Robust Principal Component Analysis Research Articles

Assessment of Prenatal Transportation Stress and Sex on Gene Expression Within the Amygdala of Brahman Calves

As the amygdala is associated with fear and anxiety, it is important to determine the potential effects of gestational stressors on behavior and stress responses in offspring. The objective of this study was to investigate the effects of prenatal transportation stress on amygdala gene expression in 25-day-old Brahman calves, focusing on sex-specific differences. Amygdala tissue samples from prenatally stressed (PNS) and control bull and heifer calves were analyzed using RNA sequencing. A thorough outlier detection process, utilizing visual inspection of multidimensional scaling plots, robust principal component analysis, and PCAGrid methods, led to the exclusion of 5 of 32 samples from subsequent analyses. Differential expression analysis revealed no significant treatment differences between the control and PNS groups within either sex. However, sex-specific differences in gene expression were identified in both the control and PNS groups. The control group showed seven differentially expressed genes between sexes, while ten were identified between PNS males and females, with seven located on the X chromosome. Among these was the ubiquitin-specific peptidase 9 X-linked gene, which plays a role in neurodevelopmental pathways. When comparing males to females, regardless of treatment, a total of 58 genes were differentially expressed, with 45 showing increased expression in females. Gene enrichment analysis indicated that many differentially expressed genes are associated with infectious disease-related pathways. Future research should explore amygdala size and functional responses to various postnatal stimuli.

Robust block tensor PCA with F-norm projection framework

Tensor principal component analysis (TPCA), also known as Tucker decomposition, ensures that the extracted “core tensor” maximizes the variance of the sample projections. Nevertheless, this method is particularly susceptible to noise and outliers. This is due to the utilization of the squared F-norm as the distance metric. In addition, it lacks constraints on the discrepancies between the original tensors and the projected tensors. To address these issues, a novel tensor-based trigonometric projection framework is proposed using F-norm to measure projection distances. Tensor data are first processed utilizing a blocking recombination technique prior to projection, thus enhancing the representation of the data at a local spatio-temporal level. Then, we present a block TPCA with the F-norm metric (BTPCA-F) and develop an iterative greedy algorithm for solving BTPCA-F. Subsequently, regarding the F-norm projection relation as the “Pythagorean Theorem”, we provide three different objective functions, namely, the tangent, cosine and sine models. These three functions directly or indirectly achieve the two objectives of maximizing projection distances and minimizing reconstruction errors. The corresponding tangent, cosine and sine solution algorithms based on BTPCA-F (called tan-BTPCA-F, cos-BTPCA-F and sin-BTPCA-F) are presented to optimize the objective functions, respectively. The convergence and rotation invariance of these algorithms are rigorously proved theoretically and discussed in detail. Lastly, extensive experimental results illustrate that the proposed methods significantly outperform the existing TPCA and the related 2DPCA algorithms.

Learnable Transform-Assisted Tensor Decomposition for Spatio-Irregular Multidimensional Data Recovery

Tensor decompositions have been successfully applied to multidimensional data recovery. However, classical tensor decompositions are not suitable for emerging spatio-irregular multidimensional data (i.e., spatio-irregular tensor), whose spatial domain is non-rectangular, e.g., spatial transcriptomics data from bioinformatics and semantic units from computer vision. By using preprocessing (e.g., zero-padding or element-wise 0-1 weighting), the spatio-irregular tensor can be converted to a spatio-regular tensor and then classical tensor decompositions can be applied, but this strategy inevitably introduces bias information, leading to artifacts. How to design a tensor-based method suitable for emerging spatio-irregular tensors is an imperative challenge. To address this challenge, we propose a learnable transform-assisted tensor singular value decomposition (LTA-TSVD) for spatio-irregular tensor recovery, which allows us to leverage the intrinsic structure behind the spatio-irregular tensor. Specifically, we design a learnable transform to project the original spatio-irregular tensor into its latent spatio-regular tensor, and then the latent low-rank structure is captured by classical TSVD on the resulting regular tensor. Empowered by LTA-TSVD, we develop spatio-irregular low-rank tensor completion (SIR-LRTC) and spatio-irregular tensor robust principal component analysis (SIR-TRPCA) models for the spatio-irregular tensor imputation and denoising respectively, and we design corresponding solving algorithms with theoretical convergence. Extensive experiments including the spatial transcriptomics data imputation and hyperspectral image denoising show SIR-LRTC and SIR-TRPCA are superior performance to competing approaches and benefit downstream applications.

