In this paper, we focus on online representation learning in non-stationary environments which may require continuous adaptation of model architecture. We propose a novel online dictionary-learning (sparse-coding) framework which incorporates the addition and deletion of hidden units (dictionary elements), and is inspired by the adult neurogenesis phenomenon in the dentate gyrus of the hippocampus, known to be associated with improved cognitive function and adaptation to new environments. In the online learning setting, where new input instances arrive sequentially in batches, the neuronal-birth is implemented by adding new units with random initial weights (random dictionary elements); the number of new units is determined by the current performance (representation error) of the dictionary, higher error causing an increase in the birth rate. Neuronal-death is implemented by imposing l1/l2-regularization (group sparsity) on the dictionary within the block-coordinate descent optimization at each iteration of our online alternating minimization scheme, which iterates between the code and dictionary updates. Finally, hidden unit connectivity adaptation is facilitated by introducing sparsity in dictionary elements. Our empirical evaluation on several real-life datasets (images and language) as well as on synthetic data demonstrates that the proposed approach can considerably outperform the state-of-art fixed-size (nonadaptive) online sparse coding of Mairal et al. (2009) in the presence of nonstationary data. Moreover, we identify certain properties of the data (e.g., sparse inputs with nearly non-overlapping supports) and of the model (e.g., dictionary sparsity) associated with such improvements.
Encoding time-series with Linear Dynamical Systems (LDSs) leads to rich models with applications ranging from dynamical texture recognition to video segmentation to name a few. In this paper, we propose to represent LDSs with infinite-dimensional subspaces and derive an analytic solution to obtain stable LDSs. We then devise efficient algorithms to perform sparse coding and dictionary learning on the space of infinite-dimensional subspaces. In particular, two solutions are developed to sparsely encode an LDS. In the first method, we map the subspaces into a Reproducing Kernel Hilbert Space (RKHS) and achieve our goal through kernel sparse coding. As for the second solution, we propose to embed the infinite-dimensional subspaces into the space of symmetric matrices and formulate the sparse coding accordingly in the induced space. For dictionary learning, we encode time-series by introducing a novel concept, namely the two-fold LDSs. We then make use of the two-fold LDSs to derive an analytical form for updating atoms of an LDS dictionary, i.e., each atom is an LDS itself. Compared to several baselines and state-of-the-art methods, the proposed methods yield higher accuracies in various classification tasks including video classification and tactile recognition.
The acquisition of Magnetic Resonance Imaging (MRI) is inherently slow. Inspired by recent advances in deep learning, we propose a framework for reconstructing MR images from undersampled data using a deep cascade of convolutional neural networks to accelerate the data acquisition process. We show that for Cartesian undersampling of 2D cardiac MR images, the proposed method outperforms the state-of-the-art compressed sensing approaches, such as dictionary learning-based MRI (DLMRI) reconstruction, in terms of reconstruction error, perceptual quality and reconstruction speed for both 3-fold and 6-fold undersampling. Compared to DLMRI, the error produced by the method proposed is approximately twice as small, allowing to preserve anatomical structures more faithfully. Using our method, each image can be reconstructed in 23 ms, which is fast enough to enable real-time applications.
A multi-way factor analysis model is introduced for tensor-variate data of any order. Each data item is represented as a (sparse) sum of Kruskal decompositions, a Kruskal-factor analysis (KFA). KFA is nonparametric and can infer both the tensor-rank of each dictionary atom and the number of dictionary atoms. The model is adapted for online learning, which allows dictionary learning on large data sets. After KFA is introduced, the model is extended to a deep convolutional tensor-factor analysis, supervised by a Bayesian SVM. The experiments section demonstrates the improvement of KFA over vectorized approaches (e.g., BPFA), tensor decompositions, and convolutional neural networks (CNN) in multi-way denoising, blind inpainting, and image classification. The improvement in PSNR for the inpainting results over other methods exceeds 1dB in several cases and we achieve state of the art results on Caltech101 image classification.
Recent learning-based super-resolution (SR) methods often focus on dictionary learning or network training. In this paper, we discuss in detail a new SR method based on local patch encoding (LPE) instead of traditional dictionary learning. The proposed method consists of a learning stage and a reconstructing stage. In the learning stage, image patches are classified into different classes by means of the proposed LPE, and then a projection matrix is computed for each class by utilizing a simple constraint. In the reconstructing stage, an input LR patch can be simply reconstructed by computing its LPE code and then multiplying the corresponding projection matrix. Furthermore, we discuss the relationship between the proposed method and the anchored neighborhood regression methods; we also analyze the extendibility of the proposed method. The experimental results on several image sets demonstrate the effectiveness of the LPE-based methods.
