Structured Dictionary Learning Research Articles

Single image super-resolution based on Bendlets analysis and structural dictionary learning

High-resolution biological tissue slice images provide opportunities for more precise observation and analysis of histopathological features. These images typically consist of enclosed contours, and Bendlets transform is an effective means to approximate such structures. In this study, we leverage Bendlet transform to incorporate multi-level image data, thereby establishing a multi-scale pyramid feature set. This approach aids in achieving a sparser representation of image textures and structures. We apply Bendlets transform to extract multi-frequency wavelet subband features and formulate structured dictionaries for both high and low resolutions based on these features. After creating these dictionaries, we compute sparse representation coefficients using the low-resolution dictionary and subsequently integrate them with the high-resolution dictionary to generate high-resolution subbands. Ultimately, through the process of inverse wavelet transformation, we completed the reconstruction of high-resolution images. This method not only significantly enhances the restoration of image details and clarity but also effectively preserves the overall structural characteristics of the original images.

Structured dictionary learning of rating migration matrices for credit risk modeling

Structured dictionary learning of rating migration matrices for credit risk modeling

Row-Column Overcomplete Structured Dictionary Learning for Enhanced Fault Detection and Isolation

To improve the monitoring performance of dictionary learning based methods, this article proposes a row-column overcomplete structured dictionary learning (RCOSDL) method for fault detection and isolation of industrial processes. Unlike conventional dictionary learning approaches which are overcomplete column-wise, the proposed method involves a dictionary that is overcomplete both row- and column-wise. The introduction of row-column overcomplete dictionary results in monitoring statistics that are more sensitive to incipient faults. In order to incorporate structured information, two graph Laplacian regularization terms, namely, manifold graph Laplacian and full graph Laplacian are considered. Whilst the inherent local geometric structure in the data is preserved in the sparse representation by the manifold graph Laplacian term, the correlation structure between process variables is preserved by using the full graph Laplacian term. Hence violation in the geometric or correlation structure will be promptly detected. To pinpoint faulty variables, a fault isolation method is developed by imposing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> / <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{2,1}$</tex-math></inline-formula> -norm constraint on the sparse coefficients. In addition, theoretical property involving the condition for guaranteed fault isolation is presented in Theorem 1. The contributions of this article include the introduction of monitoring statistics based on RCOSDL that are suitable for incipient faults, a new fault isolation scheme as well as theoretical analysis on the condition of guaranteed fault isolation. The better performance of the proposed method is illustrated by applications to numerical studies and practical industrial cases.

Locality-Adaptive Structured Dictionary Learning for Cross-Domain Recognition

Dictionary learning has achieved remarkable success on a wide range of machine learning-based applications. In this paper, a locality-adaptive structured dictionary learning (LASDL) algorithm for cross-domain recognition is proposed. In the LASDL, a projective structured double reconstruction strategy is developed to train class-oriented sub-dictionaries from the specific classes of cross-domain samples. The strategy benefits to make full advantage of the discriminative information of cross-domain data and bridge the distribution divergence between two different domains. Meanwhile, an adaptive geometrical structure preserving function is designed to not only preserve the local manifold structures spanned by the representation coefficient spaces of the source and target domains, but also impose a constraint that the coefficients should keep closer to their class centers, which is propitious to reduce the distribution divergence and make the representation more accurate. With the structured linear coding technique, the final cross-domain recognition can be efficiently performed by determining class-specific reconstruction error. The optimization of the proposed LASDL model can be efficiently solved by simple least square method and alternating direction method of multipliers (ADMM) algorithm. Extensive experimental results validate the superiority of the proposed algorithm in contrast to other state-of-the-art predecessors.

Structured Sparsity Optimization With Non-Convex Surrogates of l2,0-Norm: A Unified Algorithmic Framework.

