K-singular Value Decomposition Research Articles

A clustering K-SVD-based sparse representation method for rolling bearing fault diagnosis

It is challenging to extract weak impulse features from vibration signals corrupted by strong noise in mechanical fault diagnosis. Due to its simple calculation, fast convergence and easy implementation, K-singular value decomposition (K-SVD) has been widely used in rolling bearing fault diagnosis. However, it fails to consider the influence of noise and harmonics on atoms learning from impulse characteristics, which results in many irrelevant atoms, and then increases the difficulty of extracting the impulse features in bearing fault signals. Therefore, a clustering K-SVD-based sparse representation method is proposed in this paper and it is combined with the particle swarm optimisation (PSO)-based time-varying filter empirical mode decomposition (TVF-EMD) for rolling bearing fault diagnosis. The PSO-based TVF-EMD is developed to automatically decompose the original signal to eliminate the impact of noise and harmonics on the impulses in the signal. Then, the clustering K-SVD method is applied to perform dictionary learning on the sensitive component containing impulses to obtain a redundant dictionary of atoms with obvious impulse patterns. Finally, the orthogonal matching pursuit (OMP) algorithm is introduced to extract the fault features from rolling bearing vibration signals. The experimental results show that the proposed method can improve the robustness of the dictionary atoms to noise and achieve the extraction of rolling bearing fault features.

Seismic random noise attenuation using effective and efficient dictionary learning

Seismic data is often corrupted with random noise and thus may be of poor quality because of the low signal-to-noise ratio. The random noise may not only affect the velocity inversion and seismic migration, but also cause potential risks in post-stack processing and interpretation because of the artifacts. In this paper, we propose to apply the sparse dictionary learning algorithm to attenuate random noise in a transform-based denoising framework. The seismic data is first transformed to the sparse domain via a forward sparsity-promoting transform, then thresholded by a thresholding strategy, and finally transformed back to the time-space domain. The sparse dictionary can adapt to the complexity of the input seismic data and vary the basis functions to make the transform domain optimally sparse. Considering the challenges of low computational efficiency of the dictionary learning method because of the computational-intensive orthogonal matching pursuit (OMP) and K-singular value decomposition (K-SVD), we propose an accelerated scheme to make the processing much faster. On the one hand, we propose a fast algorithm for the sparse coding process. On the other hand, we also substitute the K-SVD method with a SVD-free strategy to make the dictionary updating process efficient. The overall efficiency of the dictionary learning method is much improved and thus is suitable for practical applications. We use synthetic and field data examples to demonstrate the performance and efficiency of the presented method.

Sub-Pixel Mapping Model Based on Total Variation Regularization and Learned Spatial Dictionary

In this research study, we deal with remote sensing data analysis over high dimensional space formed by hyperspectral images. This task is generally complex due to the large spectral, spatial richness, and mixed pixels. Thus, several spectral un-mixing methods have been proposed to discriminate mixing spectra by estimating the classes and their presence rates. However, information related to mixed pixel composition is very interesting for some applications, but it is insufficient for many others. Thus, it is necessary to have much more data about the spatial localization of the classes detected during the spectral un-mixing process. To solve the above-mentioned problem and specify the spatial location of the different land cover classes in the mixed pixel, sub-pixel mapping techniques were introduced. This manuscript presents a novel sub-pixel mapping process relying on K-SVD (K-singular value decomposition) learning and total variation as a spatial regularization parameter (SMKSVD-TV: Sub-pixel Mapping based on K-SVD dictionary learning and Total Variation). The proposed approach adopts total variation as a spatial regularization parameter, to make edges smooth, and a pre-constructed spatial dictionary with the K-SVD dictionary training algorithm to have more spatial configurations at the sub-pixel level. It was tested and validated with three real hyperspectral data. The experimental results reveal that the attributes obtained by utilizing a learned spatial dictionary with isotropic total variation allowed improving the classes sub-pixel spatial localization, while taking into account pre-learned spatial patterns. It is also clear that the K-SVD dictionary learning algorithm can be applied to construct a spatial dictionary, particularly for each data set.

