Dictionary Sparse Representation Research Articles

Structural damage detection via adaptive dictionary learning and sparse representation of measured acceleration responses

Extracting damage-sensitive features from measured acceleration responses is still a big challenge in structural damage detection (SDD). In order to obtain the sparse representation of acceleration responses for damage identification, two dictionary learning methods and a damage indicator based on the change in mean sparsity (CMS) have been proposed in this paper. The first dictionary is empirical mode decomposition (EMD)-based dictionary generated by collecting a series of intrinsic mode functions (IMFs) while the second one is sparse coding (SC)-based dictionary learned by adaptively iterative optimization. The CMS is based on variation of a sparse features set. Numerical simulations on a simply-supported beam and on a 31-bar planar truss under different damage severities illustrate the effectiveness of the proposed methods for sparse representation and the capabilities of the defined CMS for damage indication. Comparative studies show that the SC-based dictionary outperforms the EMD-based dictionary in sparse representation. Moreover, a series of SDD experimental verifications on a simply-supported beam with a rectangular section in laboratory provide a further support to the proposed methods potentially using in-site acceleration measurements.

Group sparsity with orthogonal dictionary and nonconvex regularization for exact MRI reconstruction

Compressed sensing MRI (CS-MRI) significantly accelerates scanning time via accurate reconstruction of the image from undersampled k-space data. In this work, combining two priors of sparsity and nonlocal similarity, an algorithm of group sparsity with an orthogonal dictionary (GSOD) is proposed to realize CS-MRI reconstruction within an optimization framework. To efficiently solve the resultant non-convex optimization, a lower bound of the original problem is derived, and generalized soft-thresholding is then applied to obtain the solution from that lower bound in a fast and accurate manner. Moreover, considering the important role of the dictionary in sparse representation, a modified GSOD (M-GSOD) approach is also developed in which the orthogonal dictionary is adaptively learned from the group. It is proven that the proposed sparse coding model in the M-GSOD is equivalent to the low-rank model, and the connection between the two independent models is established for the first time. Finally, a fast and accurate algorithm to solve M-GSOD is provided. Compared with the current methods, the proposed methods demonstrate a state-of-the-art performance, which shows the correctness of the non-convex regularization and optimal dictionary learning.

Fuzzy Double C-Means Clustering Based on Sparse Self-Representation

This paper introduces the popular sparse representation method into the classical fuzzy c-means clustering algorithm, and presents a novel fuzzy clustering algorithm, called fuzzy double c-means based on sparse self-representation (FDCM_SSR). The major characteristic of FDCM_SSR is that it can simultaneously address two datasets with different dimensions, and has two kinds of corresponding cluster centers. The first one is the basic feature set that represents the basic physical property of each sample itself. The second one is learned from the basic feature set by solving a spare self-representation model, referred to as discriminant feature set, which reflects the global structure of the sample set. The spare self-representation model employs dataset itself as dictionary of sparse representation. It has good category distinguishing ability, noise robustness, and data-adaptiveness, which enhance the clustering and generalization performance of FDCM_SSR. Experiments on different datasets and images show that FDCM_SSR is more competitive than other state-of-the-art fuzzy clustering algorithms.

Nonnegative Sparse Representation of Signals With a Determinant-Type Sparsity Measure Based on the DC Programming

Nonnegative sparse representation has become highly popular in certain applications in the context of signals and corresponding dictionaries that have nonnegative limitations. Applying an adaptive dictionary for sparse representation of nonnegative signals has been shown to be very effective; but constructing adaptive dictionary, i.e., dictionary learning, remains a challenge. In this paper, we attempt to design an effective and tailored algorithm for the sparse representation of nonnegative signals. We consider the so-called determinant sparsity measure formed with the determinant of the Gram matrix of sparse coefficients. Based on the determinant measure, we formulate the nonnegative dictionary learning problem that is optimization of a non-convex function. For reducing the computational complexity of the optimization, the difference of convex functions (DC) programming is employed since the non-convex function can be set to the form of difference of two convex functions. Because there are two variables in the dictionary learning problem that cannot be solved directly by DC programming, an alternation scheme is employed to treat the sparse coding and dictionary update of the dictionary learning problem alternatively with the DC programming. Our proposed novel dictionary learning algorithm has three advantages: 1) the higher recovery ratio is achieved by the proposed algorithm, even when the signals are weakly sparse; 2) the generalization ability of the proposed algorithm is greater, more often converging to a global solution than to local optimal solutions; and 3) the obtained sparse solution has a low-overlapping property that enables the solutions to be sparse and makes the proposed algorithm robust. Numerical experiments and experiments using real-world data demonstrate the effectiveness and applicability of the proposed algorithm.

