Identifiability of Kronecker-Structured Dictionaries for Tensor Data
Identifiability of Kronecker-Structured Dictionaries for Tensor Data
复制标题
DOI：
10.1109/jstsp.2018.2838092
复制
发表时间：
2017-12
影响因子：
7.5
通讯作者：
Z. Shakeri;A. Sarwate;W. Bajwa
中科院分区：
文献类型：
--
作者：
Z. Shakeri;A. Sarwate;W. Bajwa
本文推导了包含用于表示$K$ th阶张量数据的kronecker结构字典的坐标字典局部恢复的充分条件。张量观测假定是由kronecker结构字典乘以遵循可分离稀疏性模型的稀疏系数张量生成的。本文给出了底层坐标字典、系数分布和噪声分布以及保证单个坐标字典恢复到指定误差的样本数量的充分条件，作为目标函数的局部极小值，具有高概率。特别是，恢复维度为$m_k\times p_k$到估计误差$\varepsilon _k$的$K$坐标字典的样本复杂度显示为$\max _{k \in [K]}\mathcal {O}(m_kp_k^3\varepsilon _k^{-2})$。
This paper derives sufficient conditions for local recovery of coordinate dictionaries comprising a Kronecker-structured dictionary that is used for representing $K$ th-order tensor data. Tensor observations are assumed to be generated from a Kronecker-structured dictionary multiplied by sparse coefficient tensors that follow the separable sparsity model. This paper provides sufficient conditions on the underlying coordinate dictionaries, coefficient and noise distributions, and number of samples that guarantee recovery of the individual coordinate dictionaries up to a specified error, as a local minimum of the objective function, with high probability. In particular, the sample complexity to recover $K$ coordinate dictionaries with dimensions $m_k\times p_k$ up to estimation error $\varepsilon _k$ is shown to be $\max _{k \in [K]}\mathcal {O}(m_kp_k^3\varepsilon _k^{-2})$.