Kernel dictionary learning based discriminant analysis

Sparse representation based classification (SRC) has been successfully applied in many applications. But how to determine appropriate features that can best work with SRC remains an open question. Dictionary learning (DL) has played an import role in the success of sparse representation, while SRC treats the entire training set as a structured dictionary. In addition, as a linear algorithm, SRC cannot handle the data with highly nonlinear distribution. Motivated by these concerns, in this paper, we propose a novel feature learning method (termed kernel dictionary learning based discriminant analysis, KDL-DA). The proposed algorithm aims at learning a projection matrix and a kernel dictionary simultaneously such that in the reduced space the sparse representation of the data can be easily obtained, and the reconstruction residual can be further reduced. Thus, KDL-DA can achieve better performances in the projected space. Extensive experimental results show that our method outperforms many state-of-the-art methods.     

局部非负稀疏编码的高光谱目标检测方法研究

基于稀疏编码的高光谱图像处理算法能够挖掘高光谱高维数据空间中潜在的数据相关性,能自然地贴近光谱信号的本质特征。本文提出基于非负稀疏编码的高光谱目标检测算法。与经典稀疏编码模型相比,非负稀疏编码对编码系数进行非负约束,一方面使得线性编码具有明确的物理解释,另一方面增强了系数的可分性与稳健性。算法首先通过双窗口设计构造局部动态字典,然后利用目标和背景在动态字典上编码的稀疏性差异进行阈值分割最后通过统计判决实现目标检测。仿真数据以及真实数据实验结果证明了算法的有效性。      

基于稀疏分解的可伸缩图像编码

 图像编码技术的新的突破可寄希望于信号表示的深刻变革.采用基于冗余原子库的快速匹配追踪算法对图像进行稀疏分解,在分析和总结原子空间位置分布规律的基础上,提出与之相适应的块划分编码方法,节约了用于表示原子参数和投影系数的比特数.实验结果表明,本文编码器在计算复杂度、编码效率和伸缩性能等方面都优于当前同类型编码器,特别是在前两方面,其优势十分明显.比如对512×512测试图像,编码率为0.5bpp时本文编码器的平均PSNR增益达1.73dB.特别地,凭借原子库的几何特性,该编码器提供了较传统方法更灵活的伸缩性,允许通过简单的参数变换来获得任意分辨率大小的重建图像.     

基于核Fisher判别字典学习的稀疏表示分类

在基于稀疏表示分类的模式识别中,字典学习(DL) 可以为稀疏表示获得更为精简的数据表示。最近的基于Fisher判别的字典学习(FDDL)可以学 习到更加判别的稀疏字典,使得稀疏表示分类具有很强的识别性能。核空间变换可以学习到 非线性结构信息,这对判别分类非常有用。为了充分利用 核空间特性以学习更加判别的稀疏字典来提升最终的识别性能,在FDDL的基础上,提出了两 种核化的稀疏表示DL方法。首先原始训练数据被投影到高维核空间,进行基于Fisher 判别的核稀 疏表示DLFDKDL;其次在稀疏系数上附加核Fisher约束,进行基于核Fisher判别的核稀疏表 示DL(KFDKDL),使得所学习的字典具有更强的判别能力。在多个公开的图像数据库上的稀疏 表示分类实验结果验证了所提出的FDKDL和KFDKDL方法的有效性。     

基于字典对齐的迁移稀疏编码图像分类

基于稀疏编码的图像分类算法,当源域和目标域间样本服从不同分布时,从源域样本中学习到的字典无法有效对目标域样本进行编码,进而严重影响算法的分类性能。为了解决此问题,提出一种基于字典对齐的迁移稀疏编码(TSC-DA)算法。一方面,通过将字典对齐机制引入稀疏编码模型训练过程中,以减少源域和目标域间样本分布差异;另一方面,采用L2正则化项代替字典约束项,将其转化为无约束优化问题,从而回避了拉格朗日对偶法复杂的求解方式。实验结果表明,TSC-DA能够有效提高目标域的图像分类精度。     

Learning to Sense Sparse Signals: Simultaneous Sensing Matrix and Sparsifying Dictionary Optimization