Sparse Representation Based on Tunable Q‐Factor Wavelet Transform for Whale Click and Whistle Extraction

Whale sounds may mix several elements including whistle, click, and creak in the same vocalization, which may overlap in time and frequency, so it leads to conventional signal separation techniques challenging to be applied for the signal extraction. Unlike conventional signal separation techniques which are based on the frequency bands, such as WT and EMD, tunable‐Q wavelet transform (TQWT) can separate the objected signal into particular components with different structures according to its oscillation property and eliminate in‐band noise using the basis pursuit method. Considering the characteristics of oscillatory and transient impulse, we propose a novel signal separation method for whale whistle and click extraction. The proposed method is performed by the following two steps: first, TQWT is used to construct the dictionary for sparse representation. Secondly, the whale click and whistle construction are performed by designing the basis pursuit denoising (BPD) algorithm. The proposed method has been compared with one of the popular signal decomposition techniques, i.e., the EMD method. The experimental results show that the proposed method has a better performance of click and whistle signal separation in comparison with the EMD algorithm.

Facial feature extraction based on principal component analysis and class independent kernel sparse representation

In this paper, classification algorithm of kernel sparse representation has been proposed based on robust principal component analysis by using RPCA technology to generate redundant dictionary and kernel sparse representation to structure classifier and has been used for face recognition. Firstly, each training sample matrix has been decomposed into a low rank matrix and a sparse error matrix by using RPCA technology, so as to structure base dictionary and error dictionary by using the low rank matrix and error matrix respectively and generate redundancy dictionary of sparse representation of test samples. Then, kernel regularised orthogonal matching pursuit (KROMP) algorithm has been proposed to get sparse representation coefficient which has been used to complete classification and recognition of test samples. Compared with similar algorithms, algorithm in the thesis is of a high recognition rate for face recognition and has a strong ability to adapt to noise and error interference.

Joint Estimation of Dictionary and Image from Compressive Samples

Effective compressed sensing of images relies on the prior knowledge of a well-suited dictionary for sparse representation of the target image. In the absence of such knowledge, which is a typical scenario in real-world applications, the following question arises: Would it be advantageous to take an off-the-shelf overcomplete dictionary and fine-tune the dictionary with respect to (the observed part of) the image? A primary obstacle in this approach is overfitting, i.e., the loss in model generalization to the whole image. In this paper, we establish that local dictionary optimization using the compressive samples reduces the image recovery error—relative to the off-the-shelf recovery—with an overwhelming probability that depends on the sampling matrix. We present joint estimation of dictionary and image (JEDI), an iterative algorithm for dictionary fine-tuning from compressive samples and analyze its performance for image recovery. Our algorithmic analysis is supplemented with numerical simulations under different random sampling patterns and off-the-shelf dictionary initializations.

Sparse signal subspace decomposition based on adaptive over-complete dictionary

This paper proposes a subspace decomposition method based on an over-complete dictionary in sparse representation, called “sparse signal subspace decomposition” (or 3SD) method. This method makes use of a novel criterion based on the occurrence frequency of atoms of the dictionary over the data set. This criterion, well adapted to subspace decomposition over a dependent basis set, adequately reflects the intrinsic characteristic of regularity of the signal. The 3SD method combines variance, sparsity, and component frequency criteria into a unified framework. It takes benefits from using an over-complete dictionary which preserves details and from subspace decomposition which rejects strong noise. The 3SD method is very simple with a linear retrieval operation. It does not require any prior knowledge on distributions or parameters. When applied to image denoising, it demonstrates high performances both at preserving fine details and suppressing strong noise.

