Correlation Based Online Dictionary Learning Algorithm

Dictionary learning is still a challenging problem in signal and image processing. In this paper, we propose an efficient block-structured incoherent dictionary learning algorithm for sparse representations of image signals. The constrained minimization of dictionary learning is achieved by iteratively alternating between sparse coding and dictionary update. Without relying on any prior knowledge of the group structure for the input data, we develop a two-stage clustering method that identifies the underlying block structure of the dictionary under certain restricted constraints. The two-stage clustering method mainly consists of affinity propagation and agglomerative hierarchical clustering. To meet the conditions of both the upper bound and the lower bound of the mutual coherence of dictionary atoms, we introduce a regularization term for the objective function to adjust the block coherence of the overcomplete dictionary. The experiments on synthetic data and real images demonstrate that the proposed dictionary learning algorithm has lower representation error, higher visual quality and better reconstructed results than most of the state-of-the-art methods.

Dictionary learning aims to find a dictionary that can sparsely represent the training data. Methods in the literature typically solve the problem by alternating between two stages: sparse coding and dictionary update. In this paper, we propose a novel dictionary learning algorithm using rank-one projection (ROP). The key contribution is that we cast dictionary learning as an optimization with respect to a single variable which is a set of rank one matrices. The resulting algorithm is hence single-stage. An alternating direction method of multipliers (ADMM) is derived to solve the optimization problem and a lower bound of penalty parameter is computed to guarantee a global convergence despite non-convexity of the optimization formulation. From practical point of view, ROP reduces the number of tuning parameters required in benchmark algorithms. Numerical tests demonstrate that ROP outperforms benchmark algorithms for both synthetic and real data.

To speed up the convergence rate of learning dictionary in low bit-rate video coding, this paper proposes a spatio-temporal online dictionary learning (STOL) algorithm to improve the original adaptive regularized dictionary learning with K-SVD which involves a high computational complexity and interfere with the coding efficiency. Considering the intrinsic dimensionality of the primitives in training each series of 2-D sub dictionaries is low, the 3-D low-frequency and high-frequency dictionary pair would be formed by the online dictionary learning to update the atoms for optimal sparse representation and convergence. Instead of classical first-order stochastic gradient descent on the constraint set, e.g. K-SVD, the online algorithm would exploit the structure of sparse coding in the design of an optimization procedure in terms of stochastic approximations. It depends on low memory consumption and lower computational cost without the need of explicit learning rate tuning. Through drawing a cubic from i.i.d. samples of a distribution in each inner loop and alternating classical sparse coding steps for computing the decomposition coefficient of the cubic over previous dictionary, the dictionary update problem is converted to solve the expected cost instead of the empirical cost. For dynamic training data over time, online dictionary learning behaves faster than second-order iteration batch alternatives, e.g. K-SVD. Through experiments, the super-resolution reconstruction based on STOL obviously reduces the computational complexity to 40% to 50% of the K-SVD learning-based schemes with a guaranteed accuracy.

This work presents the use of Dictionary Learning methods for a sparse representation of 4D seismic data in history matching. We consider a trade-off between the number of coefficients retained in the sparse data representation, the computational cost, and how well we can capture the main features of the 4D seismic signal. K-SVD is an iterative algorithm used in Dictionary Learning problems that alternates between the calculation of the sparse representation vector and dictionary update. For the definition of the sparse representation vector, one can constrain the problem into two distinct approaches: (1) sparsity-constrained; and (2) error-constrained. We evaluated the two methods and the influence of critical parameters of the algorithm (dictionary size, number of iterations, patch size, and training dataset size) using a synthetic reservoir model. Results showed that regardless of which of the constrained approaches we used, the dictionary learning method can capture the main features of the 4D seismic signal with a sparse representation. However, the number of nonzero coefficients is highly dependent on the approach. Besides, dictionary size, number of iterations, patch size, and training dataset size, also have a significant impact on the number of coefficients and the computational cost. Consequently, the selection of these variables is crucial as it might affect the history-matching process. In a permanent-reservoir-monitoring (big data) scenario, the use of sparse representation allows us to retain the main features of the reservoir in a reasonably sized data representation that can be directly used in a history matching method, leading to improved reservoir characterization and a better understanding of the reservoir properties. This paper gives a practical implementation of a technique already used in other areas (image denoising, processing of raw seismic data, and facies representation) applied to 4D seismic data.