In this article, we present a general optimization framework that leverages structured sparsity to achieve superior recovery results. The traditional method for solving the structured sparse objectives based on l2,0-norm is to use the l2,1-norm as a convex surrogate. However, such an approximation often yields a large performance gap. To tackle this issue, we first provide a framework that allows for a wide range of surrogate functions (including non-convex surrogates), which exhibits better performance in harnessing structured sparsity. Moreover, we develop a fixed point algorithm that solves a key underlying non-convex structured sparse recovery optimization problem to global optimality with a guaranteed super-linear convergence rate. Building on this, we consider three specific applications, i.e., outlier pursuit, supervised feature selection, and structured dictionary learning, which can benefit from the proposed structured sparsity optimization framework. In each application, how the optimization problem can be formulated and thus be relaxed under a generic surrogate function is explained in detail. We conduct extensive experiments on both synthetic and real-world data and demonstrate the effectiveness and efficiency of the proposed framework.

Auto-encoder based structured dictionary learning for visual classification

Dictionary learning and deep learning can be combined to boost the performance of classification tasks. However, existing combined methods often learn multi-level dictionaries each of which is embedded in a network layer, involve a large number of parameters (elements of many dictionaries) and thus easily result in prohibitive computational cost and even overfitting. In this paper, we present a novel deep Auto-Encoder based Structured Dictionary (AESD) learning model, where we need to learn only one dictionary which is composed of class-specific sub-dictionaries, and supervision is introduced by imposing discriminative category constraints to empower the dictionary with discrimination. The encoding layers are designed with shared parameters which are exactly dependent on the dictionary carried by the decoding layer. This characterizes the learning process by forward-propagation based optimization w.r.t the dictionary only, leading to a light-weight network training. In addition to utilizing directly the trained encoding network combined with a minimum-reconstruction-residual scheme for single image based classification, to expand the application spectrum of our method, in the testing phase, we extend the proposed prototype into a Convolutional Encoder based Block Sparse Representation (CEBSR) model to promote the latent block sparsity in the joint representation of an image set, achieving improved image set based classification. Extensive experiments verify the performance of the learned dictionary for image classification, and the superiority of our extended model over the state-of-the-art image set classification methods.

A multi-class structured dictionary learning method using discriminant atom selection

In the last decade, traditional dictionary learning methods have been successfully applied to various pattern classification tasks. Although these methods produce sparse representations of signals which are robust against distortions and missing data, such representations quite often turn out to be unsuitable if the final objective is signal classification. In order to overcome, or at least to attenuate, such a weakness, several new methods which incorporate discriminant information into sparse-inducing models have emerged in recent years. In particular, methods for discriminant dictionary learning have shown to be more accurate than the traditional ones, which are only focused on minimizing the total representation error. In this work, we present both a novel multi-class discriminant measure and an innovative dictionary learning method. For a given dictionary, this new measure, which takes into account not only when a particular atom is used for representing signals coming from a certain class and the magnitude of its corresponding representation coefficient, but also the effect that such an atom has in the total representation error, is capable of efficiently quantifying the degree of discriminability of each one of the atoms. On the other hand, the new dictionary construction method yields dictionaries which are highly suitable for multi-class classification tasks. Our method was tested with two widely used databases for handwritten digit recognition and for object recognition, and compared with three state-of-the-art classification methods. The results show that our method significantly outperforms the other three achieving good recognition rates and additionally, reducing the computational cost of the classifier.

Multi-Scale Structured Dictionary Learning for 3-D Point Cloud Attribute Compression

Existing 3-D point cloud attribute compression methods are rigid for complex signals defined in spatially irregular domain, as they solely depend on geometric information or adopt pre-defined analytic bases for transform. In this article, we propose a multi-scale structured dictionary learning algorithm for 3-D point cloud attribute compression. The proposed multi-scale dictionary leverages hierarchical sparsity within signals by adapting atoms in an arborescent structure. It supports hierarchical sparse transform for encoding voxelized point cloud attributes with progressive refinement of high-frequency details from coarser to finer scales. To represent spatial blocks with varying amounts of occupied voxels, a non-uniform binary weight matrix is incorporated in dictionary learning to characterize the dimensional irregularity of signals. To guarantee optimal approximation with improved efficiency, alternating optimizations including Alternating Direction Method of Multipliers and Gauss-Seidel iterations are adopted for the weighted mixed $\ell _{2}/\ell _{1}$ -minimization. Furthermore, we develop a lossy attribute compression framework by integrating sparse transform based prediction with dedicated quantization and entropy coding routines. Experimental results demonstrate that the proposed framework outperforms the state-of-the-art transform-based coding methods and is competitive with the most recent MPEG PCC test models in point cloud attribute compression.

