An AK-BRP dictionary learning algorithm for video frame sparse representation in compressed sensing

Sparsifying transform is an important prerequisite in compressed sensing. And it is practically significant to research the fast and efficient signal sparse representation methods. In this paper, we propose an adaptive K-BRP (AK-BRP) dictionary learning algorithm. The bilateral random projection (BRP), a method of low rank approximation, is used to update the dictionary atoms. Furthermore, in the sparse coding stage, an adaptive sparsity constraint is utilized to obtain sparse representation coefficient and helps to improve the efficiency of the dictionary update stage further. Finally, for video frame sparse representation, our adaptive dictionary learning algorithm achieves better performance than K-SVD dictionary learning algorithm in terms of computation cost. And our method produces smaller reconstruction error as well.

     

Subsampled terahertz data reconstruction based on spatio-temporal dictionary learning

In this paper, the problem of terahertz pulsed imaging and reconstruction is addressed. It is assumed that an incomplete (subsampled) three dimensional THz data set has been acquired and the aim is to recover all missing samples. A sparsity-inducing approach is proposed for this purpose. First, a simple interpolation is applied to incomplete noisy data. Then, we propose a spatio-temporal dictionary learning method to obtain an appropriate sparse representation of data based on a joint sparse recovery algorithm. Then, using the sparse coefficients and the learned dictionary, the 3D data is effectively denoised by minimizing a simple cost function. We consider two types of terahertz data to evaluate the performance of the proposed approach: THz data acquired for a model sample with clear layered structures (e.g., a T-shape plastic sheet buried in a polythene pellet), and pharmaceutical tablet data (with low spatial resolution). The achieved signal-to-noise-ratio for reconstruction of T-shape data, from only 5% observation was 19 dB. Moreover, the accuracies of obtained thickness and depth measurements for pharmaceutical tablet data after reconstruction from 10% observation were 98.8%, and 99.9%, respectively. These results, along with chemical mapping analysis, presented at the end of this paper, confirm the accuracy of the proposed method.     

基于时空稀疏模型的穿戴式心电信号压缩感知方法

基于时空稀疏模型,提出一种穿戴式心电信号的压缩感知方法,利用信号的时间相关性和空间相关性,来实现心电信号的重构.同时,还提出了一种"分-合"式字典学习算法,通过利用心电信号内在的聚类结构,对训练样本进行字典学习,从而构造出符合心电信号特点的字典,并对其进行稀疏表示.从而进一步提高了心电信号的重构性能.为了验证提出的心电信号压缩感知方法的有效性,采用OSET数据库中的心电数据,将其与其他两种基准算法进行了对比.仿真实验结果表明,所提出的心电信号压缩感知方法能有效地提高心电信号重构的质量.     

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。     

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.     

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。     

改进的非负稀疏编码图像基学习算法

图像基学习是图像特征提取与表示的重要方法之一。非负稀疏编码不仅具有标准稀疏编码算法的自适应性、空间的局部性、方向性和频域的带通性,而且更能反应哺乳动物的视觉机制。本文在非负稀疏编码的基础上,利用经验模态分解技术加入了图像的结构信息,提出了结合经验模态分解的非负稀疏编码算法,保证了系数矩阵的稀疏性与所提取图像特征的结构性。学习得到的图像基不仅具有非负稀疏编码的特征,而且更好地表示出图像的结构信息。     

字典重建和空间分布关系约束下的特征选择与图像拼接

目的 针对大型图像检索领域中,复杂图像中SIFT特征描述子的冗余和高维问题,提出了一种基于字典重建和空间分布关系约束的特征选择的方法,来消除冗余特征并保留最具表现力的、保留原始空间结构性的SIFT特征描述子。方法 首先,实验发现了特征选择和字典学习方法在稀疏表示方面的内在联系,将特征选择问题转化为字典重构任务;其次,在SIFT特征选择问题中,为了保证特征空间中特征的鲁棒性,设计了新型的字典学习模型,并采用模拟退火算法进行迭代求解;最后,在字典学习的过程中,加入熵理论来约束特征的空间分布,使学习到的特征描述子能最大限度保持原始SIFT特征空间的空间拓扑关系。结果 在公开数据集Holiday大型场景图片检索数据库上,通过与国际公认的特征选择方法进行实验对比,本文提出的特征选择方法在节省内存空间和提高时间效率（30%~ 50%）的同时,还能保证所筛选的特征描述子的检索准确率比同类特征提高8%~ 14.1%;在国际通用的大型场景图片拼接数据库IPM上,验证本文方法在图像拼接应用中特征提取和特征匹配上的有效性,实验表明本文方法能节省（50% ~70%）图像拼接时间。结论 与已有的方法比较,本文的特征选择方法既不依赖训练数据集,也不丢失重要的空间结构和纹理信息,在大型图像检索、图像拼接领域和3D检索领域中,能够精简特征,提高特征匹配效率和准确率。     

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.