Sparse signal representation, analysis, and sensing have received a lot of attention in recent years from the signal processing, optimization, and learning communities. On one hand, learning overcomplete dictionaries that facilitate a sparse representation of the data as a liner combination of a few atoms from such dictionary leads to state-of-the-art results in image and video restoration and classification. On the other hand, the framework of compressed sensing (CS) has shown that sparse signals can be recovered from far less samples than those required by the classical Shannon-Nyquist Theorem. The samples used in CS correspond to linear projections obtained by a sensing projection matrix. It has been shown that, for example, a nonadaptive random sampling matrix satisfies the fundamental theoretical requirements of CS, enjoying the additional benefit of universality. On the other hand, a projection sensing matrix that is optimally designed for a certain class of signals can further improve the reconstruction accuracy or further reduce the necessary number of samples. In this paper, we introduce a framework for the joint design and optimization, from a set of training images, of the nonparametric dictionary and the sensing matrix. We show that this joint optimization outperforms both the use of random sensing matrices and those matrices that are optimized independently of the learning of the dictionary. Particular cases of the proposed framework include the optimization of the sensing matrix for a given dictionary as well as the optimization of the dictionary for a predefined sensing environment. The presentation of the framework and its efficient numerical optimization is complemented with numerous examples on classical image datasets.     

稀疏先验引导CNN学习的SAR图像目标识别方法

深度学习技术的应用给SAR图像目标识别带来了大幅度的性能提升,但其对实际应用中车辆目标局部部件的变化适应能力仍有待加强。利用数据内在先验知识,在高维语义特征中学习其内在的低维子空间结构,可以提升分类模型在车辆目标变体条件下的泛化性能。本文基于目标特征的稀疏性,提出了一种稀疏先验引导卷积神经网络（Convolution Neural Network,CNN）学习的SAR目标识别方法（CNN-TDDL）。首先,该方法利用CNN提取SAR图像目标的高维语义特征。其次,通过稀疏先验引导模块,利用特征稀疏性,对目标特征内在的低维子空间结构进行学习。分类任务驱动的字典学习层（Task-Driven Dictionary Learning,TDDL）将目标特征的低维子空间以稀疏编码的形式表示,再利用非负弹性正则网增强了稀疏编码的稳定性,使稀疏编码不仅有效地表征目标的低维子空间结构,并且能够提取更具判别性的类别特征。基于运动和静止目标获取与识别（Moving and Stationary Target Acquisition and Recognition,MSTAR）数据集以及仿真和实测配对和标记实验 （Synthetic and Measured Paired and Labeled Experiment,SAMPLE） 数据集的实验表明,相比于传统字典学习方法和典型深度学习方法,CNN-TDDL在MSTAR标准操作条件（Standard Operating Conditions, SOC）下识别精度提升0.85%~5.28%,型号识别精度提升3.97%以上,表现出更好的泛化性能。特征可视化分析表明稀疏先验引导模块显著提升了异类目标特征表示的可分性。      

基于结构化稀疏表达的高分辨率光学遥感图像的船只检测

为克服近岸船只检测中复杂港内背景干扰和基于深度学习算法的大视场光学遥感图像标注工作量大的困难,本文提出了基于小样本集的结构化稀疏表达方法来实现近岸船只检测的算法。构建由近岸船只目标,背景干扰信息和误差矩阵等三部分子字典组成的结构化稀疏表达字典,经小样本集的字典训练过程生成判别性稀疏编码。首先将多方向近岸船只目标样本与港内复杂背景信息样本经过HOG特征提取和PCA分析对原子进行初始化,然后使用K-SVD和LASSO算法对字典进行训练。在字典中引入误差矩阵对样本的类内差异进行表示,增强了稀疏编码的判别能力和系统鲁棒性。最后提出船只目标区域提取的置信度计算方法,对生成的结构化稀疏编码进行判别,提取船只目标区域,实现船只检测。通过对不同尺寸字典模型、引入误差矩阵前后的结构化稀疏表达模型进行实验,实验结果表明提出的引入误差矩阵的结构化稀疏表达方法的有效性,以及在小样本集下比现有技术方法具有更好的检测性能。      

Single-Pass K-SVD for Efficient Dictionary Learning

Sparse representation has been widely used in machine learning, signal processing and communications. K-SVD, which generalizes k-means clustering, is one of the most famous algorithms for sparse representation and dictionary learning. K-SVD is an iterative method that alternates between encoding the data sparsely by using the current dictionary and updating the dictionary based on the sparsely represented data. In this paper, we introduce a single-pass K-SVD method. In this method, the previous input data are first summarized as a condensed representation of weighted samples. Then, we developed a weighted K-SVD algorithm to learn a dictionary from the union of this representation and the newly input data. Experimental results show that our approach can approximate K-SVD’s performance well by consuming considerably less storage resource.     

$rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation

In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method—the$ K$-SVD algorithm—generalizing the$ K$-means clustering process.$ K$-SVD is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. The update of the dictionary columns is combined with an update of the sparse representations, thereby accelerating convergence. The$ K$-SVD algorithm is flexible and can work with any pursuit method (e.g., basis pursuit, FOCUSS, or matching pursuit). We analyze this algorithm and demonstrate its results both on synthetic tests and in applications on real image data.     

参数化稀疏表征在雷达探测中的应用

稀疏信号处理已经在雷达目标探测领域得到应用,并获得了优于传统方法的探测性能。然而,雷达目标探测过程中往往存在目标运动、雷达轨迹误差等未知因素,这导致预先设计的字典矩阵无法实现雷达信号的最优稀疏表征。该文将介绍字典学习的一个分支参数化稀疏表征,该方法通过构建参数化的字典矩阵,实现了对雷达探测过程中未知参数的动态学习和雷达信号的最优稀疏表征。该文还将介绍参数化稀疏表征在逆合成孔径雷达成像、合成孔径雷达自聚焦、基于微多普勒的目标识别等若干雷达探测问题中的应用。      

Object tracking using discriminative sparse appearance model

Object tracking based on sparse representation formulates tracking as searching the candidate with minimal reconstruction error in target template subspace. The key problem lies in modeling the target robustly to vary appearances. The appearance model in most sparsity-based trackers has two main problems. The first is that global structural information and local features are insufficiently combined because the appearance is modeled separately by holistic and local sparse representations. The second problem is that the discriminative information between the target and the background is not fully utilized because the background is rarely considered in modeling. In this study, we develop a robust visual tracking algorithm by modeling the target as a model for discriminative sparse appearance. A discriminative dictionary is trained from the local target patches and the background. The patches display the local features while their position distribution implies the global structure of the target. Thus, the learned dictionary can fully represent the target. The incorporation of the background into dictionary learning also enhances its discriminative capability. Upon modeling the target as a sparse coding histogram based on this learned dictionary, our tracker is embedded into a Bayesian state inference framework to locate a target. We also present a model update scheme in which the update rate is adjusted automatically. In conjunction with the update strategy, the proposed tracker can handle occlusion and alleviate drifting. Comparative results on challenging benchmark image sequences show that the tracking method performs favorably against several state-of-the-art algorithms.     

结合字典稀疏表示和非局部相似性的自适应压缩成像算法

如何以较少的观测值重构出高质量的图像是压缩成像系统的一个关键问题.本文根据图像块随机投影能量大小分布特点,提出了一种新的自适应采样方式以及针对自适应采样的有效重构算法.重构时利用了图像在字典下的稀疏表示原理和图像的非局部相似性先验知识.为实现图像的稀疏表示,文中构造了由多个方向字典和一个正交DCT字典组成的冗余字典,并用l1范数作为约束条件求解稀疏优化问题.由于充分利用了图像块的局部特性和图像的非局部特性,本文的压缩成像算法在低采样率下能重构出较高质量的图像.     

Image reconstruction with locally adaptive sparsity and nonlocal robust regularization

Sparse representation based modeling has been successfully used in many image-related inverse problems such as deblurring, super-resolution and compressive sensing. The heart of sparse representations lies on how to find a space (spanned by a dictionary of atoms) where the local image patch exhibits high sparsity and how to determine the image local sparsity. To identify the locally varying sparsity, it is necessary to locally adapt the dictionary learning process and the sparsity-regularization parameters. However, spatial adaptation alone runs into the risk of over-fitting the data because variation and invariance are two sides of the same coin. In this work, we propose two sets of complementary ideas for regularizing image reconstruction process: (1) the sparsity regularization parameters are locally estimated for each coefficient and updated along with adaptive learning of PCA-based dictionaries; (2) a nonlocal self-similarity constraint is introduced into the overall cost functional to improve the robustness of the model. An efficient alternative minimization algorithm is present to solve the proposed objective function and then an effective image reconstruction algorithm is presented. The experimental results on image deblurring, super-resolution and compressive sensing demonstrate that the proposed image reconstruct method outperforms many existing image reconstruction methods in both PSNR and visual quality assessment.     

