Robust Low-rank Tensor Decomposition with the
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ABSTRACT:
SUBMITTER: Heng Q
PROVIDER: S-EPMC10783176 | biostudies-literature | 2023 Jan
REPOSITORIES: biostudies-literature
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Project description:We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multi-scale low rank components either exactly or approximately. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering exploiting age information.
| S-EPMC5403160 | biostudies-literature
Project description:ObjectiveIdentification of networks from resting brain signals is an important step in understanding the dynamics of spontaneous brain activity. We approach this problem using a tensor-based model.MethodsWe develop a rank-recursive scalable and robust sequential canonical polyadic decomposition (SRSCPD) framework to decompose a tensor into several rank-1 components. Robustness and scalability are achieved using a warm start for each rank based on the results from the previous rank.ResultsIn simulations we show that SRSCPD consistently outperforms the multi-start alternating least square (ALS) algorithm over a range of ranks and signal-to-noise ratios (SNRs), with lower computation cost. When applying SRSCPD to resting in-vivo stereotactic EEG (SEEG) data from two subjects with epilepsy, we found components corresponding to default mode and motor networks in both subjects. These components were also highly consistent within subject between two sessions recorded several hours apart. Similar components were not obtained using the conventional ALS algorithm.ConclusionConsistent brain networks and their dynamic behaviors were identified from resting SEEG data using SRSCPD.SignificanceSRSCPD is scalable to large datasets and therefore a promising tool for identification of brain networks in long recordings from single subjects.
| S-EPMC6677658 | biostudies-literature
Project description:PurposeWe propose and evaluate a new structured low-rank method for echo-planar imaging (EPI) ghost correction called Robust Autocalibrated LORAKS (RAC-LORAKS). The method can be used to suppress EPI ghosts arising from the differences between different readout gradient polarities and/or the differences between different shots. It does not require conventional EPI navigator signals, and is robust to imperfect autocalibration data.MethodsAutocalibrated LORAKS is a previous structured low-rank method for EPI ghost correction that uses GRAPPA-type autocalibration data to enable high-quality ghost correction. This method works well when the autocalibration data are pristine, but performance degrades substantially when the autocalibration information is imperfect. RAC-LORAKS generalizes Autocalibrated LORAKS in two ways. First, it does not completely trust the information from autocalibration data, and instead considers the autocalibration and EPI data simultaneously when estimating low-rank matrix structure. Second, it uses complementary information from the autocalibration data to improve EPI reconstruction in a multi-contrast joint reconstruction framework. RAC-LORAKS is evaluated using simulations and in vivo data, including comparisons to state-of-the-art methods.ResultsRAC-LORAKS is demonstrated to have good ghost elimination performance compared to state-of-the-art methods in several complicated EPI acquisition scenarios (including gradient-echo brain imaging, diffusion-encoded brain imaging, and cardiac imaging).ConclusionsRAC-LORAKS provides effective suppression of EPI ghosts and is robust to imperfect autocalibration data.
| S-EPMC8820934 | biostudies-literature
Project description:BackgroundEpistatic miniarray profile (EMAP) studies have enabled the mapping of large-scale genetic interaction networks and generated large amounts of data in model organisms. One approach to analyze EMAP data is to identify gene modules with densely interacting genes. In addition, genetic interaction score (S score) reflects the degree of synergizing or mitigating effect of two mutants, which is also informative. Statistical approaches that exploit both modularity and the pairwise interactions may provide more insight into the underlying biology. However, the high missing rate in EMAP data hinders the development of such approaches. To address the above problem, we adopted the matrix decomposition methodology "low-rank and sparse decomposition" (LRSDec) to decompose EMAP data matrix into low-rank part and sparse part.ResultsLRSDec has been demonstrated as an effective technique for analyzing EMAP data. We applied a synthetic dataset and an EMAP dataset studying RNA-related processes in Saccharomyces cerevisiae. Global views of the genetic cross talk between different RNA-related protein complexes and processes have been structured, and novel functions of genes have been predicted.
