the training samples and the coding coefficients in the Reproducing Kernel Hilbert Space (RKHS). Consequently, a novel classifier based on the bilinear discriminative model is also proposed. Experimental results on the AR, CMU PIE, CAS-PEAL-R1, and the Sheffield (previously UMIST) face databases show that the proposed method is effective to expression, lighting, and pose variations in face recognition as well as gender classification, compared with the recently proposed face recognition methods and dictionary learning methods.     

基于过完备字典的体域网压缩感知心电重构

针对体域网远程监护中心对重构的心电信号（Electrocardiogram,ECG）精度要求高和体域网（Body sensor network,BSN）低功耗问题,提出基于过完备字典的体域网压缩感知心电重构方法. 该方法利用压缩感知理论,在传感节点端利用随机二进制矩阵对心电信号进行观测,观测值被传送至远程监护中心后,再利用基于K-SVD算法训练得到的过完备字典和块稀疏贝叶斯学习重构算法对心电信号进行重构. 仿真结果表明,当心电信号压缩率在70%～95%时,基于K-SVD过完备字典比基于离散余弦变换基的压缩感知心电重构信噪比高出5～22dB. 该方法具有信号重构精度高、功耗低和易于硬件实现的优点.     

鲁棒可预测判别字典学习人脸识别方法

提出一种可预测判别K-SVD网络模型(DKSVDN)并用于人脸识别问题。该模型构造了一种新颖的字典结构,包含类别标签字典和描述字典,以兼顾判别和重构性能。相应的稀疏编码向量由标签编码向量和描述编码向量组成。针对样本稀疏编码时间效率低的问题,利用预测神经网络与判别字典学习模型协同训练的方法来加速预测稀疏编码。此外,针对DKSVDN还特别引入一种拟梦境的训练方法用于提升模型在训练集多样性不足时的鲁棒性。通过在主流人脸数据集上的对比实验证明了该模型的优良性能。     

过完备字典稀疏表示下的RAMP重构算法

压缩感知理论将采样理论与压缩理论合二为一,成为最近几年来的研究热点。主要依据图像的稀疏性或是可压缩性的特点,使用K-均值奇异值分解（K-Means Singular Value Decomposition,K-SVD）算法训练获得过完备字典,使用高斯随机矩阵作为测量矩阵,最后通过正则化自适应匹配追踪算法作为压缩感知重构算法,提出了K-SVD过完备字典的正则化自适应匹配追踪算法（KSVD Regularized Adaptive Matching Pursuit,KSVD-RAMP）。通过对重构图像的峰值信噪比、重构时间、相对误差等客观评价指标以及主观视觉上对所提算法以及传统的贪婪算法做对比。实验结果表明,该算法比基于离散小波稀疏表示的RAMP算法的峰值信噪比提升了2~6 dB。因此,该算法重构出的图像不管在视觉效果上,还是在客观评价指标上都有一定的改善。     

基于双稀疏度K-SVD字典学习的遥感影像超分辨率重建

为了通过软件方式增强遥感影像的空间分辨率,提出了一种基于双稀疏度K-SVD字典学习的遥感影像超分辨率重建算法。基于稀疏表示理论,利用K-SVD字典学习算法求解低分辨率字典及其稀疏系数,将稀疏系数传递至高分辨率字典学习空间,形成高、低分辨率字典对,重建得到高分辨率遥感影像,并在字典学习和稀疏重建两个阶段设置了不同的稀疏度。实验分别采用TM5影像、资源三号影像以及USC_SIPI图像库中的遥感影像进行重建,结果表明,不论重建影像有无噪声,所提算法的峰值信噪比和结构相似指标均高于Bicubic法以及Zeyde的算法。K-SVD和双稀疏度参数的引入,不仅减少了字典学习时间,且具有高的空间分辨率提升能力。     