This work presents a video compression method based on sparse representation and dictionary learning algorithms. The proposed scheme achieves superb rate-distortion performance and decent subjective quality, compared to modern standards, especially at low bit-rates. Different from similar works, sparse representation is employed here for both intra-frame and block matching inter-frame motion information. Dividing video frames to reference and current frames, motion vectors and motion compensation residuals of current frames are estimated in regard to reference frames. The sparse codes of reference frames and motion compensation residuals are obtained using learned dictionaries, entropy-coded, and stored or sent to the receiver along with the coded motion field. In the receiver, after decoding the sparse codes and motion vectors, the reference frames and residuals are reconstructed employing the same learned dictionary and the current frames are recovered using the reference frames and motion fields. In the proposed scheme, the Iterative Least Square Dictionary Learning Algorithm (ILS-DLA) and K-SVD dictionary building methods are employed in the DCT domain. The compression rate and quality of the method based on the two dictionary learning algorithms are compared to each other and to H.264/AVC and HEVC modern standards. The results based on PSNR and SSIM criteria show that the proposed approach presents superior performance respect to H.264/AVC and even HEVC for higher bit-rates of QCIF video format, and the K-SVD learning algorithm performs slightly better than the ILS-DLA for the purpose.

A novel dictionary learning method for sparse representation with nonconvex regularizations

Sparse and redundant representation of data assumes an ability to describe signals as linear combinations of a few atoms from a dictionary. If the model of the signal is unknown, the dictionary can be learned from a set of training signals. Like the K-SVD, many of the practical dictionary learning algorithms are composed of two main parts: sparse-coding and dictionary-update. This paper first proposes a Stagewise least angle regression (St-LARS) method for performing the sparse-coding operation. The St-LARS applies a hard-thresholding strategy into the original least angle regression (LARS) algorithm, which enables it to select many atoms at each iteration and thus results in fast solutions while still provides good results. Then, a dictionary update method named approximated singular value decomposition (ASVD) is used on the dictionary update stage. It is a quick approximation of the exact SVD computation and can reduce the complexity of it. Experiments on both synthetic data and 3-D image denoising demonstrate the advantages of the proposed algorithm over other dictionary learning methods not only in terms of better trained dictionary but also in terms of computation time.

Slip/antiblocking agents

A supervised approach to online-learn a structured sparse and discriminative representation for object tracking is presented. Label information from training data is incorporated into the dictionary learning process to construct a robust and discriminative dictionary. This is accomplished by adding an ideal-code regularization term and classification error term to the total objective function. By minimizing the total objective function, we learn the high quality dictionary and optimal linear multiclassifier jointly using iterative reweighed least squares algorithm. Combined with robust sparse coding, the learned classifier is employed directly to separate the object from background. As the tracking continues, the proposed algorithm alternates between robust sparse coding and dictionary updating. Experimental evaluations on the challenging sequences show that the proposed algorithm performs favorably against state-of-the-art methods in terms of effectiveness, accuracy, and robustness.

Dictionary learning algorithms have received widespread acceptance when it comes to data analysis and signal representation problems. However, most existing algorithms assume isotropic noise. This is a restrictive assumption as the noise across samples may be nonuniform in a number of real world application. The aim of this article is to propose a sequential dictionary learning algorithm for measurement data vectors affected by nonuniform noise. As most of the existing algorithms, the proposed method is a two stages iterative algorithm where the effect of the noise nature appears in the sparse coding and dictionary update stages. The cost function used to derive the dictionary update stage is developed based on the link between singular value decomposition and rank one matrix approximation. Results on the simulated dictionary recovery problem and an application on face recognition dataset shows that the proposed algorithm outperforms current state of the art dictionary learning methods.