Face recognition has been widely studied due to its importance in different applications; however, most of the proposed methods fail when face images are occluded or captured under illumination and pose variations. Recently several low-rank dictionary learning methods have been proposed and achieved promising results for noisy observations. While these methods are mostly developed for single-modality scenarios, recent studies demonstrated the advantages of feature fusion from multiple inputs. We propose a multi-modal structured low-rank dictionary learning method for robust face recognition, using raw pixels of face images and their illumination invariant representation. The proposed method learns robust and discriminative representations from contaminated face images, even if there are few training samples with large intra-class variations. Extensive experiments on different datasets validate the superior performance and robustness of our method to severe illumination variations and occlusion.
A method for online tensor dictionary learning is proposed. With the assumption of separable dictionaries, tensor contraction is used to diminish a $N$-way model of $\mathcal{O}\left(L^N\right)$ into a simple matrix equation of $\mathcal{O}\left(NL^2\right)$ with a real-time capability. To avoid numerical instability due to inversion of sparse matrix, a class of stochastic gradient with memory is formulated via a least-square solution to guarantee convergence and robustness. Both gradient descent with exact line search and Newton's method are discussed and realized. Extensions onto how to deal with bad initialization and outliers are also explained in detail. Experiments on two synthetic signals confirms an impressive performance of our proposed method.
This paper introduces a method for efficiently inferring a high-dimensional distributed quantity from a few observations. The quantity of interest (QoI) is approximated in a basis (dictionary) learned from a training set. The coefficients associated with the approximation of the QoI in the basis are determined by minimizing the misfit with the observations. To obtain a probabilistic estimate of the quantity of interest, a Bayesian approach is employed. The QoI is treated as a random field endowed with a hierarchical prior distribution so that closed-form expressions can be obtained for the posterior distribution. The main contribution of the present work lies in the derivation of \emph{a representation basis consistent with the observation chain} used to infer the associated coefficients. The resulting dictionary is then tailored to be both observable by the sensors and accurate in approximating the posterior mean. An algorithm for deriving such an observable dictionary is presented. The method is illustrated with the estimation of the velocity field of an open cavity flow from a handful of wall-mounted point sensors. Comparison with standard estimation approaches relying on Principal Component Analysis and K-SVD dictionaries is provided and illustrates the superior performance of the present approach.
Traffic learning and prediction is at the heart of the evaluation of the performance of telecommunications networks and attracts a lot of attention in wired broadband networks. Now, benefiting from the big data in cellular networks, it becomes possible to make the analyses one step further into the application level. In this paper, we firstly collect a significant amount of application-level traffic data from cellular network operators. Afterwards, with the aid of the traffic "big data", we make a comprehensive study over the modeling and prediction framework of cellular network traffic. Our results solidly demonstrate that there universally exist some traffic statistical modeling characteristics, including ALPHA-stable modeled property in the temporal domain and the sparsity in the spatial domain. Meanwhile, the results also demonstrate the distinctions originated from the uniqueness of different service types of applications. Furthermore, we propose a new traffic prediction framework to encompass and explore these aforementioned characteristics and then develop a dictionary learning-based alternating direction method to solve it. Besides, we validate the prediction accuracy improvement and the robustness of the proposed framework through extensive simulation results.
Dictionary learning is a challenge topic in many image processing areas. The basic goal is to learn a sparse representation from an overcomplete basis set. Due to combining the advantages of generic multiscale representations with learning based adaptivity, multiscale dictionary representation approaches have the power in capturing structural characteristics of natural images. However, existing multiscale learning approaches still suffer from three main weaknesses: inadaptability to diverse scales of image data, sensitivity to noise and outliers, difficulty to determine optimal dictionary structure. In this paper, we present a novel multiscale dictionary learning paradigm for sparse image representations based on an improved empirical mode decomposition. This powerful data-driven analysis tool for multi-dimensional signal can fully adaptively decompose the image into multiscale oscillating components according to intrinsic modes of data self. This treatment can obtain a robust and effective sparse representation, and meanwhile generates a raw base dictionary at multiple geometric scales and spatial frequency bands. This dictionary is refined by selecting optimal oscillating atoms based on frequency clustering. In order to further enhance sparsity and generalization, a tolerance dictionary is learned using a coherence regularized model. A fast proximal scheme is developed to optimize this model. The multiscale dictionary is considered as the product of oscillating dictionary and tolerance dictionary. Experimental results demonstrate that the proposed learning approach has the superior performance in sparse image representations as compared with several competing methods. We also show the promising results in image denoising application.
