ℓ1-K-SVD: A robust dictionary learning algorithm with simultaneous update

This study aimed to explore the effect of ultrasound imaging in the diagnosis and evaluation of acupoint application in the treatment of idiopathic edema. In this study, an ultrasound imaging diagnosis based on the segmentation dictionary learning (S-DL) algorithm was proposed. In addition, the autoencoding algorithm (ASE) was compared with the traditional dictionary learning (DL) algorithm. The treatment effect, associated quantitative integral, and quality of life score of patients in two groups were compared. The results showed that the peak signal-to-noise ratio (PSNR), root mean square error (RMSE), and structural similarity (SSIM) of the S-DL algorithm were 32.45 dB, 0.654, and 0.0012, respectively, which were quite different compared to the ASE and DL algorithms, showing statistical significance (P < 0.05). As the noise level increased, the image reconstruction quality gradually decreased, but the S-DL algorithm obtained better image quality than the DL and ASE algorithms, and the difference was statistically great (P < 0.05). There was no significant difference in the average age and average course of the disease between the experimental group and the control group (P > 0.05). The overall treatment effect of patients in the experimental group was 96.77%, while that in the control group was 45.16%, and the difference between the two was statistically significant (P < 0.05). After treatment, the semiquantitative scores of fatigue, dizziness, palpitation, frequent urination, urgent urination, and dyspepsia of the experimental group were 1.18, 0.39, 0.72, 1.21, and 0.87, respectively, which were much lower than those of the control group statistically (P < 0.05). The score of quality of life of the experimental group of patients after treatment was 91.27 points, and that of the control group was 82.35 points, showing statistically great difference (P < 0.05). It showed that the algorithm performance of S-DL was relatively good, and the acupoint application therapy was better than traditional western medicine in the treatment of idiopathic edema, which reduces the discomfort of patients to a certain extent and improves the quality of life of patients.

Both interclass variances and intraclass similarities are crucial for improving the classification performance of discriminative dictionary learning (DDL) algorithms. However, existing DDL methods often ignore the combination between the interclass and intraclass properties of dictionary atoms and coding coefficients. To address this problem, in this paper, we propose a discriminative Fisher embedding dictionary learning (DFEDL) algorithm that simultaneously establishes Fisher embedding models on learned atoms and coefficients. Specifically, we first construct a discriminative Fisher atom embedding model by exploring the Fisher criterion of the atoms, which encourages the atoms of the same class to reconstruct the corresponding training samples as much as possible. At the same time, a discriminative Fisher coefficient embedding model is formulated by imposing the Fisher criterion on the profiles (row vectors of the coding coefficient matrix) and coding coefficients, which forces the coding coefficient matrix to become a block-diagonal matrix. Since the profiles can indicate which training samples are represented by the corresponding atoms, the proposed two discriminative Fisher embedding models can alternatively and interactively promote the discriminative capabilities of the learned dictionary and coding coefficients. The extensive experimental results demonstrate that the proposed DFEDL algorithm achieves superior performance in comparison with some state-of-the-art dictionary learning algorithms on both hand-crafted and deep learning-based features.

Dictionary learning algorithms have been successfully used in both reconstructive and discriminative tasks, where the input signal is represented by a linear combination of a few dictionary atoms. While these methods are usually developed under l 1 sparsity constrain (prior) in the input domain, recent studies have demonstrated the advantages of sparse representation using structured sparsity priors in the kernel domain. In this paper, we propose a supervised dictionary learning algorithm in the kernel domain for hyperspectral image classification. In the proposed formulation, the dictionary and classifier are obtained jointly for optimal classification performance. The supervised formulation is task-driven and provides learned features from the hyperspectral data that are well suited for the classification task. Moreover, the proposed algorithm uses a joint (l 12 ) sparsity prior to enforce collaboration among the neighboring pixels. The simulation results illustrate the efficiency of the proposed dictionary learning algorithm.

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.