| S-EPMC4529927 | biostudies-literature
Project description:Identifying the association and corresponding types of miRNAs and diseases is crucial for studying the molecular mechanisms of disease-related miRNAs. Compared to traditional biological experiments, computational models can not only save time and reduce costs, but also discover potential associations on a large scale. Although some computational models based on tensor decomposition have been proposed, these models usually require manual specification of numerous hyperparameters, leading to a decrease in computational efficiency and generalization ability. Additionally, these linear models struggle to analyze complex, higher-order nonlinear relationships. Based on this, we propose a novel framework, KBLTDARD, to identify potential multiple types of miRNA-disease associations. Firstly, KBLTDARD extracts information from biological networks and high-order association network, and then fuses them to obtain more precise similarities of miRNAs (diseases). Secondly, we combine logistic tensor decomposition and Bayesian methods to achieve automatic hyperparameter search by introducing sparse-induced priors of multiple latent variables, and incorporate auxiliary information to improve prediction capabilities. Finally, an efficient deterministic Bayesian inference algorithm is developed to ensure computational efficiency. Experimental results on two benchmark datasets show that KBLTDARD has better Top-1 precision, Top-1 recall, and Top-1 F1 for new type predictions, and higher AUPR, AUC, and F1 values for new triplet predictions, compared to other state-of-the-art methods. Furthermore, case studies demonstrate the efficiency of KBLTDARD in predicting multiple types of miRNA-disease associations.
| S-EPMC11257412 | biostudies-literature
Project description:The goals of fMRI acquisition include high spatial and temporal resolutions with a high signal to noise ratio (SNR). Oscillating Steady-State Imaging (OSSI) is a new fMRI acquisition method that provides large oscillating signals with the potential for high SNR, but does so at the expense of spatial and temporal resolutions. The unique oscillation pattern of OSSI images makes it well suited for high-dimensional modeling. We propose a patch-tensor low-rank model to exploit the local spatial-temporal low-rankness of OSSI images. We also develop a practical sparse sampling scheme with improved sampling incoherence for OSSI. With an alternating direction method of multipliers (ADMM) based algorithm, we improve OSSI spatial and temporal resolutions with a factor of 12 acquisition acceleration and 1.3 mm isotropic spatial resolution in prospectively undersampled experiments. The proposed model yields high temporal SNR with more activation than other low-rank methods. Compared to the standard grad- ient echo (GRE) imaging with the same spatial-temporal resolution, 3D OSSI tensor model reconstruction demonstrates 2 times higher temporal SNR with 2 times more functional activation.
| S-EPMC7751316 | biostudies-literature
Project description:PurposePropose a novel decomposition-based model employing the total generalized variation (TGV) and the nuclear norm, which can be used in compressed sensing-based dynamic MR reconstructions.Theory and methodsWe employ the nuclear norm to represent the time-coherent background and the spatiotemporal TGV functional for the sparse dynamic component above. We first design an algorithm using the classical first-order primal-dual method for solving the proposed model and then give the norm estimation for the convergence condition. The proposed model is compared with the state-of-the-art methods on different data sets under different sampling schemes and acceleration factors.ResultsThe proposed model achieves higher SERs and SSIMs than kt-SLR, kt-RPCA, L+S, and ICTGV on cardiac perfusion and breast DCE-MRI data sets under both the pseudoradial and the Cartesian sampling schemes. In addition, the proposed model better suppresses the spatial artifacts and preserves the edges.ConclusionsThe proposed model outperforms the state-of-the-art methods and generates high-quality reconstructions under different sampling schemes and different acceleration factors.
| S-EPMC7047634 | biostudies-literature
Project description:PurposeTo develop a rapid 31 P-MRSI method with high spatiospectral resolution using low-rank tensor-based data acquisition and image reconstruction.MethodsThe multidimensional image function of 31 P-MRSI is represented by a low-rank tensor to capture the spatial-spectral-temporal correlations of data. A hybrid data acquisition scheme is used for sparse sampling, which consists of a set of "training" data with limited k-space coverage to capture the subspace structure of the image function, and a set of sparsely sampled "imaging" data for high-resolution image reconstruction. An explicit subspace pursuit approach is used for image reconstruction, which estimates the bases of the subspace from the "training" data and then reconstructs a high-resolution image function from the "imaging" data.ResultsWe have validated the feasibility of the proposed method using phantom and in vivo studies on a 3T whole-body scanner and a 9.4T preclinical scanner. The proposed method produced high-resolution static 31 P-MRSI images (i.e., 6.9 × 6.9 × 10 mm3 nominal resolution in a 15-min acquisition at 3T) and high-resolution, high-frame-rate dynamic 31 P-MRSI images (i.e., 1.5 × 1.5 × 1.6 mm3 nominal resolution, 30 s/frame at 9.4T).ConclusionsDynamic spatiospectral variations of 31 P-MRSI signals can be efficiently represented by a low-rank tensor. Exploiting this mathematical structure for data acquisition and image reconstruction can lead to fast 31 P-MRSI with high resolution, frame-rate, and SNR. Magn Reson Med 78:419-428, 2017. © 2017 International Society for Magnetic Resonance in Medicine.