The sparsity of natural signals and images in a transform domain or dictionary has been extensively exploited in several applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis dictionaries has shown promise in many applications compared to fixed or analytical dictionary models. However, dictionary learning problems are typically non-convex and NP-hard, and the usual alternating minimization approaches for these problems are often computationally expensive, with the computations dominated by the NP-hard synthesis sparse coding step. In this work, we investigate an efficient method for $\ell_{0}$ "norm"-based dictionary learning by first approximating the training data set with a sum of sparse rank-one matrices and then using a block coordinate descent approach to estimate the unknowns. The proposed block coordinate descent algorithm involves efficient closed-form solutions. In particular, the sparse coding step involves a simple form of thresholding. We provide a convergence analysis for the proposed block coordinate descent approach. Our numerical experiments show the promising performance and significant speed-ups provided by our method over the classical K-SVD scheme in sparse signal representation and image denoising.
The sparsity of signals in a transform domain or dictionary has been exploited in applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis dictionaries has shown promise compared to analytical dictionary models. However, dictionary learning problems are typically non-convex and NP-hard, and the usual alternating minimization approaches for these problems are often computationally expensive, with the computations dominated by the NP-hard synthesis sparse coding step. This paper exploits the ideas that drive algorithms such as K-SVD, and investigates in detail efficient methods for aggregate sparsity penalized dictionary learning by first approximating the data with a sum of sparse rank-one matrices (outer products) and then using a block coordinate descent approach to estimate the unknowns. The resulting block coordinate descent algorithms involve efficient closed-form solutions. Furthermore, we consider the problem of dictionary-blind image reconstruction, and propose novel and efficient algorithms for adaptive image reconstruction using block coordinate descent and sum of outer products methodologies. We provide a convergence study of the algorithms for dictionary learning and dictionary-blind image reconstruction. Our numerical experiments show the promising performance and speed-ups provided by the proposed methods over previous schemes in sparse data representation and compressed sensing-based image reconstruction.
The inherent noise in the observed (e.g., scanned) binary document image degrades the image quality and harms the compression ratio through breaking the pattern repentance and adding entropy to the document images. In this paper, we design a cost function in Bayesian framework with dictionary learning. Minimizing our cost function produces a restored image which has better quality than that of the observed noisy image, and a dictionary for representing and encoding the image. After the restoration, we use this dictionary (from the same cost function) to encode the restored image following the symbol-dictionary framework by JBIG2 standard with the lossless mode. Experimental results with a variety of document images demonstrate that our method improves the image quality compared with the observed image, and simultaneously improves the compression ratio. For the test images with synthetic noise, our method reduces the number of flipped pixels by 48.2% and improves the compression ratio by 36.36% as compared with the best encoding methods. For the test images with real noise, our method visually improves the image quality, and outperforms the cutting-edge method by 28.27% in terms of the compression ratio.
Many neuroimaging studies focus on the cortex, in order to benefit from better signal to noise ratios and reduced computational burden. Cortical data are usually projected onto a reference mesh, where subsequent analyses are carried out. Several multiscale approaches have been proposed for analyzing these surface data, such as spherical harmonics and graph wavelets. As far as we know, however, the hierarchical structure of the template icosahedral meshes used by most neuroimaging software has never been exploited for cortical data factorization. In this paper, we demonstrate how the structure of the ubiquitous icosahedral meshes can be exploited by data factorization methods such as sparse dictionary learning, and we assess the optimization speed-up offered by extrapolation methods in this context. By testing different sparsity-inducing norms, extrapolation methods, and factorization schemes, we compare the performances of eleven methods for analyzing four datasets: two structural and two functional MRI datasets obtained by processing the data publicly available for the hundred unrelated subjects of the Human Connectome Project. Our results demonstrate that, depending on the level of details requested, a speedup of several orders of magnitudes can be obtained.
Linear synthesis model based dictionary learning framework has achieved remarkable performances in image classification in the last decade. Behaved as a generative feature model, it however suffers from some intrinsic deficiencies. In this paper, we propose a novel parametric nonlinear analysis cosparse model (NACM) with which a unique feature vector will be much more efficiently extracted. Additionally, we derive a deep insight to demonstrate that NACM is capable of simultaneously learning the task adapted feature transformation and regularization to encode our preferences, domain prior knowledge and task oriented supervised information into the features. The proposed NACM is devoted to the classification task as a discriminative feature model and yield a novel discriminative nonlinear analysis operator learning framework (DNAOL). The theoretical analysis and experimental performances clearly demonstrate that DNAOL will not only achieve the better or at least competitive classification accuracies than the state-of-the-art algorithms but it can also dramatically reduce the time complexities in both training and testing phases.