Automatic scoring of apnea and hypopnea events using blood oxygen saturation signals

The obstructive sleep apnea-hypopnea (OSAH) syndrome is a common and frequently undiagnosed sleep disorder. It is characterized by repeated events of partial (hypopnea) or total (apnea) obstruction of the upper airway while sleeping. To quantify the severity of the pathology, the Apnea Hypopnea Index (AHI) is used. This index is defined as the average number of apnea and hypopnea events per hour of sleep. Discriminating between these two types of events is a very challenging task and in fact most traditional methods fail to do it. A reliable recognition of such events would not only allow for an accurate estimation of the AHI index, but it would also provide useful information regarding the severity of the pathology, which is very important for clinical purposes. In this work we use a method for structured dictionary learning, which is found to be suitable for automatically differentiating between apnea and hypopnea using as a unique input blood oxygen saturation signals. The method is tested for both classification of segments and OSAH screening on the Sleep Heart Health Study database. For OSAH screening, a receiver operating characteristic curve analysis shows an average area under the curve of 0.934 and diagnostic sensitivity and specificity of 89.10% and 86.70%, respectively. These results represent important improvements with respect to all state-of-the-art procedures which where used for comparison purposes. They also provide a solid support for our conclusion that the method can be used for screening OSAH syndrome more reliably and conveniently, using only a pulse oximeter.

Learning efficient structured dictionary for image classification

Recent years have witnessed the success of dictionary learning (DL) based approaches in the domain of pattern classification. In this paper, we present an efficient structured dictionary learning (ESDL) method which takes both the diversity and label information of training samples into account. Specifically, ESDL introduces alternative training samples into the process of dictionary learning. To increase the discriminative capability of representation coefficients for classification, an ideal regularization term is incorporated into the objective function of ESDL. Moreover, in contrast with conventional DL approaches which impose computationally expensive L1-norm constraint on the coefficient matrix, ESDL employs L2-norm regularization term. Experimental results on benchmark databases (including four face databases and one scene dataset) demonstrate that ESDL outperforms previous DL approaches. More importantly, ESDL can be applied in a wide range of pattern classification tasks.

RETRACTED: A method for remote sensing image denoising based on structured dictionary learning and cloud computing

With the emerging technology of remote sensing, a huge amount of remote sensing data is collected and stored in the remote sensin02222g platform, and the transmission and processing of data on the platform is extremely wasteful. It is essential to incorporate the speedy remote sensing processing services in an integrated cloud computing architecture. In order to improve the denoising ability of remote sensing image, a new structured dictionary-based method for multispectral image denoising based on cluster is proposed. This method incorporates both the locality of spatial and the correlation across spectrum of multispectral image. Remote sensing image is divided into different groups by clustering, and sparse representation coefficients of spatial and spectral and dictionary is obtained according to the dictionary learning algorithm. After threshold processing, the similar blocks are averaged and realized with multispectral remote sensing image denoising. The algorithm is applied to denoise the noisy remote sensing image of Maoergai area in the upper Minjiang which contain typical vegetation and soil is chosen as study area, simulation results show that higher peak-signal to noise ratio can be obtained as compared to other recent image denoising methods.

Reconstructing multi-echo magnetic resonance images via structured deep dictionary learning

Multi-echo magnetic resonance (MR) images are acquired by changing the echo times (for T2 weighted) or relaxation times (for T1 weighted) of scans. The resulting (multi-echo) images are usually used for quantitative MR imaging. Acquiring MR images is a slow process and acquiring multi scans of the same cross section for multi-echo imaging is even slower. In order to accelerate the scan, compressed sensing (CS) based techniques have been advocating partial K-space (Fourier domain) scans; the resulting images are reconstructed via structured CS algorithms. In recent times, it has been shown that instead of using off-the-shelf CS, better results can be obtained by adaptive reconstruction algorithms based on structured dictionary learning. In this work, we show that the reconstruction results can be further improved by using structured deep dictionaries. Experimental results on real datasets show that by using our proposed technique the scan-time can be cut by half compared to the state-of-the-art.