基于自适应子空间重建的杂波抑制

针对红外图像中背景杂波抑制困难的问题,提出了一种基于自适应子空间重建的杂波抑制方法.该方法首先根据稀疏编码理论,学习得到描述红外小目标的超完备字典,接着依次提取测试图像中的图像子块,并计算其在超完备字典中的表示系数,根据背景子块和红外小目标在稀疏域中表示系数的差异性,自适应地选择字典中的原子构成子空间对图像子块进行重构,从而得到原图与重构图像之间的残差图像.实验结果表明,该方法得到的残差图像,能够有效抑制杂波,提高红外图像的信噪比.     

基于图像稀疏表示的红外小目标检测算法

基于超完备字典的图像稀疏表示是一种新的图像表示理论,利用超完备字典的冗余性可以有效地捕捉图像的各种结构特征,从而实现图像的有效表示.针对红外小目标检测问题,提出了一种基于图像稀疏表示的检测方法,该方法采用二维高斯模型生成样本图像,继而构造超完备目标字典,然后依次提取测试图像的图像子块并计算其在超完备字典中的表示系数,背...     

Context-aware joint dictionary learning for color image demosaicking

Most digital cameras are overlaid with color filter arrays (CFA) on their electronic sensors, and thus only one particular color value would be captured at every pixel location. When producing the output image, one needs to recover the full color image from such incomplete color samples, and this process is known as demosaicking. In this paper, we propose a novel context-constrained demosaicking algorithm via sparse-representation based joint dictionary learning. Given a single mosaicked image with incomplete color samples, we perform color and texture constrained image segmentation and learn a dictionary with different context categories. A joint sparse representation is employed on different image components for predicting the missing color information in the resulting high-resolution image. During the dictionary learning and sparse coding processes, we advocate a locality constraint in our algorithm, which allows us to locate most relevant image data and thus achieve improved demosaicking performance. Experimental results show that the proposed method outperforms several existing or state-of-the-art techniques in terms of both subjective and objective evaluations.     

Sparse representation for robust face recognition by dictionary decomposition

Sparse representation-based classification (SRC) method has gained great success in face recognition due to its encouraging and impressive performance. However, in SRC the data used to train or test are usually corrupted, and hence the performance is affected. This paper proposes a robust face recognition approach by means of learning a class-specific dictionary and a projection matrix. Firstly, the training data are decomposed into class-specific dictionary, non-class-specific dictionary, and sparse error matrix. Secondly, in order to correct the corrupted test data, the data are projected onto their corresponding underlying subspace, and a projection matrix between the original training data and the class-specific dictionary is learned. Then, the features of the class-specific dictionary and the corrected test data are extracted by using Eigenface method. Finally, the SRC is performed to classify. Extensive experiments conducted on publicly available data sets show that the proposed algorithm performs better than some state-of-the-art methods.     

Multi-modality medical image fusion based on separable dictionary learning and Gabor filtering

Sparse representation (SR) has been widely used in image fusion in recent years. However, source image, segmented into vectors, reduces correlation and structural information of texture with conventional SR methods, and extracting texture with the sliding window technology is more likely to cause spatial inconsistency in flat regions of multi-modality medical fusion image. To solve these problems, a novel fusion method that combines separable dictionary optimization with Gabor filter in non-subsampled contourlet transform (NSCT) domain is proposed. Firstly, source images are decomposed into high frequency (HF) and low frequency (LF) components by NSCT. Then the HF components are reconstructed sparsely by separable dictionaries with iterative updating sparse coding and dictionary training. In the process, sparse coefficients and separable dictionaries are updated by orthogonal matching pursuit (OMP) and manifold-based conjugate gradient method, respectively. Meanwhile, the Gabor energy as weighting factor is utilized to guide the LF components fusion, and this further improves the fusion degree of low-significant feature in the flat regions. Finally, the fusion components are transformed to obtain fusion image by inverse NSCT. Experimental results demonstrate the more competitive results of the proposal, leading to the state-of-art performance on both visual quality and objective assessment.     

核稀疏保持投影及生物特征识别应用

稀疏表示系数包含较强的鉴别信息,稀疏保持投影(Sparsity Preserving Projections,SPP)利用稀疏表示系数进行特征提取.本文通过核方法获取高维特征空间的核稀疏表示系数,并利用核稀疏表示系数构造邻接矩阵,提出核稀疏保持投影(Kernel Sparsity Preserving Projections,KSPP).核稀疏表示系数比稀疏表示系数包含更强的鉴别信息,因此KSPP可以比SPP提取更有效的鉴别特征.在多个数据库上的生物特征识别实验,KSPP都取得了不错的实验结果.