FUSION OF MULTI-SCALE DEMS FROM DESCENT AND NAVCM IMAGES OF CHANG’E-3 USING COMPRESSED SENSING METHOD

Abstract. The multi-source DEMs generated using the images acquired in the descent and landing phase and after landing contain supplementary information, and this makes it possible and beneficial to produce a higher-quality DEM through fusing the multi-scale DEMs. The proposed fusion method consists of three steps. First, source DEMs are split into small DEM patches, then the DEM patches are classified into a few groups by local density peaks clustering. Next, the grouped DEM patches are used for sub-dictionary learning by stochastic coordinate coding. The trained sub-dictionaries are combined into a dictionary for sparse representation. Finally, the simultaneous orthogonal matching pursuit (SOMP) algorithm is used to achieve sparse representation. We use the real DEMs generated from Chang’e-3 descent images and navigation camera (Navcam) stereo images to validate the proposed method. Through the experiments, we have reconstructed a seamless DEM with the highest resolution and the largest spatial coverage among the input data. The experimental results demonstrated the feasibility of the proposed method.

A Perturbation-Based Approach for Compressed Sensing Radar Imaging

This letter is concerned with two-dimensional radar imaging via compressed sensing. First, a perturbation-based sparse representation dictionary is established to alleviate the basis mismatch effect, reduce the memory requirement, and accelerate the imaging process. Then, an iterative algorithm based on variational Bayesian inference is developed for sparse recovery that is user-parameter-free and suitable for imposing a priori constraint. Experimental results based on both synthetic and real data verify the performance of the proposed approach.

Low dose CT image statistical iterative reconstruction algorithms based on off-line dictionary sparse representation

Though reduced number of projection angles or lower current intensity of X-ray tube can reduce radiation dose and therefore relieve damage to human bodies, the former one will result in incomplete projection data while the later a declined signal to noise ratio of projection data. Two low-dose CT image reconstruction methods based on off-line dictionary sparse representation were proposed to solve the above problems. The offline dictionary was trained from the clear CT images which were selected from existing images, and saved for the low dose CT image reconstruction. For the limited angle scanned reconstruction, the iterative algorithm based on the trained dictionary was proposed to narrow the solution space and improve the reconstruction results. For the low X-ray tube scanned reconstruction, a statistical iterative reconstruction algorithm based on the trained dictionary was introduced to improve the performance of resisting noise. The experimental results show that both of the two approaches can precisely reconstruct CT images even when radiation dose is less than 10% of original amount.

A Novel Multi-Focus Image Fusion Method Based on Stochastic Coordinate Coding and Local Density Peaks Clustering

The multi-focus image fusion method is used in image processing to generate all-focus images that have large depth of field (DOF) based on original multi-focus images. Different approaches have been used in the spatial and transform domain to fuse multi-focus images. As one of the most popular image processing methods, dictionary-learning-based spare representation achieves great performance in multi-focus image fusion. Most of the existing dictionary-learning-based multi-focus image fusion methods directly use the whole source images for dictionary learning. However, it incurs a high error rate and high computation cost in dictionary learning process by using the whole source images. This paper proposes a novel stochastic coordinate coding-based image fusion framework integrated with local density peaks. The proposed multi-focus image fusion method consists of three steps. First, source images are split into small image patches, then the split image patches are classified into a few groups by local density peaks clustering. Next, the grouped image patches are used for sub-dictionary learning by stochastic coordinate coding. The trained sub-dictionaries are combined into a dictionary for sparse representation. Finally, the simultaneous orthogonal matching pursuit (SOMP) algorithm is used to carry out sparse representation. After the three steps, the obtained sparse coefficients are fused following the max L1-norm rule. The fused coefficients are inversely transformed to an image by using the learned dictionary. The results and analyses of comparison experiments demonstrate that fused images of the proposed method have higher qualities than existing state-of-the-art methods.