A new nonconvex multi-view subspace clustering via learning a clean low-rank representation tensor

Abstract Recently, low-rank tensor representation has achieved impressive results for multi-view subspace clustering (MSC). The typical MSC methods utilize the tensor nuclear norm as a convex surrogate of the tensor multi-rank to obtain a low-rank representation, which exhibits limited robustness when dealing with noisy and complex data scenarios. In this paper, we introduce an innovative clean low-rank tensor representation approach that combines the idea of tensor robust principal component analysis (TRPCA) with a new nonconvex tensor multi-rank approximation regularization. This integration enhances the robustness of the low-rank representation, resulting in improved performance. Furthermore, to better capture the local geometric features, we employ a higher-order manifold regularization term. To effectively address our new model, we develop an iterative algorithm that has been proven to converge to the desired Karush-Kuhn-Tucker (KKT) point. The numerical experiments on widely used datasets serve to demonstrate the efficacy and effectiveness of our new method.

Online Tree-Structure-Constrained RPCA for Background Subtraction of X-ray Coronary Angiography Images

Background and objectiveBackground subtraction of X-ray coronary angiograms (XCA) can significantly improve the diagnosis and treatment of coronary vessel diseases. The XCA background is complex and dynamic due to structures with different intensities and independent motion patterns, making XCA background subtraction challenging. MethodsThe current work proposes an online tree-structure-constrained robust PCA (OTS-RPCA) method to subtract the XCA background. A morphological closing operation is used as a pre-processing step to remove large-scale structures like the spine, chest and diaphragm. In the following, the XCA sequence is decomposed into three different subspaces: low-rank background, residual dynamic background and vascular foreground. A tree-structured norm is introduced and applied to the vascular submatrix to guarantee the vessel spatial coherency. Moreover, the residual dynamic background is separately extracted to remove noise and motion artifacts from the vascular foreground. The proposed algorithm also employs an adaptive regularization coefficient that tracks the vessel area changes in the XCA frames. ResultsThe proposed method is evaluated on two datasets of real clinical and synthetic low-contrast XCA sequences of 38 patients using the global and local contrast-to-noise ratio (CNR) and structural similarity index (SSIM) criteria. For the real XCA dataset, the average values of global CNR, local CNR and SSIM are 6.27, 3.07 and 0.97, while these values over the synthetic low-contrast dataset are obtained as 5.15, 2.69 and 0.94, respectively. The implemented quantitative and qualitative experiments verify the superiority of the proposed method over seven selected state-of-the-art methods in increasing the coronary vessel contrast and preserving the vessel structure. ConclusionsThe proposed OTS-RPCA background subtraction method accurately subtracts backgrounds from XCA images. Our method might provide the basis for reducing the contrast agent dose and the number of needed injections in coronary interventions.

Robust generalized PCA for enhancing discriminability and recoverability

The dependency of low-dimensional embedding to principal component space seriously limits the effectiveness of existing robust principal component analysis (PCA) algorithms. Simply projecting the original sample coordinates onto orthogonal principal component directions may not effectively address various noise-corrupted scenarios, impairing both discriminability and recoverability. Our method addresses this issue through a generalized PCA (GPCA), which optimizes regression bias rather than sample mean, leading to more adaptable properties. And, we propose a robust GPCA model with joint loss and regularization based on the ℓ2,μ norm and ℓ2,ν norms, respectively. This approach not only mitigates sensitivity to outliers but also enhances feature extraction and selection flexibility. Additionally, we introduce a truncated and reweighted loss strategy, where truncation eliminates severely deviated outliers, and reweighting prioritizes the remaining samples. These innovations collectively improve the GPCA model’s performance. To solve the proposed model, we propose a non-greedy iterative algorithm and theoretically guarantee the convergence. Experimental results demonstrate that the proposed GPCA model outperforms the previous robust PCA models in both recoverability and discrimination.

Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions

AbstractIn this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous significant nonconvex and nonsmooth optimization problems in the current literature including the linearly constrained difference-of-convex problems. Relying on the successive linearization and alternating direction method of multipliers (ADMM), the proposed algorithm exhibits the global subsequential convergence to a stationary point of the underlying problem. We also establish the convergence of the full sequence generated by our algorithm under the Kurdyka–Łojasiewicz property and some mild assumptions. The efficiency of the proposed algorithm is tested on a robust principal component analysis problem and a nonconvex optimal power flow problem.