| S-EPMC5562044 | biostudies-literature
Project description:BackgroundCardiac T2 mapping is a valuable tool for diagnosing myocardial edema, inflammation, and infiltration, yet its spatial resolution is limited by the single-shot balanced steady-state free precession acquisition and duration of the cardiac quiescent period, which may reduce sensitivity in detecting focal lesions in the myocardium. To improve spatial resolution without extending the acquisition window, this study examined a novel accelerated Cartesian cardiac T2 mapping technique.MethodsWe introduce a novel improved-resolution cardiac T2 mapping approach leveraging a calibrationless space-contrast-coil locally low-rank tensor (SCC-LLRT)-constrained reconstruction algorithm in conjunction with Cartesian undersampling trajectory. The method was validated with phantom imaging and in vivo imaging that involved 13 healthy participants and 20 patients. The SCC-LLRT algorithm was compared with a conventional locally low-rank (LLR)-constrained algorithm and a nonlinear inversion (NLINV) reconstruction algorithm. The improved-resolution T2 mapping (1.4 mm × 1.4 mm) was compared globally and regionally with the regular-resolution T2 mapping (2.3 mm × 1.9 mm) according to the 16-segment model of the American Heart Association. The agreement between the improved-resolution and regular-resolution T2 mappings was evaluated by linear regression and Bland-Altman analyses. Image quality was scored by two experienced reviewers on a five-point scale (1, worst; 5, best).ResultsIn healthy participants, SCC-LLRT significantly reduced artifacts (4.50±0.39) compared with LLR (2.31±0.60; P<0.001) and NLINV (3.65±0.56; P<0.01), suppressed noise (4.12±0.35) compared with NLINV (2.65±0.50; P<0.001), and improved the overall image quality (4.38±0.40) compared with LLR (2.54±0.41; P<0.001) and NLINV (3.04±0.50; P<0.001). Compared with the regular-resolution T2 mapping, the proposed method significantly improved the sharpness of myocardial boundaries (4.46±0.60 vs. 3.04±0.50; P<0.001) and the conspicuity of papillary muscles and fine structures (4.46±0.63 vs. 2.65±0.30; P<0.001). Myocardial T2 values obtained with the proposed method correlated significantly with those from regular-resolution T2 mapping in both healthy participants (r=0.79; P<0.01) and patients (r=0.94; P<0.001).ConclusionsThe proposed SCC-LLRT-constrained reconstruction algorithm in conjunction with Cartesian undersampling pattern achieved improved-resolution cardiac T2 mapping of comparable accuracy, precision, and scan-rescan reproducibility compared with the regular-resolution T2 mapping. The higher resolution improved the sharpness of myocardial borders and the conspicuity of image fine details, which may increase diagnostic confidence in cardiac T2 mapping for detecting small lesions.
| S-EPMC11485370 | biostudies-literature
Project description:PurposeTo evaluate an algorithm for calibrationless parallel imaging to reconstruct undersampled parallel transmit field maps for the body and brain.MethodsUsing a combination of synthetic data and in vivo measurements from brain and body, 3 different approaches to a joint transmit and receive low-rank tensor completion algorithm are evaluated. These methods included: 1) virtual coils using the product of receive and transmit sensitivities, 2) joint-receiver coils that enforces a low rank structure across receive coils of all transmit modes, and 3) transmit low rank that uses a low rank structure for both receive and transmit modes simultaneously. The performance of each is investigated for different noise levels and different acceleration rates on an 8-channel parallel transmit 7 Tesla system.ResultsThe virtual coils method broke down with increasing noise levels or acceleration rates greater than 2, producing normalized RMS error greater than 0.1. The joint receiver coils method worked well up to acceleration factors of 4, beyond which the normalized RMS error exceeded 0.1. Transmit low rank enabled an eightfold acceleration, with most normalized RMS errors remaining below 0.1.ConclusionThis work demonstrates that undersampling factors of up to eightfold are feasible for transmit array mapping and can be reconstructed using calibrationless parallel imaging methods.
| S-EPMC7611890 | biostudies-literature