Boosted Dictionary Learning for Image Compression

Sparse representations over redundant dictionaries have shown to produce high-quality results in various signal and image processing tasks. Recent advancements in learning-based dictionary design have made image compression using data-adaptive learned dictionaries a promising field. In this paper, we present a boosted dictionary learning framework to construct an ensemble of complementary specialized dictionaries for sparse image representation. Boosted dictionaries along with a competitive sparse coding form our ensemble model which can provide us with more efficient sparse representations. The constituent dictionaries of the ensemble are obtained using a coherence regularized dictionary learning model for which two novel dictionary optimization algorithms are proposed. These algorithms improve the generalization properties of the trained dictionary compared with several incoherent dictionary learning methods. Based on the proposed ensemble model, we then develop a new image compression algorithm using boosted multi-scale dictionaries learned in the wavelet domain. Our algorithm is evaluated for the compression of natural images. Experimental results demonstrate that the proposed algorithm has better rate–distortion performance as compared with several competing compression methods, including analytic and learned dictionary schemes.

A video semantic detection method based on locality-sensitive discriminant sparse representation and weighted KNN

Video semantic detection has been one research hotspot in the field of human-computer interaction. In video features-oriented sparse representation, the features from the same category video could not achieve similar coding results. To address this, the Locality-Sensitive Discriminant Sparse Representation (LSDSR) is developed, in order that the video samples belonging to the same video category are encoded as similar sparse codes which make them have better category discrimination. In the LSDSR, a discriminative loss function based on sparse coefficients is imposed on the locality-sensitive sparse representation, which makes the optimized dictionary for sparse representation be discriminative. The LSDSR for video features enhances the power of semantic discrimination to optimize the dictionary and build the better discriminant sparse model. More so, to further improve the accuracy of video semantic detection after sparse representation, a weighted K-Nearest Neighbor (KNN) classification method with the loss function that integrates reconstruction error and discrimination for the sparse representation is adopted to detect video semantic concepts. The proposed methods are evaluated on the related video databases in comparison with existing sparse representation methods. The experimental results show that the proposed methods significantly enhance the power of discrimination of video features, and consequently improve the accuracy of video semantic concept detection.

Towards Dictionaries of Optimal Size: A Bayesian Non Parametric Approach

Solving inverse problems usually calls for adapted priors such as the definition of a well chosen representation of possible solutions. One family of approaches relies on learning redundant dictionaries for sparse representation. In image processing, dictionary learning is applied to sets of patches. Many methods work with a dictionary with a number of atoms that is fixed in advance. Moreover optimization methods often call for the prior knowledge of the noise level to tune regularization parameters. We propose a Bayesian non parametric approach that is able to learn a dictionary of adapted size. The use of an Indian Buffet Process prior permits to learn an adequate number of atoms. The noise level is also accurately estimated so that nearly no parameter tuning is needed. We illustrate the relevance of the resulting dictionaries on numerical experiments.

Automatic approach to solve the morphological galaxy classification problem using the sparse representation technique and dictionary learning

The observation of celestial objects in the sky is a practice that helps astronomers to understand the way in which the Universe is structured. However, due to the large number of observed objects with modern telescopes, the analysis of these by hand is a difficult task. An important part in galaxy research is the morphological structure classification based on the Hubble sequence. In this research, we present an approach to solve the morphological galaxy classification problem in an automatic way by using the Sparse Representation technique and dictionary learning with K-SVD. For the tests in this work, we use a database of galaxies extracted from the Principal Galaxy Catalog (PGC) and the APM Equatorial Catalogue of Galaxies obtaining a total of 2403 useful galaxies. In order to represent each galaxy frame, we propose to calculate a set of 20 features such as Hu’s invariant moments, galaxy nucleus eccentricity, gabor galaxy ratio and some other features commonly used in galaxy classification. A stage of feature relevance analysis was performed using Relief-f in order to determine which are the best parameters for the classification tests using 2, 3, 4, 5, 6 and 7 galaxy classes making signal vectors of different length values with the most important features. For the classification task, we use a 20-random cross-validation technique to evaluate classification accuracy with all signal sets achieving a score of 82.27 % for 2 galaxy classes and up to 44.27 % for 7 galaxy classes.