     

稀疏性正则化非负矩阵分解的在线学习方法

针对非负矩阵分解效率低的不足,提出一种基于在线学习的稀疏性非负矩阵分解的快速方法.通过对目标函数添加正则化项来控制分解后系数矩阵的稀疏性,将问题转化成稀疏表示的字典学习问题,利用在线字典学习算法求解目标函数,并对迭代过程的矩阵更新进行转换,采取块坐标下降法进行矩阵更新,提高算法收敛速度.实验结果表明,该方法在有效保持图像特征信息的同时,运行效率得到提高.     

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EMD距离的稀疏自编码器

KL散度在机器学习领域被广泛地用于模型损失函数之中来度量分布的距离。在稀疏自编码器中,KL散度被用作损失函数的惩罚项来度量神经元输出与稀疏参数的距离,使得神经元输出趋近稀疏参数,从而抑制神经元的激活以得到稀疏编码。在WGAN中,Wasserstein距离被用于解决GAN的梯度消失和模式塌陷问题,使得GAN的训练更加稳定。得益于Wasserstein距离在GAN中的成功应用,提出了基于EMD距离的稀疏自编码器SAE-EMD。实验结果表明,相比于使用KL散度与JS散度,使用EMD距离作为惩罚项的稀疏自编码器可以使得真实样本与重构样本之间的重构误差减小,并且随着惩罚参数的增大,编码更加稀疏。     

随钻测量用MEMS陀螺信号稀疏提取

针对随钻测量用MEMS陀螺检测信号特性,提出采用稀疏表示的方法进行信号提取.首先从检测的陀螺调制信号构成角度,分析其信号稀疏特性;然后分析检测信号特性,构造与之最相似的过完备词典;比较已有稀疏重构算法优劣性,提出一种改进的稀疏度自适应匹配追踪算法对陀螺调制信号进行稀疏提取,进而解调真实陀螺信号;最后采用提出的改进SAMP算法于新构造的过完备字典中进行陀螺信号稀疏提取实验,并与小波阈值提取法进行实验对比,实验结果表明:采用新构造的字典和改进的SAMP算法,可以有效提取MEMS陀螺真实信号,提取效果优于传统小波阈值法.     

Denoising sound signals in a bioinspired non-negative spectro-temporal domain

The representation of sound signals at the cochlea and auditory cortical level has been studied as an alternative to classical analysis methods. In this work, we put forward a recently proposed feature extraction method called approximate auditory cortical representation, based on an approximation to the statistics of discharge patterns at the primary auditory cortex. The approach here proposed estimates a non-negative sparse coding with a combined dictionary of atoms. These atoms represent the spectro-temporal receptive fields of the auditory cortical neurons, and are calculated from the auditory spectrograms of clean signal and noise. The denoising is carried out on noisy signals by the reconstruction of the signal discarding the atoms corresponding to the noise. Experiments are presented using synthetic (chirps) and real data (speech), in the presence of additive noise. For the evaluation of the new method and its variants, we used two objective measures: the perceptual evaluation of speech quality and the segmental signal-to-noise ratio. Results show that the proposed method improves the quality of the signals, mainly under severe degradation.     