The Noise Attenuation and Stochastic Clutter Removal of Ground Penetrating Radar Based on the K-SVD Dictionary Learning

The ground penetrating radar (GPR) data in the complex detection environment is non-stationary, non-Gaussian, and non-uniform, so the traditional noise attenuation methods are difficult to meet the requirements of denoising. Therefore, we introduced the K-singular value decomposition (K-SVD) dictionary learning into the denoising of GPR signals. It uses the orthogonal matching pursuit (OMP) algorithm to sparse decompose different radar data and trains the overcomplete dictionary with sample characteristics. K-SVD makes full use of the prior information and can extract features according to the sample data adaptively, which means it has strong sparse representation competence. Because radar signals can be sparsely represented in the dictionary, whereas the random noise does not have a sparse representation, the K-SVD dictionary can be used to distinguish effective signals from noise in the GPR data. We used the discrete cosine transform (DCT) and K-SVD dictionaries to process the Gaussian noise and stochastic clutter in the GPR profile. The results show that both K-SVD and DCT can effectively suppress the Gaussian noise. But for the clutter generated by the random medium, the DCT dictionary also causes damage to the effective signals while removing the noise; whereas the K-SVD dictionary learning algorithm uses the DCT dictionary as the initial dictionary and carries out adaptive learning on the noisy data, considering the information in the block and the global observation to complete the denoising, with good denoising effect and high fidelity. We finally verified the effectiveness and practicability of the K-SVD method for measured data.

The colour block registration method of fuzzy image under multi-layer P-spline geometric transformation

In order to overcome the problem that the traditional similarity measure is easy to be affected by the grey-scale migration, this paper proposes a colour block registration method of fuzzy image under the multi-layer P-spline geometric transformation. This method mainly sets sparse coding as similarity measure, and divides two images that are not registered into image blocks. K-singular value decomposition (K-SVD) algorithm is used to train image blocks, acquire analysis dictionary and find sparse coefficients. The multi-layer P-spline geometric transformation is used to simulate the fuzzy image, and the gradient descent method is used to optimise the objective function to complete the colour block registration of the fuzzy image under the multi-layer P-spline geometric transformation. The experimental results show that the registration time is the lowest, the root mean square error is kept below 0.04, and the registration accuracy is up to 100%.

The colour block registration method of fuzzy image under multi-layer P-spline geometric transformation

In order to overcome the problem that the traditional similarity measure is easy to be affected by the grey-scale migration, this paper proposes a colour block registration method of fuzzy image under the multi-layer P-spline geometric transformation. This method mainly sets sparse coding as similarity measure, and divides two images that are not registered into image blocks. K-singular value decomposition (K-SVD) algorithm is used to train image blocks, acquire analysis dictionary and find sparse coefficients. The multi-layer P-spline geometric transformation is used to simulate the fuzzy image, and the gradient descent method is used to optimise the objective function to complete the colour block registration of the fuzzy image under the multi-layer P-spline geometric transformation. The experimental results show that the registration time is the lowest, the root mean square error is kept below 0.04, and the registration accuracy is up to 100%.

Separation‐based model for low‐dose CT image denoising

Low-dose computed tomography (LDCT) image often contains mottle noise and streak artefacts, which seriously interfere with clinical diagnosis. In this study, the separation-based (SEPB) method is proposed for mottle noise and streak artefacts suppression and structure preservation. In it, the LDCT image is decomposed into the structural image with residual mottle noise and the streak artefacts image with residual structural details by the image decomposition structural-preserving image smoothing method. The structural image is filtered by the K-singular value decomposition algorithm to remove the residual mottle noise, and the structural details in the streak artefacts image are extracted by the morphological component analysis theory. The extracted structural details are added to the filtered structural image to get the LDCT result image. Meanwhile, in the process of extracting the structural details, the streak artefacts dictionary learned from the streak artefacts image is corrected by the local intuitional fuzzy entropy to remove its structural atoms. The experiments are conducted on the modified Shepp–Logan phantom, the pelvis phantom and the clinical abdominal data to evaluate the proposed SEPB method. Compared to several comparative denoising methods, the experimental results show that the SEPB method has better performance in subjective visual effect and objective indicators.

Image restoration based on sparse representation using feature classification learning

In the image inpainting method based on sparse representation, the adaptability of over-complete dictionary has a great influence on the result of image restoration. If the over-complete dictionary cannot effectively reflect the differences between different local features, it may result in the loss of texture details, resulting in blurred or over-smooth phenomenon in restored images. In view of these problems, we propose an image restoration method based on sparse representation using feature classification learning. Firstly, we perform singular value decomposition on the local gradient vector. According to the relationship between the main orientation and the secondary orientation, we classify all the local patches into three categories: smooth patch, edge patch and texture patch. Secondly, we use K-Singular Value Decomposition method to learn over-complete dictionaries that adapt to different features. Finally, we use Orthogonal Matching Pursuit method to calculate the sparse coding of target patches with different local features on their corresponding over-complete dictionaries, and use the over-complete dictionary and corresponding sparse coding to restore the damaged pixels. A series of experiments on various restoration tasks show the superior performance of the proposed method.