Ground penetrating radar clutter suppression based on the weighted tensor Schatten p-paradigm minimization of tensor principal components

The issue of clutter suppression in ground-penetrating radar (GPR) detection has consistently been a prominent area of research. The existing tensor robust principal component analysis (TRPCA) approach encounters a challenge when handling different singular values, whereby all singular values are reduced to the same degree, leading to loss of information in the low-rank part. To address the aforementioned issues, this study developed a TRPCA method based on weighted tensor Schatten p-paradigm minimisation (p-TRPCA). This approach assigns distinct weights to each singular value by using a weighted tensor Schatten p-paradigm, facilitating the optimal decomposition of GPR data into low-rank clutter and sparse target components. The processing of target echoes is then completed by applying a threshold judgement to the results. The efficacy of the proposed method was validated through simulations and real-world testing. Its performance was benchmarked against established advanced clutter removal techniques in terms of peak signal-to-noise ratio (PSNR) and signal-to-clutter ratio. The findings demonstrated that the method effectively delineated the low-rank clutter matrix and sparse target matrix within the B-scan image and exhibited superior SNR compared to other methods.

Machine learning-driven assessment of heavy metal contamination in the impounded lakes of China's South‐to‐North Water Diversion Project: Identifying spatiotemporal patterns and ecological risks

The Eastern Route of China's South-to-North Water Diversion Project (SNWDP-ER) traverses through impounded lakes that are potentially vulnerable to heavy metals (HMs) contamination although the understanding remains elusive. This study employed machine learning approaches, including super-clustering of Self-Organizing Map (SOM) and Robust Principal Component Analysis (RPCA), to elucidate the spatiotemporal patterns and assess ecological risks associated with HMs in the surface sediments of Gao-Bao-Shaobo Lake (GBSL) and Dongping Lake (DPL). We collected 184 surface sediments from 47 stations across the two important impounded lakes over four seasons. The results revealed higher HMs concentrations in the south-central GBSL and west-central DPL, with a notable increase in contamination in autumn. The comprehensive risk assessment, utilizing various indicators such as the Sediment Quality Guidelines (SQGs), Improved Potential Ecological Risk Index (IPERI), Geo-accumulation Index (Igeo), Contamination Factor (CF), and Enrichment Factor (EF), identified arsenic (As), cadmium (Cd), nickel (Ni), and chromium (Cr) as primary contaminants of concern. Positive Matrix Factorization (PMF) model, coupled with Spearman analysis, attributed over 70 % of HMs pollution to anthropogenic activities. This research provides a nuanced understanding of HMs pollution in the context of large-scale water diversion projects and offers a scientific basis for targeted pollution mitigation strategies.

Smooth robust principal component analysis based on multidimensional transform tensor for dynamic MRI

Dynamic magnetic resonance imaging (DMRI) stands as a sophisticated medical imaging technique pivotal to clinical practice, but the protracted duration of its imaging poses a substantial constraint on its practical application. This paper introduces a smooth robust principal component analysis model based on multidimensional transform tensors for accelerating DMR imaging. Specifically, the proposed method breaks down data into low-rank and sparse parts for reconstruction, respectively. The low-rank part employs a multidimensional adaptive transformation framework to generate transform tensors with favorable low-rank properties along three dimensions of DMR data. As for the sparse part, precise reconstruction can be achieved with the sparsity of the data after sparse transformation. In addition, to enhance the preservation of image details, this paper introduces a novel weighted tensor total variation regularization, imposing varying degrees of constraints based on smoothness in different dimensions. Experimental results demonstrate that the proposed method realizes superior reconstruction effects in comparison to existing advanced methods.

Insights into the Flavor Profile of Yak Jerky from Different Muscles Based on Electronic Nose, Electronic Tongue, Gas Chromatography-Mass Spectrometry and Gas Chromatography-Ion Mobility Spectrometry.

