L1-Norm Higher-Order Orthogonal Iterations for Robust Tensor Analysis

Chachlakis, Dimitris G.; Prater-Bennette, Ashley; Markopoulos, Panos P.

doi:10.1109/icassp40776.2020.9053701

Cited by 9 publications

(4 citation statements)

References 22 publications

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“…The method achieved higher precision and faster speed. Chachlakis et al (2020) presented an L1-norm HOOI algorithm and achieved better data reconstruction and classification results.…”

Section: Tucker Decompositionmentioning

confidence: 99%

Improved Tucker decomposition algorithm for noise suppression of 3D GPR data in road detection

Yan

Zhang

2023

Near Surface Geophysics

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The echo data of ground‐penetrating radar (GPR) have a low signal‐to‐noise ratio. Denoising and interference suppression are important for improving the accuracy of underground target recognition and detection. In this paper, a new method of noise analysis and suppression of 3D GPR is proposed, transforming the problem of noise reduction into an optimization problem regarding a third‐order tensor. This method is improved with the following features; a bidimensional empirical mode decomposition (BEMD) algorithm is employed to decompose the 3D GPR noise. The main source of the noise is determined by computing the standard deviation of each component decomposed. For the shortcoming of the existing GPR denoising methods that reduce the dimension of 3D GPR data, the proposed approach can denoise 3D GPR data directly to avoid the loss of data caused by reducing the dimension. This preserves the desired signal and extracts noise through the Tucker decomposition of 3D GPR data. An improved high‐order orthogonal iteration algorithm is utilized to optimize the decomposition. The peak signal‐to‐noise ratio (PSNR) of the signal for each survey line is calculated to evaluate the effectiveness of noise reduction. Simulations and real data sets are provided to compare the performance of algorithms. The results show that the mean PSNR after noise suppression with our method is 8.915 dB and 16.458 dB higher than wavelet transform and singular value decomposition algorithms, respectively. This demonstrates that the proposed approach can better suppress 3D GPR noise and provides technical support for improving 3D GPR data quality and road detection accuracy.

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“…The method achieved higher precision and faster speed. Chachlakis et al (2020) presented an L1-norm HOOI algorithm and achieved better data reconstruction and classification results.…”

Section: Tucker Decompositionmentioning

confidence: 99%

Improved Tucker decomposition algorithm for noise suppression of 3D GPR data in road detection

Yan

Zhang

2023

Near Surface Geophysics

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“…As mentioned in Section IV-B, the CP and Tucker decompositions are approximated in practice by minimizing the leastsquares criterion, resulting in algorithms sensitive to sparse, non-Gaussian noise. To alleviate this problem and obtain more robust approximations of tensor decompositions [102], [103], [94] replace least-squares loss with the 1 -norm.…”

Section: Robust Tensor Decompositionmentioning

confidence: 99%

Tensor Methods in Computer Vision and Deep Learning

et al. 2021

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Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a long history of applications in a wide span of computer vision problems. With the advent of the deep learning paradigm shift in computer vision, tensors have become even more fundamental. Indeed, essential ingredients in modern deep learning architectures, such as convolutions and attention mechanisms, can readily be considered as tensor mappings. In effect, tensor methods are increasingly finding significant applications in deep learning, including the design of memory and compute efficient network architectures, improving robustness to random noise and adversarial attacks, and aiding the theoretical understanding of deep networks.This article provides an in-depth and practical review of tensors and tensor methods in the context of representation learning and deep learning, with a particular focus on visual data analysis and computer vision applications. Concretely, besides fundamental work in tensor-based visual data analysis methods, we focus on recent developments that have brought on a gradual increase of tensor methods, especially in deep learning architectures, and their implications in computer vision applications. To further enable the newcomer to grasp such concepts quickly, we provide companion Python notebooks, covering key aspects of the paper and implementing them, step-by-step with TensorLy.

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“…On the other hand, L1-HOOI is an iterative process that provably attains a higher L1-Tucker metric when initialized at the solution of L1-HOSVD [22,34]. Initialized at {Q n,0 } n∈[N ] (typically by means of L1-HOSVD), at every iteration i ≥ 1, L1-HOOI updates Q n,i by solving max.…”

Section: Outliers and L1-tuckermentioning

confidence: 99%

Dynamic L1-Norm Tucker Tensor Decomposition

Chachlakis

Dhanaraj

Prater-Bennette

et al. 2021

IEEE J. Sel. Top. Signal Process.

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Tucker decomposition is a standard method for processing multi-way (tensor) measurements and finds many applications in machine learning and data mining, among other fields. When tensor measurements arrive in a streaming fashion or are too many to jointly decompose, incremental Tucker analysis is preferred. In addition, dynamic basis adaptation is desired when the nominal data subspaces change. At the same time, it has been documented that outliers in the data can significantly compromise the performance of existing methods for dynamic Tucker analysis. In this work, we present Dynamic L1-Tucker: an algorithm for dynamic and outlier-resistant Tucker analysis of tensor data. Our experimental studies on both real and synthetic datasets corroborate that the proposed method (i) attains high basis estimation performance, (ii) identifies/rejects outliers, and (iii) adapts to nominal subspace changes.

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L1-Norm Higher-Order Orthogonal Iterations for Robust Tensor Analysis

Cited by 9 publications

References 22 publications

Improved Tucker decomposition algorithm for noise suppression of 3D GPR data in road detection

Improved Tucker decomposition algorithm for noise suppression of 3D GPR data in road detection

Tensor Methods in Computer Vision and Deep Learning

Dynamic L1-Norm Tucker Tensor Decomposition

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