MLK-SVD, the new approach in deep dictionary learning

The aim of this study is to improve the classification efficiency of advanced methods using a multilayered dictionary learning framework. This paper presents the new idea of “multilayered K-singular value decomposition (MLK-SVD)” dictionary learning as a multilayer method of classification. This method starts by building a sparse representation at the patch level and relies on a hierarchy of learned dictionaries to output a global sparse representation for the whole image. In this research using class labels of training data, the label information is associated with each dictionary item (columns of the dictionary matrix) to enforce discrimination in sparse codes during the dictionary learning process. Also, this algorithm instead of learning one shallow dictionary learned multiple levels of dictionaries. The proposed formulation of deep dictionary learning provides the basis to develop more efficient dictionary learning algorithms. It relies on a succession of sparse coding and pooling steps in order to find an efficient representation of the data for classification. The performance of the proposed method is evaluated on MNIST and CIFAR-10 datasets, and results show that this method can help in advancing the state of the art.

Multiscale Supervised Kernel Dictionary Learning for SAR Target Recognition

In this article, a supervised nonlinear dictionary learning (DL) method, called multiscale supervised kernel DL (MSK-DL), is proposed for target recognition in synthetic aperture radar (SAR) images. We use Frost filters with different parameters to extract an SAR image’s multiscale features for data augmentation and noise suppression. In order to reduce the computation cost, the dimension of each scale feature is reduced by principal component analysis (PCA). Instead of the widely used linear DL, we learn multiple nonlinear dictionaries to capture the nonlinear structure of data by introducing the dimension-reduced features into the nonlinear reconstruction error terms. A classification model, which is defined as a discriminative classification error term, is learned simultaneously. Hence, the objective function contains the nonlinear reconstruction error terms and a classification error term. Two optimization algorithms, called multiscale supervised kernel K-singular value decomposition (MSK-KSVD) and multiscale supervised incremental kernel DL (MSIK-DL), are proposed to compute the multidictionary and the classifier. Experiments on the moving and stationary target automatic recognition (MSTAR) data set are performed to evaluate the effectiveness of the two proposed algorithms. And the experimental results demonstrate that the proposed scheme outperforms some representative common machine learning strategies, state-of-the-art convolutional neural network (CNN) models and some representative DL methods, especially in terms of its robustness against training set size and noise.

Sparse representation based computed tomography images reconstruction by coupled dictionary learning algorithm

It is very interesting to reconstruct high-resolution computed tomography (CT) medical images that are very useful for clinicians to analyse the diseases. This study proposes an improved super-resolution method for CT medical images in the sparse representation domain with dictionary learning. The sparse coupled K-singular value decomposition (KSVD) algorithm is employed for dictionary learning purposes. Images are divided into two sets of low resolution (LR) and high resolution (HR), to improve the quality of low-resolution images, the authors prepare dictionaries over LR and HR image patches using the KSVD algorithm. The main idea behind the proposed method is that sparse coupled dictionaries learn about each patch and establish the relationship between sparse coefficients of LR and HR image patches to recover the HR image patch for LR image. The proposed method is compared to conventional algorithms in terms of mean peak signal-to-noise ratio and structural similarity index measurements by using three different data set images, including CT chest, CT dental and CT brain images. The authors also analysed the proposed improved method for different dictionary sizes and patch size to obtain a similar high-resolution image. These parameters play an essential role in the reconstruction of the HR images.

A wavelet denoising approach based on unsupervised learning model

Image denoising plays an important role in image processing, which aims to separate clean images from noisy images. A number of methods have been presented to deal with this practical problem over the past several years. The best currently available wavelet-based denoising methods take advantage of the merits of the wavelet transform. Most of these methods, however, still have difficulties in defining the threshold parameter which can limit their capability. In this paper, we propose a novel wavelet denoising approach based on unsupervised learning model. The approach taken aims at exploiting the merits of the wavelet transform: sparsity, multi-resolution structure, and similarity with the human visual system, to adapt an unsupervised dictionary learning algorithm for creating a dictionary devoted to noise reduction. Using the K-Singular Value Decomposition (K-SVD) algorithm, we obtain an adaptive dictionary by learning over the wavelet decomposition of the noisy image. Experimental results on benchmark test images show that our proposed method achieves very competitive denoising performance and outperforms state-of-the-art denoising methods, especially in the peak signal to noise ratio (PSNR), the structural similarity (SSIM) index, and visual effects with different noise levels.

