Explore the vast range of titles available.

We present an alternative strategy for truncating the higher-order singular value decomposition (T-HOSVD). An error expression for an approximate Tucker decomposition with orthogonal factor matrices is presented, leading us to propose a novel truncation strategy for the HOSVD, which we refer to as the sequentially truncated higher-order singular value decomposition (ST-HOSVD). This decomposition retains several favorable properties of the T-HOSVD, while reducing the number of operations required to compute the decomposition and practically always improving the approximation error. Three applications are presented, demonstrating the effectiveness of ST-HOSVD. In the first application, ST-HOSVD, T-HOSVD, and higher-order orthogonal iteration (HOOI) are employed to compress a database of images of faces. On average, the ST-HOSVD approximation was only 0.1\\% worse than the optimum computed by HOOI, while cutting the execution time by a factor of 20. In the second application, classification of handwritten digits, ST-HOSVD achieved a speedup factor of 50 over T-HOSVD during the training phase, and reduced the classification time and storage costs, while not significantly affecting the classification error. The third application demonstrates the effectiveness of ST-HOSVD in compressing results from a numerical simulation of a partial differential equation. In such problems, ST-HOSVD inevitably can greatly improve the running time. We present an example wherein the 2 hour 45 minute calculation of T-HOSVD was reduced to just over one minute by ST-HOSVD, representing a speedup factor of 133, while even improving the memory consumption.

This report provides a global view of how gene expression is affected by DNA replication. We analyzed synchronized cultures of Saccharomyces cerevisiae under conditions that prevent DNA replication initiation without delaying cell cycle progression. We use a higher‐order singular value decomposition to integrate the global mRNA expression measured in the multiple time courses, detect and remove experimental artifacts and identify significant combinations of patterns of expression variation across the genes, time points and conditions. We find that, first, ∼88% of the global mRNA expression is independent of DNA replication. Second, the requirement of DNA replication for efficient histone gene expression is independent of conditions that elicit DNA damage checkpoint responses. Third, origin licensing decreases the expression of genes with origins near their 3′ ends, revealing that downstream origins can regulate the expression of upstream genes. This confirms previous predictions from mathematical modeling of a global causal coordination between DNA replication origin activity and mRNA expression, and shows that mathematical modeling of DNA microarray data can be used to correctly predict previously unknown biological modes of regulation. In this first global view of how DNA replication affects transcription, ∼88% of global gene expression is found to be independent of DNA replication, significantly lowering the recently measured upper bound to replication‐dependent mRNA expression. The requirement of DNA replication for efficient histone gene expression is found to be independent of conditions that elicit DNA damage checkpoint responses. Origin licensing is found to decrease expression of genes with origins near their 3′ ends, experimentally revealing for the first time that downstream origins can regulate the expression of upstream genes, and demonstrating that mathematical modeling of DNA microarray data can be used to correctly predict previously unknown biological modes of regulation. The recent analogy of the tensor higher‐order singular value decomposition (HOSVD) with the matrix singular value decomposition (SVD), which already enables the interpretation of the HOSVD in terms of the cellular states, biological processess and experimental artifacts that compose the data tensor, is extended by mathematically defining the operation of HOSVD data reconstruction, and by computationally using this operation to remove experimental artifacts from the data.

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions of higher-order tensors (i.e., N-way arrays with N ≥ 3) have applications in psychometrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

Cardiac cine magnetic resonance imaging (MRI) can be considered the optimal criterion for measuring cardiac function. This imaging technique can provide us with detailed information about cardiac structure, tissue composition and even blood flow, which makes it highly used in medical science. But due to the image time acquisition and several other factors the MRI sequences can easily get corrupted, causing radiologists to misdiagnose 40 million people worldwide each and every single year. Hence, the urge to decrease these numbers, researchers from different fields have been introducing novel tools and methods in the medical field. Aiming to the same target, we consider in this work the application of the higher order dynamic mode decomposition (HODMD) technique. The HODMD algorithm is a linear method, which was originally introduced in the fluid dynamics domain, for the analysis of complex systems. Nevertheless, the proposed method has extended its applicability to numerous domains, including medicine. In this work, HODMD in used to analyze sets of MR images of a heart, with the ultimate goal of identifying the main patterns and frequencies driving the heart dynamics. Furthermore, a novel interpolation algorithm based on singular value decomposition combined with HODMD is introduced, providing a three-dimensional reconstruction of the heart. This algorithm is applied (i) to reconstruct corrupted or missing images, and (ii) to build a reduced order model of the heart dynamics. •Data-driven method for analyzing MRI datasets taken from healthy and unhealthy mice.•Interpolation technique for the recovery of missing data in cardiac MRI.•Reduced order model providing new databases for 3D reconstructions of the heart.