Semi‐supervised uncorrelated dictionary learning for colour face recognition

Colour images are increasingly used in the fields of computer vision, pattern recognition and machine learning, since they can provide more identifiable information than greyscale images. Thus, colour face recognition has attracted accumulating attention. Its key problem is how to remove the similarity between colour component images and take full advantage of colour difference information. Decision‐level similarity reduction between colour component images directly affects the recognition effect, but it has been found in no work. In this study, the authors propose a novel colour face recognition approach named semi‐supervised uncorrelated dictionary learning (SUDL), which realises decision‐level similarity reduction and fusion of all colour components in face images. SUDL employs the labelled and unlabelled colour face image samples into structured dictionary learning to achieve three uncorrelated discriminating dictionaries corresponding to three colour components of face images, and then uses these dictionaries and the sparse coding technique to make a classification decision. Experimental results in multiple public colour face image databases demonstrate that the dictionary decorrelation, structured dictionary learning and unlabelled samples used in the proposed approach are effective and reasonable, and the proposed approach outperforms several representative colour face recognition methods in recognition rates, despite of its poor time performance.

Structured Dictionary Learning for Image Denoising under Mixed Gaussian and Impulse Noise.

Although image denoising as a basic task of image restoration has been widely studied in the past decades, there are not many studies on mixed noise denoising. In this paper, we propose two structured dictionary learning models to recover images corrupted by mixed Gaussian and impulse noise. These two models can be merged as ℓp-norm fidelity plus ℓq-norm regularization. The fidelity term is used to fit image patches and the regularization term is employed for sparse coding. Particularly, we utilize proximal (and proximal linearized) alternating minimization methods as the main solvers to deal with these two models. We remove the Gaussian noise under the assumption that the uncorrupted image can be approximated with a linear representation under an appropriate orthogonal basis. We use different ways to remove impulse noise for these two models. The experimental results are reported to compare the existing methods and demonstrate the performance of the proposed denoising model is better than the other existing methods in terms of some quality assessment metrics.

Analysis of fast structured dictionary learning.

Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data and can outperform analytical models. In particular, alternating optimization algorithms have been popular for learning such models. In this work, we focus on alternating minimization for a specific structured unitary sparsifying operator learning problem and provide a convergence analysis. While the algorithm converges to the critical points of the problem generally, our analysis establishes under mild assumptions, the local linear convergence of the algorithm to the underlying sparsifying model of the data. Analysis and numerical simulations show that our assumptions hold for standard probabilistic data models. In practice, the algorithm is robust to initialization.

Structured dictionary learning using mixed-norms and group-sparsity constraint

Recently, sparse representation and dictionary learning have shown significant performance in machine vision. In particular, several supervised dictionary learning methods have been proposed for classification aim and increasing its accuracy. Among them, structured dictionary learning is an interesting approach which captures the discriminative properties of each class and common features among all classes in class-specific sub-dictionaries and a distinct shared sub-dictionary, respectively. It extracts the structural information that exists in samples of each class to increase the classification accuracy. Therefore, in this paper, a group-based structured dictionary learning method is proposed that captures structural information in each class and learns class-specific and shared sub-dictionaries based on mixed $$l_{2,1}$$ norm. Also, mixed $$l_{2,1}$$ norm is used for acquiring the sparse coefficients of data samples based on the learned sub-dictionaries. Then, classification is done by finding the class with (1) minimum reconstruction error or (2) maximum number of nonzero groups based on $$l_{1,0}$$ norm. The proposed method is evaluated by conducting experiments on Extended YaleB, AR and CMU-PIE face databases and the USPS handwritten digits database. The experimental results demonstrate the effectiveness of the proposed method in data representation and classification.

