In this paper, we propose a very simple and elegant patch-based, machine learning technique for image denoising using the higher order singular value decomposition (HOSVD). The technique simply ...groups together similar patches from a noisy image (with similarity defined by a statistically motivated criterion) into a 3D stack, computes the HOSVD coefficients of this stack, manipulates these coefficients by hard thresholding, and inverts the HOSVD transform to produce the final filtered image. Our technique chooses all required parameters in a principled way, relating them to the noise model. We also discuss our motivation for adopting the HOSVD as an appropriate transform for image denoising. We experimentally demonstrate the excellent performance of the technique on grayscale as well as color images. On color images, our method produces state-of-the-art results, outperforming other color image denoising algorithms at moderately high noise levels. A criterion for optimal patch-size selection and noise variance estimation from the residual images (after denoising) is also presented.
Tensors or multiway arrays are functions of three or more indices (i, j, k, . . . )-similar to matrices (two-way arrays), which are functions of two indices (r, c) for (row, column). Tensors have a ...rich history, stretching over almost a century, and touching upon numerous disciplines; but they have only recently become ubiquitous in signal and data analytics at the confluence of signal processing, statistics, data mining, and machine learning. This overview article aims to provide a good starting point for researchers and practitioners interested in learning about and working with tensors. As such, it focuses on fundamentals and motivation (using various application examples), aiming to strike an appropriate balance of breadth and depth that will enable someone having taken first graduate courses in matrix algebra and probability to get started doing research and/or developing tensor algorithms and software. Some background in applied optimization is useful but not strictly required. The material covered includes tensor rank and rank decomposition; basic tensor factorization models and their relationships and properties (including fairly good coverage of identifiability); broad coverage of algorithms ranging from alternating optimization to stochastic gradient; statistical performance analysis; and applications ranging from source separation to collaborative filtering, mixture and topic modeling, classification, and multilinear subspace learning.
Featured Cover Sung, Dongsuk; Risk, Benjamin B.; Owusu‐Ansah, Maame ...
NMR in biomedicine,
July 2020, 2020-07-00, 20200701, Letnik:
33, Številka:
7
Journal Article
Recenzirano
The cover image is based on the Research Article Optimized truncation to integrate multi–channel MRS data using rank–R singular value decompositionOptimized truncation to integrate multi–channel MRS ...data using rank–R singular value decomposition Dongsuk Sung et al., https://doi.org/10.1002/nbm.4297.
Pruning is a very effective solution to alleviate the difficulty of deploying neural networks on resource-constrained devices. However, most of the existing methods focus on the inherent parameters ...of the network itself, but rarely consider the contribution of the output feature map. In this paper, we propose the FPC, a novel filter pruning method based on the contribution of the output feature map, which considers the diverse information carried by different output feature maps. According to the above characteristic, FPC can evaluate the contribution of output feature maps and then effectively delete low contribution part without reducing the performance of the model. In this paper, we firstly use Singular Value Decomposition (SVD) to decompose the output feature map. Then we analyze the contribution of the output feature map to the model performance. Finally, we delete the filters with lower contribution output feature maps. Extensive experimental results show that our proposed FPC can produce excellent compression results. For example, with VGG-16, we can reduce the FLOPs by 65.62% and increase the accuracy by 0.25% on CIFAR-10. With ResNet-110, we can reduce FLOPs by 50.66% and increase the accuracy by 0.09% on CIFAR-100.
•The reason for the failure of traditional SVD denoising is investigated.•PMI is proposed to quantity the informativeness of a mechanical signal.•RSVD can extract weak fault feature under large ...interferences and noise.•The performance is validated by denoising sound and vibration signals.
Singular value decomposition (SVD), as an effective signal denoising tool, has been attracting considerable attention in recent years. The basic idea behind SVD denoising is to preserve the singular components (SCs) with significant singular values. However, it is shown that the singular values mainly reflect the energy of decomposed SCs, therefore traditional SVD denoising approaches are essentially energy-based, which tend to highlight the high-energy regular components in the measured signal, while ignoring the weak feature caused by early fault. To overcome this issue, a reweighted singular value decomposition (RSVD) strategy is proposed for signal denoising and weak feature enhancement. In this work, a novel information index called periodic modulation intensity is introduced to quantify the diagnostic information in a mechanical signal. With this index, the decomposed SCs can be evaluated and sorted according to their information levels, rather than energy. Based on that, a truncated linear weighting function is proposed to control the contribution of each SC in the reconstruction of the denoised signal. In this way, some weak but informative SCs could be highlighted effectively. The advantages of RSVD over traditional approaches are demonstrated by both simulated signals and real vibration/acoustic data from a two-stage gearbox as well as train bearings. The results demonstrate that the proposed method can successfully extract the weak fault feature even in the presence of heavy noise and ambient interferences.