一种基于K-SVD的说话人识别方法

为了充分提取语音中的个人特征信息,类比矢量量化,提出了一种基于K-均值奇异值分解(K-SVD)的说话人识别方法。利用K-SVD训练得到的字典可较好地保存语音信号中的个人特征信息。利用这一特性,通过K-SVD从训练数据中提取包含说话人个人特征信息的字典,利用该字典实现说话人识别。相对于传统方法,该方法能够更好地利用语音的稀疏性保存语音中的个人特征信息并减小重构误差。实验仿真结果表明,与基于矢量量化的说话人识别方法相比,该方法在多说话人的情况下具有更好的识别率,具有更高的实用价值。     

近邻局部OMP稀疏表示图像去噪

目的 基于分类的稀疏字典去噪算法改善了字典训练阶段的效率问题,但稀疏分解阶段仍是全字典匹配,影响算法运行速度。为了解决稀疏去噪算法在稀疏分解阶段因复杂矩阵运算及字典全局搜索导致的算法效率低,以及冗余的稀疏字典因无法描述图像具体特征而影响图像去噪效果的问题,提出改进算法。方法 首先稀疏分解阶段,在原正交匹配追踪算法基础上引入字典原子聚类思想,提出局部正交匹配追踪算法,将全局搜索优化为局部搜索;为保证局部搜索仍能保持良好的匹配结果,提出近邻择优策略,计算聚类中心与信号原子的距离,从而按照某一阈值自适应地选择最优的n个子字典作为稀疏分解的匹配空间;最后将图像分解为内容簇和背景簇,对内容簇采用基于近邻的局部K奇异值分解（K-SVD）算法去噪,背景簇采用均值滤波方法去噪。结果 对USC标准数据库中大量图像进行去噪实验,本文算法去噪结果的峰值信噪比值比K-SVD算法平均提高了1.53 dB,比2维块匹配（BM3D）算法平均提高了0.72 dB,比聚类的稀疏表示去噪（CSR）算法平均提高了0.5 dB;运行时间比原算法提高了23.2%。结论 本文算法针对灰度图像去噪,在去噪效果及去噪效率方面均有改善,尤其对细节纹理较丰富的灰度图像去噪具有一定的应用价值。     

基于K-PSO稀疏表示的故障分类方法研究

针对现代复杂生产过程中不能准确识别、分类多种故障的问题,提出一种改进的稀疏表示故障分类方法。该方法依据信号的稀疏表示来判断故障所属类别。其具体实现过程首先是利用K-均值奇异值分解(K-SVD)算法构造过完备字典,使其包含原信息的主要特征,再通过粒子群(PSO)算法有效地搜索并寻找稀疏分解中产生的在过完备字典范围中的最匹配原子,最后利用以该匹配原子为基础的稀疏表示结果实现对多故障问题的分类识别。运用数值仿真验证了该算法的可行性和有效性。同时,针对柴油机燃油系统的故障分类,将该方法与基于BP神经网络和SVM的分类识别方法进行比较,实验表明该算法在故障分类上具有更好的效果。     

Gabor特征集结合判别式字典学习的稀疏表示图像识别

稀疏编码中字典的选择无论对图像重建还是模式分类都有重要影响,为此提出Gabor特征集结合判别式字典学习的稀疏表示图像识别算法.考虑到Gabor局部特征对光照、表情和姿态等变化的鲁棒性,首先提取图像对应不同方向、不同尺度的多个Gabor特征;然后将降维的增广Gabor特征矩阵作为初始特征字典,通过对该字典的学习得到字典原子对应类别标签的新结构化字典,新字典中特定类的子字典对相关的类具有好的表示能力,同时应用Fisher判别约束编码系数,使它们具有小的类内散度和大的类间散度;最后同时用具有判别性的重构误差和编码系数来进行模式分类.基于3个数据库的实验结果表明本文方法具有可行性和有效性.     

基于类标一致和局部特征约束的字典学习算法

为了提高字典学习算法的分类性能,提出基于原子的类标一致和局部特征约束的字典学习算法（LCLCDL）。利用原子和训练样本的类标设计判别稀疏矩阵,并构造类标一致模型作为判别式项,促使同类训练样本对应的编码系数尽可能地相似。利用原子和编码系数矩阵的行向量（Profiles）构造局部特征模型作为判别式项,使其继承训练样本的结构特征。实验结果表明LCLCDL算法比5个稀疏编码和字典学习算法可取得更高的分类性能。     

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.