Sparse Representation Based Fisher Discrimination Dictionary Learning for Image Classification

This dissertation describes a novel selection-based dictionary learning method with a sparse representation to tackle the object tracking problem in computer vision. The sparse representa- tion has been widely used in many applications including visual tracking, compressive sensing, image de-noising and image classification, and learning a good dictionary for the sparse rep- resentation is critical for obtaining high performance. The most popular existing dictionary learning algorithms are generalized from K-means, which compute the dictionary columns to minimize the overall target reconstruction error iteratively. For better discriminative capability to differentiate target-object (positive) from background (negative) data, a class of dictionary algorithms has been developed to learn the dictionary from both the positive and the negative data. However, these methods do not work well for visual tracking in a dynamic environment in which the background can change considerably between frames in a non-linear way. The background cannot be modeled statically with the usual linear models. In this tdissertation, I report on the development of a selection-based dictionary learning algorithm (K-Selection) that constructs the dictionary by choosing its columns from the training data. Each column is the most representative basis for the whole dataset, which also has a clear physical meaning. With locality-constraints, the subspace represented by the learned dictionary is not restricted to the training data alone, and is also less sensitive to outliers. The sparse representation based on this dictionary learning method supports a more robust tracker trained on the target-object data alone. This is because the learned dictionary has more discriminative power and can better distinguish the object from the background clutter. By extending the dictionary with encoded spatial information, I present a new tracking algorithm which is robust to dynamic appearance changes and occlusions. The performance of the proposed algorithms have been validated for several challenging visual tracking applications through a series of comparative experiments.

In this paper, we present an automated system for robust biometric recognition based upon sparse representation and dictionary learning. In sparse representation, extracted features from the training data are used to develop a dictionary. Training data of real world applications are likely to be exposed to geometric transformations, which is a big challenge for designing of discriminative dictionaries. Classification is achieved by representing the extracted features of the test data as a linear combination of entries in the dictionary. We propose joint weighted dictionary learning and classifier training (JWDL-CT) approach which simultaneously learns from a set of training samples along with weight vectors that correspond to the atoms in the learnt dictionary. The components of the weight vector associated with an atom represent the relationship between the atom and each of the classes. The weight vectors and atoms are jointly obtained during the dictionary learning. In the proposed method, a constraint is imposed on the correlation between the atoms to decrease the similarity between these atoms. The proposed dictionary learning objective function enhances the class-discrimination capabilities of individual atoms that renders the designed dictionaries especially suitable for classification of query images with very sparse representation. Experiments conducted on the West Virginia University (WVU) and the University of Notre Dame (UND) datasets for ear recognition show that the proposed method outperforms other state-of-the-art classifiers.

S184. Sparse representation and classification of neural spikes using supervised dictionary learning

A new multi-view sparse representation classification (SRC) algorithm based on joint supervised dictionary and classifier learning (MSRC-JSDC) is proposed for synthetic aperture radar (SAR) image classification. Unlike most existing sparse representation methods for SAR image classification, MSRC-JSDC learns a supervised sparse model from training samples by utilizing sample label information, rather than directly employs a predefined one. Moreover, a supervised classifier is jointly designed during dictionary learning, which can further promote the classification performance compared with unsupervised reconstruction based classifier. In the meantime, to enhance the representation capability of the sparse model, classification error is back propagated to the dictionary learning procedure to optimize dictionary atoms. In order to extract more recognition information from collected SAR images, a multi-view strategy is applied in testing stage. A new sparse constraint is introduced into multi-view sparse representation procedure so that both inner correlation and complementary information among multiple views can be extracted. This is helpful for alleviating the influence of SAR image's sensitivity on classification performance in such challenging scenarios as large depression variation and noise corruption. Extensive experiments on the moving and stationary target acquisition and recognition (MSTAR) database demonstrate that the proposed method is more robust and performs better than some state-of-the-art approaches.

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.