Airborne electromagnetic data denoising based on dictionary learning

Time-domain airborne electromagnetic (AEM) data are frequently subject to interference from various types of noise, which can reduce the data quality and affect data inversion and interpretation. Traditional denoising methods primarily deal with data directly, without analyzing the data in detail; thus, the results are not always satisfactory. In this paper, we propose a method based on dictionary learning for EM data denoising. This method uses dictionary learning to perform feature analysis and to extract and reconstruct the true signal. In the process of dictionary learning, the random noise is filtered out as residuals. To verily the effectiveness of this dictionary learning approach for denoising, we use a fixed overcomplete discrete cosine transform (ODCT) dictionary algorithm, the method-of-optimal-directions (MOD) dictionary learning algorithm, and the K-singular value decomposition (K-SVD) dictionary learning algorithm to denoise decay curves at single points and to denoise profile data for different time channels in time-domain AEM. The results show obvious differences among the three dictionaries for denoising AEM data, with the K-SVD dictionary achieving the best performance.

Analysis of feature representation in dictionary learning and sparse coding algortihms for low resolution image

Super-Resolution (SR) is used to recover a high-resolution (HR) image from the image with low-resolution (LR). SR is important in the biometric identification and the face recognition is an area that bring attention to people. However, the performance of the current systems is affected by the resolution of the input images. Thus, this paper is focusing on the analysis of feature representations in dictionary learning and sparse coding methods for LR image. The input image is the Lena image in grey scale. A total number of 23 features were extracted from the image patches to develop different learned dictionaries using the k-singular value decomposition (k-SVD) algorithm. The denoised images were then produced by using the Douglas-Rachford algorithm. Most of the feature representations were able to produce a final image with Peak-to-Signal Noise Ratio (PSNR) and Structural Similarity Index Matric (SSIM) values of approximately 29 dB to 30 dB and 0.8300 to 0.8600 respectively. However, the denoised image produced with gradient direction obtained only 27.6676 dB and 0.7881 for PSNR and SSIM. Therefore, when different features were extracted for conducting the dictionary learning and sparse coding algorithm, denoised image with different PSNR and SSIM were produced at the end of the process.

A New Method for Long-Distance Data Reconstruction in Big Data Environment

In a big data environment, the data from long-term monitoring are of great importance in intelligent diagnoses, prognostic and health management of industrial components. However, in practice, it is difficult to ensure high reconstructive accuracy making the preservation performance of low-frequency information (e.g., periodic fault impulses) stable. To address this issue, this article proposes a new data reconstruction method that combines a smoothing sparse low-rank matrix (SSLRM) with online dictionary learning. This article first presents the design of SSLRM model for decomposing the raw data into a low resonance component (LRC) and a high resonance component (HRC), such that the periodic fault impulse can be isolated and preserved in advance. Then, both LRC and HRC are, respectively, reconstructed using an online dictionary learning algorithm, i.e., Hankel K-singular value decomposition; thus, the reconstructed data can be obtained accordingly. Both simulation case and engineering case are applied to show the effectiveness and practicality of the proposed approach.

Chaotic signal denoising algorithm based on sparse decomposition**Project supported by the National Natural Science Foundation of China (Grant No. 61872083) and the Natural Science Foundation of Guangdong Province, China (Grant Nos. 2017A030310659 and 2019A1515011123).

Denoising of chaotic signal is a challenge work due to its wide-band and noise-like characteristics. The algorithm should make the denoised signal have a high signal to noise ratio and retain the chaotic characteristics. We propose a denoising method of chaotic signals based on sparse decomposition and K-singular value decomposition (K-SVD) optimization. The observed signal is divided into segments and decomposed sparsely. The over-complete atomic library is constructed according to the differential equation of chaotic signals. The orthogonal matching pursuit algorithm is used to search the optimal matching atom. The atoms and coefficients are further processed to obtain the globally optimal atoms and coefficients by K-SVD. The simulation results show that the denoised signals have a higher signal to noise ratio and better preserve the chaotic characteristics.