Recently, tensor Singular Value Decomposition (t-SVD)-based low-rank tensor completion (LRTC) has achieved unprecedented success in addressing various pattern analysis issues. However, existing ...studies mostly focus on third-order tensors while order-<inline-formula> <tex-math notation="LaTeX">d </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">d\geq 4 </tex-math></inline-formula>) tensors are commonly encountered in real-world applications, like fourth-order color videos, fourth-order hyper-spectral videos, fifth-order light-field images, and sixth-order bidirectional texture functions. Aiming at addressing this critical issue, this paper establishes an order-<inline-formula> <tex-math notation="LaTeX">d </tex-math></inline-formula> tensor recovery framework including the model, algorithm and theories by innovatively developing a novel algebraic foundation for order-<inline-formula> <tex-math notation="LaTeX">d </tex-math></inline-formula> t-SVD, thereby achieving exact completion for any order-<inline-formula> <tex-math notation="LaTeX">d </tex-math></inline-formula> low t-SVD rank tensors with missing values with an overwhelming probability. Emperical studies on synthetic data and real-world visual data illustrate that compared with other state-of-the-art recovery frameworks, the proposed one achieves highly competitive performance in terms of both qualitative and quantitative metrics. In particular, as the observed data density becomes low, i.e., about 10%, the proposed recovery framework is still significantly better than its peers. The code of our algorithm is released at https://github.com/Qinwenjinswu/TIP-Code
Purpose
To obtain high‐sensitivity CEST maps by exploiting the spatiotemporal correlation between CEST images.
Methods
A postprocessing method accomplished by multilinear singular value decomposition ...(MLSVD) was used to enhance the CEST SNR by exploiting the correlation between the Z‐spectrum for each voxel and the low‐rank property of the overall CEST data. The performance of this method was evaluated using CrCEST in ischemic mouse brain at 11.7 tesla. Then, MLSVD CEST was applied to obtain Cr, amide, and amine CEST maps of the ischemic mouse brain to demonstrate its general applications.
Results
Complex‐valued Gaussian noise was added to CEST k‐space data to mimic a low SNR situation. MLSVD CEST analysis was able to suppress the noise, recover the degraded CEST peak, and provide better CrCEST quality compared to the smoothing and singular value decomposition (SVD)‐based denoising methods. High‐resolution Cr, amide, and amine CEST maps of an ischemic stroke using MLSVD CEST suggest that CrCEST is also a sensitive pH mapping method, and a wide range of pH changes can be detected by combing CrCEST with amine CEST at high magnetic fields.
Conclusion
MLSVD CEST provides a simple and efficient way to improve the SNR of CEST images.
Choosing suitable load indexes of load profiles is of vital importance for load profiles clustering, which has wide applications in load forecasting, power grid planning and electricity price ...designing. To obtain a set of load indexes with rigorous mathematical theory and clear physical meaning, this study proposed a singular value decomposition (SVD) based method to extract indexes. First, empirical rank-l approximation derived from SVD is proposed to extract load indexes. The relationship between singular values and relative approximation error guarantees the indexes retain major characteristics of load profiles, while the invariance of right singular vectors over seasons and sample sizes endows the indexes with good generalisation ability. Then the right singular vectors are discretised to determine definition of indexes and reveal physical meanings of the indexes. Finally, the new set of indexes extracted by the proposed method are applied in indirectly clustering in the case study, which verify the validity of the indexes, the performance of the clustering method and the advantages of the new indexes over the existing load shape indexes.
A reversible image-hiding algorithm based on a novel chaotic system is proposed using compressive sensing (CS) and singular value sampling (SVS) techniques. In the first stage, a novel mathematical ...model is constructed to extract the plain messages from the secret plain image, and the public-key Rivest–Shamir–Adleman (RSA) algorithm is adopted to encrypt these messages, obtaining the corresponding cipher messages. Then, another mathematical model of key transformation is constructed to transform above messages into the initial keys, which is used to produce a random key stream. In the second stage, the secret plain image is scrambled by a pre-encryption operation, and the corresponding singular values are obtained by singular value decomposition (SVD). Then, these values are partitioned, and zero blocks are identified and removed. Thereafter, the singular values of the blocks with non-zero elements are sampled by CS, with filled by zero elements again. In the third stage, high energy coefficients are removed and replaced by zero elements to obtain new sampling values. Then, the carrier image is processed by discrete wavelet transform (DWT). Next, new sampling values are embedded into the wavelet coefficients, and the inverse DWT is performed. Thus, a new carrier image containing the secrets is obtained. The advantages are: (1) A new chaotic system ImpTDCS is proposed to have a better behavior. (2) A novel model EMM is built to extract plain messages from secret image. (3) Multi-images can be embedded, which can hide more secret information each time. (4) SVD is operated followed by SVS on non-zero blocks, reducing transmission bandwidth. (5) High energy coefficients of SVS are removed before embedding operation, guaranteeing effectively the visual quality of carrier image containing secrets.
•A new chaotic system ImpTDCS is proposed to have a better behavior.•A novel model EMM is built to extract plain messages from secret image.•Multi-images can be embedded, with high energy coefficients of SVS removed.
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