We present a structural matching technique for robust classification based on image sets. In set based classification, a probe set is matched with a number of gallery sets and assigned the label of the most similar set. We represent each image set by a sparse dictionary and compute a similarity matrix by matching all the dictionary atoms of the gallery and probe sets. The similarity matrix comprises the sparse coding coefficients and forms a fully connected directed graph. The nodes of the graph are the dictionary atoms and the edges are the sparse coefficients. The graph is converted to an undirected graph with positive edge weights and spectral clustering is used to cut the graph into two balanced partitions using the normalized cut algorithm. This process is repeated until the graph reduces to critical and non-critical partitions. A critical partition contains atoms with the same gallery label along with one or more probe atoms whereas a noncritical partition either consists of only probe atoms or atoms with multiple gallery labels with no probe atom. Using the critical partitions, we define a novel set based similarity measure and assign the probe set the label of the gallery set with maximum similarity. The proposed algorithm is applied to image set based face recognition using two standard databases. Comparison with existing techniques shows the validity and robustness of our algorithm in the presence of outlier images.

We propose a scheme for supervised image classification that uses privileged information, in the form of keypoint annotations for the training data, to learn strong models from small and/or biased training sets. Our main motivation is the recognition of animal species for ecological applications such as biodiversity modelling, which is challenging because of long-tailed species distributions due to rare species, and strong dataset biases such as repetitive scene background in camera traps. To counteract these challenges, we propose a visual attention mechanism that is supervised via keypoint annotations that highlight important object parts. This privileged information, implemented as a novel privileged pooling operation, is only required during training and helps the model to focus on regions that are discriminative. In experiments with three different animal species datasets, we show that deep networks with privileged pooling can use small training sets more efficiently and generalize better.

We address the issue of detecting hidden periodicity when the signal exhibits periodic correlation, but is additionally affected by non-Gaussian noise with unknown characteristics. This scenario is common in various applications. The conventional approach for identifying periodically correlated (PC) behavior involves the frequency domain-based analysis. In our investigation, we also employ such an approach; however, we use a robust version of the discrete Fourier transform incorporating the Huber function-based M-estimation, unlike the classical algorithm. Building upon this approach, we propose robust coherent and incoherent statistics originally designed to identify hidden periodicity in pure PC models. The novelty of this paper lies in introducing robust coherent and incoherent statistics through the application of the robust discrete Fourier transform in classical algorithms and proposing a new technique for period estimation based on the proposed methodology. We explore two types of PC models and two types of additive noise, resulting in PC signals disturbed by non-Gaussian additive noise. Detecting hidden periodicity in such cases proves to be significantly more challenging than in classical scenarios. Through Monte Carlo simulations, we demonstrate the effectiveness of the proposed robust approaches and their superiority over classical. To further substantiate our findings, we analyze three datasets in which hidden periodicity had previously been confirmed in the literature. Among them, two datasets correspond to the condition monitoring area, being a main motivation of our research.

In the process of signal and image acquisition and transmission, there is not only the additive white Gaussian noise interference, but also the non-Gaussian noise interference. The performance of a standard reconstruction algorithm, known as compressed sensing, can be significantly reduced if it is used to recover the signal affected by non-Gaussian noise. In this paper, LpLq-ADMM algorithm $(p \in(0,2), q \in(0,1))$ based on alternating direction method of multipliers is proposed to improve the reconstruction accuracy and the robustness of signal and image restoration in impulsive SαS (symmetric α-stable) noise. Lp-norm is used as the loss function term to enhance the data restoration ability in SαS noise and Lq-norm is used as the generalized non-convex penalty term to guarantee the sparsity of the signal. In order to efficiently solve the cost function model with minimum non-convex and nonsmooth, reduce the computational complexity of the objective function and improve the processing ability of high-dimensional data, in this paper, the alternating direction method of multipliers (ADMM) is used to solve the cost function model. The appropriate p and q values are selected via numerical simulation experiments to achieve the optimal reconstruction accuracy and robustness of sparse signals in SαS noise. The reconstruction probability of sparse signals and image recovery performance are analyzed under the optimal p and q values. The simulation results show that LpLq-ADMM algorithm has great noise suppression ability to SαS noise, and its Peak Signal to Noise Ratio (PSNR) and signal recovery probability is higher than other recovery algorithms.

