Multidimensional Harmonic Retrieval via Coupled Canonical Polyadic Decomposition—Part I: Model and Identifiability

Mikael Sørensen; Lieven De Lathauwer

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Multidimensional Harmonic Retrieval via Coupled Canonical Polyadic Decomposition—Part I: Model and Identifiability

机译：通过耦合规范多态分解进行多维谐波检索—第一部分：模型和可识别性

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Multidimensional Harmonic Retrieval (MHR) is a fundamental problem in signal processing. We make a connection with coupled Canonical Polyadic Decomposition (CPD), which allows us to better exploit the rich MHR structure than existing approaches in the derivation of uniqueness results. We discuss both deterministic and generic conditions. We obtain a deterministic condition that is both necessary and sufficient but which may be difficult to check in practice. We derive mild deterministic relaxations that are easy to verify. We also discuss the variant in which the generators have unit norm. We narrow the transition zone between generic uniqueness and generic non-uniqueness to two values of the number of harmonics. We explain differences with one-dimensional HR.

机译：多维谐波检索（MHR）是信号处理中的一个基本问题。我们将其与经典多态分解（CPD）结合在一起，这使我们在推导唯一性结果时比现有方法更好地利用丰富的MHR结构。我们讨论确定性条件和通用条件。我们获得的确定性条件既必要又充分，但是在实践中可能很难检查。我们得出易于验证的轻度确定性松弛。我们还将讨论生成器具有单位范数的变体。我们将通用唯一性和通用非唯一性之间的过渡区域缩小为两个谐波数量值。我们用一维HR解释差异。

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来源
《IEEE Transactions on Signal Processing》 |2017年第2期|517-527|共11页
作者
Mikael Sørensen; Lieven De Lathauwer;
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作者单位

Department of Electrical Engineering, ESAT-STADIUS Center for Dynamical Systems, Signal Processing, and Data Analytics, Katholieke Universiteit Leuven Leuven, Belgium;

Department of Electrical Engineering, ESAT-STADIUS Center for Dynamical Systems, Signal Processing, and Data Analytics, Katholieke Universiteit Leuven Leuven, Belgium;

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正文语种 eng
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Tensile stress; Harmonic analysis; Matrix decomposition; Antenna arrays; Writing; Indexes;

机译：拉伸应力谐波分析矩阵分解天线阵写作索引;

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专利

1. Multidimensional Harmonic Retrieval via Coupled Canonical Polyadic Decomposition—Part II: Algorithm and Multirate Sampling [J] . Mikael Sørensen, Lieven De Lathauwer IEEE Transactions on Signal Processing . 2017,第2期

机译：通过耦合规范多Adadic分解进行多维谐波检索—第二部分：算法和多速率采样
2. COUPLED CANONICAL POLYADIC DECOMPOSITIONS AND (COUPLED) DECOMPOSITIONS IN MULTILINEAR RANK-(Lr,n, Lr,n, 1) TERMS-PART I: UNIQUENESS [J] . Sorensen Mikael, De Lathauwer Lieven SIAM Journal on Matrix Analysis and Applications . 2015,第2期

机译：多线性级中的耦合规范聚分解和（耦合）分解-（Lr，n，Lr，n，1）术语第一部分：唯一性
3. COUPLED CANONICAL POLYADIC DECOMPOSITIONS AND ( COUPLED) DECOMPOSITIONS IN MULTILINEAR RANK-(Lr,n, Lr,n, 1) TERMS-PART II: ALGORITHMS [J] . Sorensen Mikael, Domanov Ignat, De Lathauwer Lieven SIAM Journal on Matrix Analysis and Applications . 2015,第3期

机译：多线性秩的耦合规范聚分解和（耦合）分解-（Lr，n，Lr，n，1）术语第二部分：算法
4. Multidimensional ESPRIT: A coupled canonical polyadic decomposition approach [C] . Sorensen Mikael, De Lathauwer Lieven IEEE Sensor Array and Multichannel Signal Processing Workshop . 2014

机译：多维ESPRIT：耦合规范多态分解方法
5. Parallel Algorithms for Computing and Applications of the Dense Canonical Polyadic Decomposition [D] . Hayashi, Koby B. 2018

机译：用于计算和应用的并行算法和致密的规范多adic分解
6. A Joint Fault Diagnosis Scheme Based on Tensor Nuclear Norm Canonical Polyadic Decomposition and Multi-Scale Permutation Entropy for Gears [O] . Mao Ge, Yong Lv, Cancan Yi, 2018

机译：基于张量核规范规范多差分解和齿轮多尺度排列熵的关节故障诊断方案
7. Multidimensional Harmonic Retrieval via Coupled Canonical Polyadic Decomposition - Part I: Model and Identifiability [O] . Sorensen Mikael, De Lathauwer Lieven 2017

机译：通过耦合规范多态分解进行多维谐波检索-第一部分：模型和可识别性
8. When are Overcomplete Topic Models Identifiable? Uniqueness of Tensor Tucker Decompositions with Structured Sparsity. [R] . Anandkumar, A., Hsu, D., Janzamin, M., 2013

机译：何时超完整主题模型可识别？具有结构稀疏性的Tensor Tucker分解的唯一性。

Multidimensional Harmonic Retrieval via Coupled Canonical Polyadic Decomposition—Part I: Model and Identifiability

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