Improved sparse representation with low-rank representation for robust face recognition

In this paper, an approach to learn a robust sparse representation dictionary for face recognition is proposed. As well known, sparse representation algorithm can effectively tackle slight occlusion problems for face recognition. However, if images are corrupted by heavy noise, performance will be not guaranteed. In this paper, to enhance the robustness of sparse representation to serious noise in face images, we integrate low rank representation into dictionary learning to alleviate the influence of unfavorable factors such as large scale noise and occlusion. Among which we extract eigenfaces by singular value decomposition (SVD) from the low rank pictures to reduce dictionary atoms and, thereby, optimize the efficiency of improved algorithm. Otherwise, we characterize each image using the histogram of orientated gradient (HOG) feature which has been proven to be an effective descriptor for face recognition in particular. The performance of the proposed Low-rank and HOG feature based ESRC (LH_ESRC) algorithm on several popular face databases such as the Extended Yale B database and CMU_PIE face database shows the effectiveness of our method. In addition, we evaluate the robustness of our method by adding different proportions of randomly noise and block occlusion and real disgusts. Experimental results illustrate the benefits of our approach.

Image fusion via nonlocal sparse K-SVD dictionary learning.

Image fusion aims to merge two or more images captured via various sensors of the same scene to construct a more informative image by integrating their details. Generally, such integration is achieved through the manipulation of the representations of the images concerned. Sparse representation plays an important role in the effective description of images, offering a great potential in a variety of image processing tasks, including image fusion. Supported by sparse representation, in this paper, an approach for image fusion by the use of a novel dictionary learning scheme is proposed. The nonlocal self-similarity property of the images is exploited, not only at the stage of learning the underlying description dictionary but during the process of image fusion. In particular, the property of nonlocal self-similarity is combined with the traditional sparse dictionary. This results in an improved learned dictionary, hereafter referred to as the nonlocal sparse K-SVD dictionary (where K-SVD stands for the K times singular value decomposition that is commonly used in the literature), and abbreviated to NL_SK_SVD. The performance of the NL_SK_SVD dictionary is applied for image fusion using simultaneous orthogonal matching pursuit. The proposed approach is evaluated with different types of images, and compared with a number of alternative image fusion techniques. The resultant superior fused images using the present approach demonstrates the efficacy of the NL_SK_SVD dictionary in sparse image representation.

Ground-roll separation of seismic data based on morphological component analysis in two-dimensional domain

Ground roll is an interference wave that severely degrades the signal-to-noise ratio of seismic data and affects its subsequent processing and interpretation. In this study, according to differences in morphological characteristics between ground roll and reflected waves, we use morphological component analysis based on two-dimensional dictionaries to separate ground roll and reflected waves. Because ground roll is characterized by low-frequency, low-velocity, and dispersion, we select two-dimensional undecimated discrete wavelet transform as a sparse representation dictionary of ground roll. Because of a strong local correlation of the reflected wave, we select two-dimensional local discrete cosine transform as the sparse representation dictionary of reflected waves. A sparse representation model of seismic data is constructed based on a two-dimensional joint dictionary then a block coordinate relaxation algorithm is used to solve the model and decompose seismic record into reflected wave part and ground roll part.The good effects for the synthetic seismic data and application of real seismic data indicate that when using the model, strong-energy ground roll is considerably suppressed and the waveform of the reflected wave is effectively protected.

Discriminative Bayesian Dictionary Learning for Classification.

We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a finite approximation of Beta Process. It also computes sets of Bernoulli distributions that associate class labels to the learned dictionary atoms. This association signifies the selection probabilities of the dictionary atoms in the expansion of class-specific data. Furthermore, the non-parametric character of the proposed approach allows it to infer the correct size of the dictionary. We exploit the aforementioned Bernoulli distributions in separately learning a linear classifier. The classifier uses the same hierarchical Bayesian model as the dictionary, which we present along the analytical inference solution for Gibbs sampling. For classification, a test instance is first sparsely encoded over the learned dictionary and the codes are fed to the classifier. We performed experiments for face and action recognition; and object and scene-category classification using five public datasets and compared the results with state-of-the-art discriminative sparse representation approaches. Experiments show that the proposed Bayesian approach consistently outperforms the existing approaches.