Incoherent dictionary learning with log-regularizer based on proximal operators

Event-related potentials (ERPs) are one of the most popular control signals for brain-computer interfaces (BCIs). However, they are very weak and sensitive to the experimental settings including paradigms, stimulation parameters and even surrounding environments, resulting in a diversity of ERP patterns across different BCI experiments. It's still a challenge to develop a general decoding algorithm that can adapt to the ERP diversities of different BCI datasets with small training sets. This study compared a recently developed algorithm, i.e., discriminative canonical pattern matching (DCPM), with seven ERP-BCI classification methods, i.e., linear discriminant analysis (LDA), stepwise LDA, bayesian LDA, shrinkage LDA, spatial-temporal discriminant analysis (STDA), xDAWN and EEGNet for the single-trial classification of two private EEG datasets and three public EEG datasets with small training sets. The feature ERPs of the five datasets included P300, motion visual evoked potential (mVEP), and miniature asymmetric visual evoked potential (aVEP). Study results showed that the DCPM outperformed other classifiers for all of the tested datasets, suggesting the DCPM is a robust classification algorithm for assessing a wide range of ERP components.

Industrial fault diagnosis based on active learning and semi-supervised learning using small training set

The purpose of this correspondence is to report on some nxasurements of output SNR (signal-to-noise ratio or S/N), characteristics for a square-law detector extracting signals from non-Gaussian noise, specifically, impulsive noise. Non-Garlssian noise arises in varioas communication media such as the atmosphere, wire lines, and under water. In experimental and theoretical investigations of the effects of non-Gaussian noise on various communications systems, a simple correlator is often considered because it is possible to obtain theoretical predictions of the (S/N), for signal and additive non-Gaussian noise at the correlator input if an appropriate noise model is available for calculating the required fourth-order moment. Middleton (1962), in his analysis of correlator performance in non-Gaussian background noise, employed the so-called Poisson impulse noise model. His theoretical predictions reveal that impulsive noise always degrades the (S/N), as compared with Gaussian noise backgrounds having the same spectral distribution for a given input SNR. However, his theoretical formulas are rather difficult to check experimentally in their full generality and assess the relative importance of various parameters. We compare a study restricted to the case of a square-law detector with Middleton's results.

Sequential dictionary learning algorithms have been successfully applied to a number of image processing problems. In a number of these problems however, the data used for dictionary learning are structured matrices with notions of smoothness in the column direction. This prior information which can be traduced as a smoothness constraint on the learned dictionary atoms has not been included in existing dictionary learning algorithms. In this paper, we remedy to this situation by proposing a regularized sequential dictionary learning algorithm. The proposed algorithm differs from the existing ones in their dictionary update stage. The proposed algorithm generates smooth dictionary atoms via the solution of a regularized rank-one matrix approximation problem where regularization is introduced via penalization in the dictionary update stage. Experimental results on synthetic and real data illustrating the performance of the proposed algorithm are provided.

According to the image processing theory, complex texture image regions have larger entropy values, an adaptive steganography algorithm in the sparse domain is proposed here. The algorithm first divides an image into nonoverlapping image blocks, then computes the entropy of each block and chooses the mean of all entropies as a threshold. Image blocks whose entropy is higher than the threshold are selected for sparse decomposition as complex texture image regions. The secret message is embedded into the decomposition coefficients, and then the stego image is reconstructed with modified coefficients. The experimental results prove that, given the same payload, the proposed adaptive algorithm has a better performance against the steganalyzer.

This keynote discusses the behavior of noise in indoor power line communications (PLC) channels. Some ideas to improve system performance based on the knowledge of PLC noise are also introduced. The power-line noise at an outlet is the sum of noise waveforms produced and emitted to the lines from the appliances connected to the power-line network. In the design and the analysis of wireless communication systems, stationary additive white Gaussian noise (AWGN) is often assumed. In PLC systems, however, the statistical behavior of the man-made noise is quite different from that of the stationary AWGN. The fact that the noise in power-lines is not AWGN is often believed to be a cause of low quality of communications. However, Gaussian is the distribution of the largest entropy, and communications under non-Gaussian noise may achieve better performance if the system is designed to adapt the noise statistics. In other words, PLC systems retain large potential for performance improvement if the behavior of the noise is clarified and taken into account in the system design. For narrow-band indoor PLC, we have a mathematically tractable and accurate model based on experimental measurements. In this model, the noise is expressed as a Gaussian process whose instantaneous variance is a periodic time function. With this assumption and representation, the cyclostationary features of power-line noise can be described in close form formula with a small set of parameters. In wide-band indoor PLC, we have made measurements with high speed sampling (50MHz) with long observation duration (10.4s).