A novel efficient camera calibration approach based on K-SVD sparse dictionary learning

Camera calibration is essential for accurate product visual inspection. In this paper, a novel efficient camera calibration approach based on K-Singular Value Decomposition (K-SVD) sparse dictionary learning is presented, in which, (1) the nonlinear optimization model with ten calibration parameters is formulated, (2) a large amount of images of checkerboards are acquired offline at different locations in the working volume of the camera to construct a sparse dictionary through K-SVD sparse dictionary learning, which enables such non-linear optimization model appropriately initialized and efficiently converges, and (3) in addition, the sparse dictionary can be further updated with the new acquired image so that it can be used to timely characterize the camera variation due to lens aging, and still be used to obtain appropriate initial values. Finally, three experiments are demonstrated to validate the efficiency of the presented approach. The results show that (1) the camera can be accurately calibrated with only one image, which can save almost more than 60 percent calibration time, and is very beneficial to online calibration for quality inspection, and (2) the calibration is much more accurate than that of traditional approaches with only one image having identical grid pixels.

Edge-Guided Depth Image Super-Resolution Based on KSVD

This paper proposes an edge-guided super-resolution algorithm for single frame depth images based on K singular value decomposition (KSVD). Compared with conventional algorithms, the proposed algorithm has two key contributions. Firstly it suppresses the jagged edge effect of up-sampled depth images by KSVD, which learns a complete dictionary to describe the mapping between the jagged edges and corresponding smooth ones. Secondly it improves the joint bilateral filter based on connectivity. The improved filter can not only preserve the sharpness of the edges during the interpolation, but also suppress noise. The proposed algorithm has been extensively tested on the Middlebury dataset and compared with some existing state-of-the-art methods. Both quantitative and qualitative experimental results show its performance superiority.

Artificial Intelligence Recognition Simulation of 3D Multimedia Visual Image Based on Sparse Representation Algorithm

With the rapid development of computer networks and multimedia technologies, images, which are important carriers of information dissemination, have made human cognition of things easier. Image recognition is a basic research task in computer vision, multimedia search, image understanding and other fields. This paper proposes a hierarchical feature learning structure that is completely automatically based on the original pixels of the image, and uses the K-SVD (K-Singular Value Decomposition) algorithm with label consistency constraints to train the discriminant dictionary. For different types of image data sets, the algorithm only extracts image blocks. After dense sampling, an efficient OMP (Orthogonal Matching Pursuit) encoder is used to obtain a layered sparse representation. The improved SIFT (Scale Invariant Feature Transform) algorithm is used to solve the difficult problem of multimedia visual image stereo matching. The feature point extraction and stereo matching of multimedia visual images, different scales and different viewpoint images are analyzed separately. Aiming at a large number of low-dimensional geometric features of 3D images, this paper studies the extraction and sorting strategies of low-dimensional geometric features of 3D images. A sparse representation method for 3D images is proposed, and the sparseness of image features is evaluated. This further improves the accuracy of 3D image representation and the robustness of 3D image recognition algorithms.

A Novel Approach to Mammogram Classification using Spatio-Temporal and Texture Feature Extraction using Dictionary based Sparse Representation Classifier

Cancer is a chronic disease and increasing rapidly worldwide. Breast cancer is one of the most crucial cancer which affects the women health and causes death of the women. In order to predict the breast cancer, mammogram is considered as a promising technique which helps to identify the early stages of cancer. However, several schemes have been developed during last decade to overcome the performance related issues but achieving the desired performance is still challenging task. To overcome this issue, we introduce a novel and robust approach of feature extraction and classification. According to the proposed approach, first of all, we apply pre-processing stage where image binarization is applied using Niblack’s method and later Region of Interest (ROI) extraction and segmentation schemes are applied. In the next phase of work, we developed a mixed strategy of feature extraction where we consider Gray Level Co-occurrence Matrix (GLCM), Histogram of oriented Gradients (HoG) with Principal Component Analysis (PCA) for dimension reduction, Scale-invariant Feature Transform (SIFT), and non-parametric Discrete Wavelet Transform (DWT) features are extracted. Finally, we present K-Singular value decomposition (SVD) based dictionary learning scheme and applied the Sparse representation classifier (SRC) classification approach and performance is evaluated using MATLAB tool. An extensive experimental study is carried out which shows that the proposed approach achieves classification accuracy as 98.13%, Precision as 97.58%, Recall as 98.36%, and F-Score 97.95%. The performance of proposed approach is compared with the state-of-art techniques which shows that the proposed approach gives better performance.