It is well known that different muscles of yak exhibit distinctive characteristics, such as muscle fibers and metabolomic profiles. We hypothesized that different muscles could alter the flavor profile of yak jerky. Therefore, the objective of this study was to investigate the differences in flavor profiles of yak jerky produced by longissimus thoracis (LT), triceps brachii (TB) and biceps femoris (BF) through electronic nose (E-nose), electronic tongue (E-tongue), gas chromatography-mass spectrometry (GC-MS) and gas chromatography-ion mobility spectrometry (GC-IMS). The results indicated that different muscles played an important role on the flavor profile of yak jerky. And E-nose and E-tongue could effectively discriminate between yak jerky produced by LT, TB and BF from aroma and taste points of view, respectively. In particular, the LT group exhibited significantly higher response values for ANS (sweetness) and NMS (umami) compared to the BF and TB groups. A total of 65 and 47 volatile compounds were characterized in yak jerky by GC-MS and GC-IMS, respectively. A principal component analysis (PCA) model and robust principal component analysis (rPCA) model could effectively discriminate between the aroma profiles of the LT, TB and BF groups. Ten molecules could be considered potential markers for yak jerky produced by different muscles, filtered based on the criteria of relative odor activity values (ROAV) > 1, p < 0.05, and VIP > 1, namely 1-octen-3-ol, eucalyptol, isovaleraldehyde, 3-carene, D-limonene, γ-terpinene, hexanal-D, hexanal-M, 3-hydroxy-2-butanone-M and ethyl formate. Sensory evaluation demonstrated that the yak jerky produced by LT exhibited superior quality in comparison to that produced by BF and TB, mainly pertaining to lower levels of tenderness and higher color, taste and aroma levels. This study could help to understand the specific contribution of different muscles to the aroma profile of yak jerky and provide a scientific basis for improving the quality of yak jerky.

Multi-Fingerprints Indoor Localization for Variable Spatial Environments: A Naive Bayesian Approach.

Fingerprint-based indoor localization has been a hot research topic. However, the current fingerprint-based indoor localization approaches still rely on a single fingerprint database, where the average level of data at reference points is used as the fingerprint representation. In variable environmental conditions, the variations in signals caused by changes in the environmental states introduce significant deviations between the average level and the actual fingerprint characteristics. This deviation leads to a mismatch between the constructed fingerprint database and the real-world conditions, thereby affecting the effectiveness of fingerprint matching. Meanwhile, the sharp noise interference caused by uncertainties such as personnel movement has a significant interference on the creation of the fingerprint database and fingerprint matching in online stage. Examination of the sampling data after denoising with Robust Principal Component Analysis (RPCA) revealed distinct multi-fingerprint characteristics with clear boundaries at certain access points. Based on these observations, the concept of constructing a fingerprint database using multiple fingerprints is introduced and its feasibility is explored. Additionally, a multi-fingerprint solution based on naive Bayes classification is proposed to accurately represent fingerprint characteristics under different environmental conditions. This method is based on the online stage fingerprints. The corresponding state space is selected using the naive Bayes classifier, enabling the selection of an appropriate fingerprint database for matching. Through simulations and empirical evaluations, the proposed multi-fingerprints construction scheme consistently outperforms the traditional single-fingerprint database in terms of positioning accuracy across all tested localization algorithms.

Emotion recognition from multichannel EEG signals based on low-rank subspace self-representation features

In recent years, emotion recognition based on electroencephalogram (EEG) has become the research focus in human–computer interaction (HCI), but deficiencies in EEG feature extraction and noise suppression are still challenging. In this paper, a novel robust low-rank subspace self-representation (RLSR) of EEG is developed for emotion recognition. Instead of using classical time–frequency EEG feature, the data-driven based EEG self-representation in low-rank subspace is extracted for emotion characterization. The Robust Principal Component Analysis (RPCA) is incorporated to separate the noise part in the process of solving self-representation. The accuracy and robustness of the result are improved because of the superior features and noise suppression. To fully exploit the effective knowledge of different EEG frequency bands, the Tucker decomposition based data dimensionality reduction is introduced. Experiments conducted on the public dataset DEAP reveal that the average accuracies of the proposed method can reach to 93.04 % and 93.13 % for binary classification of valence and arousal, respectively. The average accuracy reaches to 88.82 % of four-class classification.