Hyperspectral image (HSI) denoising can be implemented in a low-dimensional spectral subspace to utilize the high correlations across different bands and reduce the imposed computational burden, and subspace learning is a key strategy for achieving improved denoising performance. In the previously developed subspace-based HSI denoising methods, the subspace learning task is usually seriously deteriorated by noise or suffers from high computational costs, and subspace dimensionality determination has not been carefully and specifically studied for subspace denoising. In this paper, we propose a highly efficient HSI denoising method by developing a robust and adaptive subspace learning algorithm. Specifically, we introduce a semisequentially truncated higher-order singular value decomposition scheme for jointly performing basic estimation and learning a robust subspace basis, and the subspace dimensionality is adaptively detected by designing an appropriate information-theoretic criterion. Then we conduct noise reduction by applying a bandwise denoiser in the subspace since various subspace bands generally have significantly different noise levels. The applied bandwise denoiser can be a single-band deep learning method, which do not require hyperspectral training data when the hyperspectral training data are few in number and more difficult to obtain than single-band images. The proposed HSI denoising method is very fast and effective. Experimental results demonstrate that the proposed method can achieve state-of-the-art denoising performance.

An ultrasonic reverse time migration imaging method, based on high-order singular value decomposition, is proposed in the study to solve the problems of low signal-to-noise ratio (SNR) and excessive artifacts in defect ultrasonic detection imaging results of materials with high noise levels. In this method, based on the 3D structural properties of the ultrasonic full-matrix capture data, higher-order singular value decomposition is directly performed with the 3D data. The method overcomes the difficulty in selecting the number of singular values in the original singular value decomposition noise-reduction algorithm and realizes the one-step noise reduction processing of all the signals. Subsequently, the reverse time migration imaging is performed in the frequency domain, and high-quality acoustic images are obtained. The effects of the number of array elements, the center frequency of the excitation signal, and the number of defects on the denoising effect of the algorithm are investigated. It was experimentally demonstrated that the method could suppress the interference of noise signals and significantly improve the imaging SNR compared with total focusing method and the reverse time migration.

Noise usually affects the reliability of quantitative analysis in diffusion-weighted (DW) magnetic resonance imaging (MRI), especially at high b-values and/or high spatial resolution. Higher-order singular value decomposition (HOSVD) has recently emerged as a simple, effective, and adaptive transform to exploit sparseness within multidimensional data. In particular, the patch-based HOSVD denoising has demonstrated superb performance when applied to T1-, T2-, and proton density-weighted MRI data. In this study, we aim to investigate the feasibility of denoising DW data using the HOSVD transform. With the low signal-to-noise ratio in typical DW data, the patch-based HOSVD denoising suffers from stripe artifacts in homogeneous regions because of the HOSVD bases learned from the noisy patches. To address this problem, we propose a novel denoising method. It first introduces a global HOSVD-based denoising as a prefiltering stage to guide the subsequent patch-based HOSVD denoising stage. The HOSVD bases from the patch groups in prefiltered images are then used to transform the noisy patch groups in original DW data. Experiments were performed using simulated and in vivo DW data. Results show that the proposed method significantly reduces stripe artifacts compared with conventional patch-based HOSVD denoising methods, and outperforms two state-of-the-art denoising methods in terms of denoising quality and diffusion parameters estimation.

In this paper, we present a novel four-dimensional (4D) parameter estimation method to localize the mixed far-field (FF) and near-field (NF) targets using bistatic MIMO arrays and higher-order singular value decomposition (HOSVD). The estimated four parameters include the angle-of-departure (AOD), angle-of-arrival (AOA), range-of-departure (ROD), and range-of-arrival (ROA). In the method, we store array data in a tensor form to preserve the inherent multidimensional properties of the array data. First, the observation data are arranged into a third-order tensor and its covariance tensor is calculated. Then, the HOSVD of the covariance tensor is performed. From the left singular vector matrices of the corresponding module expansion of the covariance tensor, the subspaces with respect to transmit and receive arrays are obtained, respectively. The AOD and AOA of the mixed FF and NF targets are estimated with signal-subspace, and the ROD and ROA of the NF targets are achieved using noise-subspace. Finally, the estimated four parameters are matched via a pairing method. The Cramér–Rao lower bound (CRLB) of the mixed target parameters is also derived. The numerical simulations demonstrate the superiority of the tensor-based method.