Projective dictionary pair learning (DPL) provides an effective solution to the image classification problem by jointly learning two dictionaries, i.e., the synthesis dictionary and the analysis dictionary, for the purpose of image representation and discrimination. However, the DPL algorithm focuses only on dictionary learning, ignores the importance of feature learning. Therefore, we propose a new deep dictionary pair learning (DDPL) network that combines feature learning and dictionary learning in an end-to-end architecture. Specifically, the DPL approach is embedded in a deep convolutional neural network (DCNN) by introducing two dictionary learning layers. In other words, the DCNN is used to learn high-quality and appropriate image features, while the DPL uses the learned deep features for dictionary learning and guides the update of the deep network. Finally, our network architecture is trained by a backpropagation algorithm that minimizes the standard deep dictionary pair learning loss function, which is simpler than the traditional alternating direction method of multipliers (ADMM) optimization algorithm. Experimental results on three SAR image classification datasets show that our approach significantly outperforms some state-of-the-art SAR classification methods in terms of classification accuracy.KeywordsSAR image classificationProjective dictionary pair learningNeural networksDeep learning

Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data-adaptive dictionaries that have promising applications in image compression and image enhancement. The most common sparse dictionary learning algorithms use the techniques of matching pursuit and K-SVD iteratively for sparse coding and dictionary learning respectively. While this technique produces good results, it requires a large number of iterations to converge to an optimal solution. In this article, we use a closed-form stabilized convex optimization technique for both sparse coding and dictionary learning. The approach results in providing the best possible dictionary and the sparsest representation resulting in minimum reconstruction error. We have used the proposed algorithm for compressed sensing of satellite images. Once the image is reconstructed from the compressively sensed samples, we use adaptive spatial and frequency domain filtering techniques to move towards exact image recovery. It is seen from the results that the proposed algorithm provides much better reconstruction results than conventional sparse dictionary techniques for a fixed number of iterations. Depending upon the number of details present in the image, the proposed algorithm is seen to reach the optimal solution with a significantly lower number of iterations. Consequently, high PSNR and low MSE is obtained using the proposed algorithm for our compressive sensing framework.

Discriminative analysis-synthesis dictionary learning for image classification

Among the numerous techniques followed to learn a linear classifier through the discriminative dictionary and sparse representations learning of signals, the techniques to learn a nonparametric Bayesian classifier jointly and discriminately with the dictionary and the corresponding sparse representations have drawn considerable attention from researchers. These techniques jointly learn two sets of sparse representations, one for the training samples over the dictionary and the other for the corresponding labels over the dictionary classifier. At the prediction stage, the representations of the test samples computed over the learned dictionary do not truly represent the corresponding labels, exposing weakness in the joint learning claim of these techniques. We mitigate this problem and strengthen the joint by learning a set of weights over the dictionary to represent the training data and further optimizing the same weights over the dictionary classifier to represent the labels of the corresponding classes of the training data. Now, at the prediction stage, the representation weights of the test samples computed over the learned dictionary also represent the labels of the corresponding classes of the test samples, resulting in the accurate reconstruction of the labels of the classes by the learned dictionary classifier. Overall, a reduction in the size of the Bayesian model’s parameters also improves training time. We analytically and nonparametrically derived the posterior conditional probabilities of the model from the overall joint probability of the model using Bayes’ theorem. We used the Gibbs sampler to solve the joint probability of the model using the derived conditional probabilities, which also supports our claim of efficient optimization of the coupled/joint dictionaries and the sparse representation parameters. We demonstrated the effectiveness of our approach through experiments on the standard datasets, i.e., the Extended YaleB and AR face databases for face recognition, Caltech-101 and Fifteen Scene Category databases for categorization, and UCF sports action database for action recognition. We compared the results with the state-of-the-art methods in the area. The classification accuracies, i.e., 93.25%, 89.27%, 94.81%, 98.10%, and 95.00%, of our approach on the datasets have increases of 0.5 to 2% on average. The overall average error margin of the confidence intervals in our approach is 0.24 compared with the second-best approach, JBDC, for which it is 0.34. The AUC–ROC scores of our approach are 0.98 and 0.992, which are better than those of others, i.e., 0.960 and 0.98, respectively. Our approach is also computationally efficient.