Association of Ultraprocessed Foods Intake with Untargeted Metabolomics Profiles in Adolescents and Young Adults in the DONALD Cohort Study

BackgroundHigh consumption of ultraprocessed foods (UPFs) continues to draw significant public health interest because of the associated negative health outcomes. Metabolomics can contribute to the understanding of the biological mechanisms through which UPFs may influence health. ObjectivesTo investigate urine and plasma metabolomic biomarkers of UPF intake in adolescents and young adults. MethodsWe used data from the Dortmund Nutritional and Anthropometric Longitudinally Designed study to investigate cross-sectional associations of UPF intake with concentrations of urine metabolites in adolescents using 3d weighed dietary records (3d-WDR) and 24-h urine samples (n = 339), and associations of repeatedly assessed UPF intake with concentrations of circulating plasma metabolites in young adults with 3–6 3d-WDRs within 5 y preceding blood measurement (n = 195). Urine and plasma samples were analyzed using mass spectrometry-based metabolomics. Biosample-specific metabolite patterns (MPs) were determined using robust sparse principal components analysis. Multivariable linear regression models were applied to assess the associations of UPF consumption (as a percentage of total food intake in g/d) with concentrations of individual metabolites and MP scores. ResultsThe median proportion of UPF intake was 22.0% [interquartile range (IQR): 12.3, 32.9] in adolescents and 23.2% (IQR: 16.0, 31.6) in young adults. We identified 42 and 6 UPF intake-associated metabolites in urine and plasma samples, respectively. One urinary MP, “xenobiotics and amino acids” [β = 0.042, 95% confidence interval (CI): 0.014, 0.070] and 1 plasma MP, “lipids, xenobiotics, and amino acids” (β = 0.074, 95% CI: 0.031, 0.117) showed positive association with UPF intake. Both patterns shared 29 metabolites, mostly of xenobiotic metabolism. ConclusionsWe identified urine and plasma metabolites associated with UPF intake in adolescents and young adults, which may represent some of the biological mechanisms through which UPFs may influence metabolism and health.

A robust underwater polarization image recovery based on Angle of Polarization with low-rank and sparse decomposition

Underwater imaging method based on the Angle of Polarization (AoP) is extremely popular due to its ability to remove the backscattered light effectively. However, existing methods overlook a potentially important phenomenon: the AoP contains significant noise in the real world, which leads to inaccurate estimations of key parameters. In this study, we propose a novel robust underwater polarization image recovery method based on AoP with low-rank and sparse decomposition. Based on the analysis of polarization, the AoP of backscattering exhibits low-rank characteristics, whereas the AoP of noise and targets demonstrates sparsity. Considering different sparsity of AoP, we combine Robust Principal Component Analysis and Alternating Direction Multiplier Method (RPCA-ADMM) with an adaptive threshold shrinkage method for low-rank and sparse decomposition, the AoP of the backscattering is obtained. Moreover, according to the low-rank component of the AoP, the Degree of Linear Polarization (DoLP) of backscattering can be effectively and automatically estimated without considering whether the background region exists, relying on a frequency prior strategy. Finally, the degraded image is recovered utilizing underwater polarization imaging model. Extensive experimental results demonstrate that the recovered images from the proposed method have abundant detail, high contrast, and minimal color distortion, which is competitive with most state-of-the-art methods.

Anomaly Detection for Charging Voltage Profiles in Battery Cells in an Energy Storage Station Based on Robust Principal Component Analysis

Lithium-ion batteries, with their high energy density, long cycle life, and non-polluting advantages, are widely used in energy storage stations. Connecting lithium batteries in series to form a battery pack can achieve the required capacity and voltage. However, as the batteries are used for extended periods, some individual cells in the battery pack may experience abnormal failures, affecting the performance and safety of the battery pack. At the same time, as batteries operate in complex environments, the data collected by sensors are susceptible to random noise and drift interference, which can affect the accuracy of anomaly detection in individual battery cells. In order to solve this problem, this article proposes an anomaly detection method for battery cells based on Robust Principal Component Analysis (RPCA), taking the historical operation and maintenance data of a large-scale battery pack from an energy storage station as the research subject. Firstly, theRPCA is used to denoise the observed voltage data of the battery cells to an extreme degree, obtaining a baseline charging state curve for a cell consistency assessment. This also solves the problem of sensor outputs being affected by random noise. To further detect and identify abnormal battery cells, the RPCA is used to extract outlier components. Based on the Average Deviation-3σ principle and by utilizing Gaussian distribution probability characteristics, battery cells are conducted to screen, and the serial numbers of the anomaly cells are obtained. Finally, the effectiveness and accuracy of this anomaly detection method for battery cells are compared and verified through different statistical distributions.