Surface Material Retrieval Using Weakly Paired Cross-Modal Learning

In this paper, we investigate the cross-modal material retrieval problem, which permits the user to submit a multimodal query including tactile and auditory modalities, and retrieve the image results of visual modalities. Since multiple significantly different modalities are involved in this process, we encounter more challenges compared with the existing cross-modal retrieval tasks. Our focus is to learn cross-modal representations when the modalities are significantly different and with minimal supervision. A novelty is that we establish a framework that deals with weakly paired multimodal fusion method for heterogenous tactile and auditory modalities and weakly paired cross-modal transfer for visual modality. A structured dictionary learning method with a low rank and common classifier is developed to obtain the modal-invariant representation. Finally, some cross-modal validations on publicly available data sets are performed to show the advantages of the proposed method. Note to Practitioners —Cross-modal retrieval is an important task for industrial intelligence. In this paper, we establish a framework to effectively solve the cross-modal material retrieval problem. In the developed framework, the user may submit a multimodal query including acceleration and sound about an object, and the system may return the most relevant retrieved images. Such a framework may find extensive applications in many fields, because it can be flexible to deal with a multiple-modal query and uses the minimal category label supervision without the need of strong sample pairing information between modalities. Compared with the previous material analysis systems, this paper goes beyond previously proposed surface material classification approaches as it returns an ordered list of perceptually similar surface materials for a query.

Learning Mixtures of Separable Dictionaries for Tensor Data: Analysis and Algorithms

This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing the separable dictionary learning model. Two different approaches for learning mixture of separable dictionaries are explored and sufficient conditions for local identifiability of the underlying dictionary are derived in each case. Moreover, computational algorithms are developed to solve the problem of learning mixture of separable dictionaries in both batch and online settings. Numerical experiments are used to show the usefulness of the proposed model and the efficacy of the developed algorithms.

Improved Structured Dictionary Learning via Correlation and Class Based Block Formation

In recent years, the creation of the block-structured dictionary has attracted a lot of interest. It involves a two-step process: block formation and dictionary update. Both the steps are important in producing an effective dictionary. The existing works mostly assume that the block structure is known a priori while learning the dictionary. For finding the unknown block structure of a given dictionary, the sparse agglomerative clustering (SAC) is most commonly used. It groups atoms based on their consistency in sparse coding of the data over the given dictionary. This paper explores two innovations toward improving the reconstruction, as well as the classification ability achieved with the block-structured dictionary. First, we propose a novel block structuring approach that makes use of the correlation among dictionary atoms. Unlike the SAC approach, which groups diverse atoms, in the proposed approach the blocks are formed by grouping the top most correlated atoms of the dictionary. The proposed block clustering approach is noted to yield significant reduction in redundancy. It also provides a direct control on the block size when compared with the existing SAC-based block structuring. Second, we present a novel dictionary learning rule, which includes the class-specific reconstruction error as a regularization to further enhance the classification ability of the block dictionary. The impact of the proposed innovations on the reconstruction ability has been demonstrated on synthetic data while that on the classification ability has been assessed on both speaker verification and face recognition tasks.

Discriminative Structured Dictionary Learning on Grassmann Manifolds and Its Application on Image Restoration.

Image restoration is a difficult and challenging problem in various imaging applications. However, despite of the benefits of a single overcomplete dictionary, there are still several challenges for capturing the geometric structure of image of interest. To more accurately represent the local structures of the underlying signals, we propose a new problem formulation for sparse representation with block-orthogonal constraint. There are three contributions. First, a framework for discriminative structured dictionary learning is proposed, which leads to a smooth manifold structure and quotient search spaces. Second, an alternating minimization scheme is proposed after taking both the cost function and the constraints into account. This is achieved by iteratively alternating between updating the block structure of the dictionary defined on Grassmann manifold and sparsifying the dictionary atoms automatically. Third, Riemannian conjugate gradient is considered to track local subspaces efficiently with a convergence guarantee. Extensive experiments on various datasets demonstrate that the proposed method outperforms the state-of-the-art methods on the removal of mixed Gaussian-impulse noise.