In this paper we show that the computational complexity of the iterative thresholding and K-residual-means (ITKrM) algorithm for dictionary learning can be significantly reduced by using dimensionality-reduction techniques based on the Johnson–Lindenstrauss lemma. The dimensionality reduction is efficiently carried out with the fast Fourier transform. We introduce the iterative compressed-thresholding and K-means (IcTKM) algorithm for fast dictionary learning and study its convergence properties. We show that IcTKM can locally recover an incoherent, overcomplete generating dictionary of $$K$$ atoms from training signals of sparsity level $$S$$ with high probability. Fast dictionary learning is achieved by embedding the training data and the dictionary into $$m< d$$ dimensions, and recovery is shown to be locally stable with an embedding dimension which scales as low as $$m = O(S\log ^4S\log ^3 K)$$. The compression effectively shatters the data dimension bottleneck in the computational cost of ITKrM, reducing it by a factor O(m/d). Our theoretical results are complemented with numerical simulations which demonstrate that IcTKM is a powerful, low-cost algorithm for learning dictionaries from high-dimensional data sets.

Two common problems are often encountered in analysis dictionary learning (ADL) algorithms. The first one is that the original clean signals for learning the dictionary are assumed to be known, which otherwise need to be estimated from noisy measurements. This, however, renders a computationally slow optimization process and potentially unreliable estimation (if the noise level is high), as represented by the Analysis K-SVD (AK-SVD) algorithm. The other problem is the trivial solution to the dictionary, for example, the null dictionary matrix that may be given by a dictionary learning algorithm, as discussed in the learning overcomplete sparsifying transform (LOST) algorithm. Here we propose a novel optimization model and an iterative algorithm to learn the analysis dictionary, where we directly employ the observed data to compute the approximate analysis sparse representation of the original signals (leading to a fast optimization procedure) and enforce an orthogonality constraint on the optimization criterion to avoid the trivial solutions. Experiments demonstrate the competitive performance of the proposed algorithm as compared with three baselines, namely, the AK-SVD, LOST, and NAAOLA algorithms.

Incoherent dictionary learning with log-regularizer based on proximal operators

Natural stimuli are highly redundant, possessing significant spatial and temporal correlations. While sparse coding has been proposed as an efficient strategy employed by neural systems to encode sensory stimuli, the underlying mechanisms are still not well understood. Most previous approaches model the neural dynamics by the sparse representation dictionary itself and compute the representation coefficients offline. In reality, faced with the challenge of constantly changing stimuli, neurons must compute the sparse representations dynamically in an online fashion. Here, we describe a leaky linearized Bregman iteration (LLBI) algorithm which computes the time varying sparse representations using a biologically motivated network of leaky rectifying neurons. Compared to previous attempt of dynamic sparse coding, LLBI exploits the temporal correlation of stimuli and demonstrate better performance both in representation error and the smoothness of temporal evolution of sparse coefficients.

In this paper we propose a novel face hallucination algorithm to synthesize a high-resolution face image from several low-resolution input face images. As described in Liu et al. [8]'s work, face hallucination uses two models: a global parametric model which synthesizes global face shapes from eigenfaces, and a local parametric model which enhances the local high frequency details. We follow a similar process to develop a robust face hallucination algorithm. Firstly, we obtain eigenfaces from a number of low resolution face images extracted from a video sequence using a face tracking algorithm. Then we compute the difference between the interpolated low-resolution face and the mean face, and use this difference face as the query to retrieve approximate sparse eigenfaces representation. The eigenfaces are combined using the coefficients obtained from sparse representation and added into the interpolated low-resolution face. In this way, the global shape of the interpolated low resolution face can be successfully enhanced. Secondly, we improve the example-based super-resolution method [7] for local high frequency information enhancement. Our proposed algorithm uses the Approximate Nearest Neighbors (ANN) search method to find a number of nearest neighbors for a stack of queries, instead of finding the exact match for each low frequency patch as presented in [7]. Median filtering is used to remove the noise from the nearest neighbors in order to enhance the signal. Our proposed algorithm uses sparse representation and the ANN method to enhance both global face shape and local high frequency information while greatly improving the processing speed, as confirmed empirically.