Multivariate statistical analysis and bespoke deviation network modeling for geochemical anomaly detection of rare earth elements

Rare earth elements (REEs), a significant subset of critical minerals, play an indispensable role in modern society and are regarded as “industrial vitamins,” making them crucial for global sustainability. Geochemical survey data proves highly effective in delineating metallic mineral prospects. Separating geochemical anomalies associated with specific types of mineralization from the background reflecting geological processes has long been a significant subject in exploration geochemistry. The processing of high-dimensional, non-linear geochemical survey data necessitates a systematic framework to address common issues, including missing values, the closure effect, the selection of appropriate multivariate analysis methods, and anomaly detection techniques in order to detect geochemical anomalies associated with mineral occurrences. The Curnamona Province in South Australia is considered an emerging REE province with significant REE mineralization potential. In this study, we use data from this region to evaluate the performance of a novel machine learning-based framework that incorporates data pre-processing, multivariate statistical analysis, and anomaly recognition to address challenges such as missing data, noise interference, data imbalance and high non-linearity. We utilize lithogeochemical data to map potential greenfield regions of REE mineralization. The primary advantages of our framework lie in its provision of an effective random forest-based data imputation method, utilization of isometric log-ratio transformation to eliminate the closure effect, and reduction of the impact of outliers on data interpretation through robust principal component analysis. Additionally, the framework utilizes a deviation network to learn anomaly scores from complex, non-linear data under imbalanced data conditions, identifying geochemical anomalies associated with REE occurrences by leveraging prior knowledge rather than those caused by data noise or anthropogenic factors. The anomalous areas identified by this framework delineate all known REE deposits and extend to the surrounding regions. Furthermore, a close spatial coupling relationship exists between these strongly anomalous areas and the felsic granite intrusions. The comprehensive workflow for processing geochemical data proposed in this study can effectively address common challenges in the geochemical exploration of critical minerals. The identified geochemical anomalies can provide important clues for subsequent exploration.

High-Resolution Identification of Sound Sources Based on Sparse Bayesian Learning with Grid Adaptive Split Refinement

Sound source identification technology based on a microphone array has many application scenarios. The compressive beamforming method has attracted much attention due to its high accuracy and high-resolution performance. However, for the far-field measurement problem of large microphone arrays, existing methods based on fixed grids have the defect of basis mismatch. Due to the large number of grid points representing potential sound source locations, the identification accuracy of traditional grid adjustment methods also needs to be improved. To solve this problem, this paper proposes a sound source identification method based on adaptive grid splitting and refinement. First, the initial source locations are obtained through a sparse Bayesian learning framework. Then, higher-weight candidate grids are retained, and local regions near them are split and updated. During the iteration process, Green’s function and the source strength obtained in the previous iteration are multiplied to get the sound pressure matrix. The robust principal component analysis model of the Gaussian mixture separates and replaces the sound pressure matrix with a low-rank matrix. The actual sound source locations are gradually approximated through the dynamically adjusted sound pressure low-rank matrix and optimized grid transfer matrix. The performance of the method is verified through numerical simulations. In addition, experiments on a standard aircraft model are conducted in a wind tunnel and speakers are installed on the model, proving that the proposed method can achieve fast, high-precision imaging of low-frequency sound sources in an extensive dynamic range at long distances.

Damage Identification of Plate Structures Based on a Non-Convex Approximate Robust Principal Component Analysis

Damage Identification of Plate Structures Based on a Non-Convex Approximate Robust Principal Component Analysis

Bayesian Dictionary Learning on Robust Tubal Transformed Tensor Factorization.

The recent study on tensor singular value decomposition (t-SVD) that performs the Fourier transform on the tubes of a third-order tensor has gained promising performance on multidimensional data recovery problems. However, such a fixed transformation, e.g., discrete Fourier transform and discrete cosine transform, lacks being self-adapted to the change of different datasets, and thus, it is not flexible enough to exploit the low-rank and sparse property of the variety of multidimensional datasets. In this article, we consider a tube as an atom of a third-order tensor and construct a data-driven learning dictionary from the observed noisy data along the tubes of the given tensor. Then, a Bayesian dictionary learning (DL) model with tensor tubal transformed factorization, aiming to identify the underlying low-tubal-rank structure of the tensor effectively via the data-adaptive dictionary, is developed to solve the tensor robust principal component analysis (TRPCA) problem. With the defined pagewise tensor operators, a variational Bayesian DL algorithm is established and updates the posterior distributions instantaneously along the third dimension to solve the TPRCA. Extensive experiments on real-world applications, such as color image and hyperspectral image denoising and background/foreground separation problems, demonstrate both effectiveness and efficiency of the proposed approach in terms of various standard metrics.