Laplacian sparse dictionary learning for image classification based on sparse representation

Sparse representation is a mathematical model for data representation that has proved to be a powerful tool for solving problems in various fields such as pattern recognition, machine learning, and computer vision. As one of the building blocks of the sparse representation method, dictionary learning plays an important role in the minimization of the reconstruction error between the original signal and its sparse representation in the space of the learned dictionary. Although using training samples directly as dictionary bases can achieve good performance, the main drawback of this method is that it may result in a very large and inefficient dictionary due to noisy training instances. To obtain a smaller and more representative dictionary, in this paper, we propose an approach called Laplacian sparse dictionary (LSD) learning. Our method is based on manifold learning and double sparsity. We incorporate the Laplacian weighted graph in the sparse representation model and impose the l₁-norm sparsity on the dictionary. An LSD is a sparse overcomplete dictionary that can preserve the intrinsic structure of the data and learn a smaller dictionary for each class. The learned LSD can be easily integrated into a classification framework based on sparse representation. We compare the proposed method with other methods using three benchmark-controlled face image databases, Extended Yale B, ORL, and AR, and one uncontrolled person image dataset, i-LIDS-MA. Results show the advantages of the proposed LSD algorithm over state-of-the-art sparse representation based classification methods.     

Sparse coding for image classification base on spatial pyramid representation

Many efforts have been devoted to apply sparse coding for image classification with the aim of minimizing the reconstruction error and classification error. So far, the approaches have been proposed either separate the reconstruction and classification process which leave rooms for further optimization or form a complicated training model which cannot be resolved efficiently. In this paper, we first propose extracting the spatial pyramid representation as the image feature which forms the foundation of dictionary learning and sparse coding. Then we develop a novel sparse coding model which can learn the dictionary and classifier simultaneously in which form we can get the optimal result and can be solved efficiently by K-SVD. Experiments show that the suggested approach, in terms of classification accuracy and computation time, outperforms other well-known approaches.     

基于低秩稀疏分解与协作表示的图像分类算法

目前,大部分图像分类算法为了获取较高的性能均需要充分的训练学习过程,然而在实际应用中,往往存在训练样本不足及过拟合等问题。为了避免上述问题出现,在朴素贝叶斯最近邻分类算法的原理框架下,基于非负稀疏编码、低秩稀疏分解以及协作表示提出一种非参数学习的图像分类算法。首先,基于非负稀疏编码和最大值汇聚操作表示图像信息,并构建具有低秩性质的同类训练图像集的局部特征矩阵;其次,采用低秩稀疏分解结合别类标签信息构建两类视觉词典以充分利用同类图像的相关性和差异性;最后基于协作表示表征测试图像并进行分类决策,实验结果验证了所提算法的有效性。     

基于预测稀疏编码的快速单幅图像超分辨率重建

针对经典的基于稀疏编码的图像超分辨率算法在重建过程中运算量大、计算效率低的缺点,提出一种基于预测稀疏编码的单幅图像超分辨率重建算法。训练阶段,该算法在传统的稀疏编码误差函数基础上叠加编码预测误差项构造目标函数,并采用交替优化过程最小化该目标函数;测试阶段,仅需将输入的低分辨图像块和预先训练得到的低分辨率字典相乘就能预测出重建系数,从而避免了求解稀疏回归问题。实验结果表明,与经典的基于稀疏编码的单幅图像超分辨率算法相比,该算法能够在显著减少重建阶段运算时间的同时几乎完全保留超分辨率视觉效果。     

基于Gabor特征和支持向量引导字典学习的人脸识别

稀疏编码中的字典学习在稀疏表示的图像识别中扮演着重要的作用。由于Gabor特征对表情、光照和姿态等变化具有一定的鲁棒性,提出一种基于Gabor特征和支持向量引导字典学习（GSVGDL）的稀疏表示人脸识别算法。先提取图像的Gabor特征,然后用增广Gabor特征矩阵来构造初始字典。字典学习模型中综合了重构误差项、判别项和正则化项,判别项公式化定义为所有编码向量对平方距离的加权总和;通过字典学习同时得到字典原子与类别标签相对应的结构化字典和线性分类器。该字典学习方法能够自适应地为不同的编码向量对分配不同的权值,提高了字典的判别性能。实验结果表明该方法具有很好的识别精度和较高的识别效率。     

最优方向耦合字典学习的遥感影像超分辨率重建

针对遥感影像超分辨率重建问题,提出了一种改进联合字典学习的超分辨率重建模型。利用最优方向字典更新算法进行耦合字典对的学习,将由低分辨率字典学习得到的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。该算法通过优化,实现训练样本自动截取,通过验证实验表明：与已有的经典算法相比,提出的算法定量评价指标有明显改善,同时,在字典学习过程中所需时间远少于现有经典算法,大大提高了遥感影像重建的效率,其重建影像更加清晰,几何纹理结构更加明显,证明了该算法的高效性。