The Residual Quantization (RQ) framework is revisited where the quantization distortion is being successively reduced in multi-layers. Inspired by the reverse-water-filling paradigm in rate-distortion theory, an efficient regularization on the variances of the codewords is introduced which allows to extend the RQ for very large numbers of layers and also for high dimensional data, without getting over-trained. The proposed Regularized Residual Quantization (RRQ) results in multi-layer dictionaries which are additionally sparse, thanks to the soft-thresholding nature of the regularization when applied to variance-decaying data which can arise from de-correlating transformations applied to correlated data. Furthermore, we also propose a general-purpose pre-processing for natural images which makes them suitable for such quantization. The RRQ framework is first tested on synthetic variance-decaying data to show its efficiency in quantization of high-dimensional data. Next, we use the RRQ in super-resolution of a database of facial images where it is shown that low-resolution facial images from the test set quantized with codebooks trained on high-resolution images from the training set show relevant high-frequency content when reconstructed with those codebooks.
We address the problem of defining a group sparse formulation for Principal Components Analysis (PCA) - or its equivalent formulations as Low Rank approximation or Dictionary Learning problems - which achieves a compromise between maximizing the variance explained by the components and promoting sparsity of the loadings. So we propose first a new definition of the variance explained by non necessarily orthogonal components, which is optimal in some aspect and compatible with the principal components situation. Then we use a specific regularization of this variance by the group-$\ell_{1}$ norm to define a Group Sparse Maximum Variance (GSMV) formulation of PCA. The GSMV formulation achieves our objective by construction, and has the nice property that the inner non smooth optimization problem can be solved analytically, thus reducing GSMV to the maximization of a smooth and convex function under unit norm and orthogonality constraints, which generalizes Journee et al. (2010) to group sparsity. Numerical comparison with deflation on synthetic data shows that GSMV produces steadily slightly better and more robust results for the retrieval of hidden sparse structures, and is about three times faster on these examples. Application to real data shows the interest of group sparsity for variables selection in PCA of mixed data (categorical/numerical) .
Convolutional Sparse Coding (CSC) is an increasingly popular model in the signal and image processing communities, tackling some of the limitations of traditional patch-based sparse representations. Although several works have addressed the dictionary learning problem under this model, these relied on an ADMM formulation in the Fourier domain, losing the sense of locality and the relation to the traditional patch-based sparse pursuit. A recent work suggested a novel theoretical analysis of this global model, providing guarantees that rely on a localized sparsity measure. Herein, we extend this local-global relation by showing how one can efficiently solve the convolutional sparse pursuit problem and train the filters involved, while operating locally on image patches. Our approach provides an intuitive algorithm that can leverage standard techniques from the sparse representations field. The proposed method is fast to train, simple to implement, and flexible enough that it can be easily deployed in a variety of applications. We demonstrate the proposed training scheme for image inpainting and image separation, while achieving state-of-the-art results.
This paper addresses image classification through learning a compact and discriminative dictionary efficiently. Given a structured dictionary with each atom (columns in the dictionary matrix) related to some label, we propose cross-label suppression constraint to enlarge the difference among representations for different classes. Meanwhile, we introduce group regularization to enforce representations to preserve label properties of original samples, meaning the representations for the same class are encouraged to be similar. Upon the cross-label suppression, we don't resort to frequently-used $\ell_0$-norm or $\ell_1$-norm for coding, and obtain computational efficiency without losing the discriminative power for categorization. Moreover, two simple classification schemes are also developed to take full advantage of the learnt dictionary. Extensive experiments on six data sets including face recognition, object categorization, scene classification, texture recognition and sport action categorization are conducted, and the results show that the proposed approach can outperform lots of recently presented dictionary algorithms on both recognition accuracy and computational efficiency.
Magnetic Resonance Imaging (MRI) offers high-resolution \emph{in vivo} imaging and rich functional and anatomical multimodality tissue contrast. In practice, however, there are challenges associated with considerations of scanning costs, patient comfort, and scanning time that constrain how much data can be acquired in clinical or research studies. In this paper, we explore the possibility of generating high-resolution and multimodal images from low-resolution single-modality imagery. We propose the weakly-supervised joint convolutional sparse coding to simultaneously solve the problems of super-resolution (SR) and cross-modality image synthesis. The learning process requires only a few registered multimodal image pairs as the training set. Additionally, the quality of the joint dictionary learning can be improved using a larger set of unpaired images. To combine unpaired data from different image resolutions/modalities, a hetero-domain image alignment term is proposed. Local image neighborhoods are naturally preserved by operating on the whole image domain (as opposed to image patches) and using joint convolutional sparse coding. The paired images are enhanced in the joint learning process with unpaired data and an additional maximum mean discrepancy term, which minimizes the dissimilarity between their feature distributions. Experiments show that the proposed method outperforms state-of-the-art techniques on both SR reconstruction and simultaneous SR and cross-modality synthesis.