The sparse prior has been widely adopted to establish data models for numerous applications. In this context, most of them are based on one of three foundational paradigms: the conventional sparse representation, the convolutional sparse representation, and the multi‐layer convolutional sparse representation. When the data morphology has been adequately addressed, a sparse representation can be obtained by solving the sparse coding problem specified by the data model. This article presents a comprehensive overview of these three models and their corresponding sparse coding problems and demonstrates that they can be solved using convex and non‐convex optimization approaches. When the data morphology is not known or cannot be analyzed, it must be learned from training data, thereby formulating dictionary learning problems. This article addresses two different dictionary learning paradigms. In an unsupervised scenario, dictionary learning involves the alternating or joint resolution of sparse coding and dictionary updating. Another option is to create a recurrent neural network by unrolling algorithms designed to solve sparse coding problems. These networks can then be used in a supervised learning setting to facilitate the training of dictionaries via forward‐backward optimization. This article lists numerous applications in various domains and outlines several directions for future research related to the sparse prior.This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Statistical Models > Nonlinear Models

The accuracy of compressive-sensing-based image reconstruction largely depends on the performance of dictionaries used for sparse representation. Dictionaries are frequently obtained through dictionary learning (DL) process by using a set of training samples. However, conventional DL methods are limited by two factors. First, the sparse level for each training sample is fixed, which may lead under-fitting or over-fitting of sparse representation of a sample. Second, only the features of original samples are used for training dictionary. In fact, the objective samples will become different after removing the representation of one or more selected atoms during the DL process, yielding implicit features. Unfortunately, these features cannot be utilized by conventional DL methods. To overcome the two limitations, we propose a novel DL scheme named adaptive multilayered DL (AMDL) by dividing the sparse representation into several layers. The number of atoms selected for each layer is determined adaptively based on the correlation between atoms and residuals. Hence, the features of different layers are utilized and the under-fitting or over-fitting of sparse coding can be reduced. The proposed scheme can be employed to improve exiting dictionary learning methods, such as the method of direction (MOD), the k-singular value decomposition (K-SVD), and the online DL (ODL). Experimental results demonstrate that the proposed scheme could provide more accurate sparse representation for compressive-sensing-based image reconstruction, compared to the standard DL scheme.

Sparse representation matrix is of great significance for compressed sensing (CS). When dictionaries learned from training data are used instead of predefined dictionaries, signal reconstruction accuracy would be improved. In this paper, we learn dictionaries for compressed image reconstruction based on bilinear generalized approximate message passing (BiGAMP). Stochastic mapping is performed on the training data which are composed of image blocks, to conform to the statistical model of BiGAMP methodology. Square dictionary and overcomplete dictionary are learned respectively for blocked image sparse representation, and are applied to image CS reconstruction. Simulation results show that our learned dictionaries lead to improved image CS reconstruction performance in comparison to predefined dictionaries and dictionaries learned with K-SVD method.

In this paper, we present an automated system for robust biometric recognition based upon sparse representation and dictionary learning. In sparse representation, extracted features from the training data are used to develop a dictionary. Classification is achieved by representing the extracted features of the test data as a linear combination of entries in the dictionary. Dictionary learning for sparse representation has shown to improve the results in classification and recognition tasks since class labels can be used in obtaining the atoms of learnt dictionary. We propose a joint weighted dictionary learning which simultaneously learns from a set of training samples an over complete dictionary along with weight vectors that correspond to the atoms in the learnt dictionary. The components of the weight vector associated with an atom represent the relationship between the atom and each of the classes. The weight vectors and atoms are jointly obtained during the dictionary learning. In the proposed method, a constraint is imposed on the correlation between the obtained atoms that represent different classes to decrease the similarity between these atoms. In addition, we use smoothed L0 norm which is a fast algorithm to find the sparsest solution. Experiments conducted on the West Virginia University (WVU) and the University of Notre Dame (UND) datasets for ear recognition show that the proposed method outperforms other state-of-the-art classifiers.

Joint distances by sparse representation and locality-constrained dictionary learning for robust leaf recognition

Discriminative dictionary pair learning based on differentiable support vector function for visual recognition