Identification of Sparse Linear Operators
Identification of Sparse Linear Operators
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稀疏线性算子的辨识
DOI：
10.1109/tit.2013.2280599
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发表时间：
2012
影响因子：
2.5
通讯作者：
H. Bölcskei
中科院分区：
文献类型：
--
作者：
Reinhard Heckel;H. Bölcskei
我们考虑了从线性确定性算子对给定探测信号的响应来识别该算子的问题。对于一大类线性算子，我们证明了如果算子的扩展函数的总支撑面积满足Δ≤1/2，则稳定可辨识性是可能的。这一结果对扩展函数的任意(可能是分段的)支撑区域成立，不对支撑区域的总范围施加限制，最重要的是，不要求在识别之前已知支撑区域。此外，我们证明了当Δ；lt；；1时，几乎所有算子的稳定可辨识性都是可能的。这一结果令人惊讶，因为它表明在辨认之前不存在不知道扩展函数的支撑域的惩罚。给出了可证明恢复所有Δ≤为1/2的算子和几乎所有Δ为1的算子的算法。
We consider the problem of identifying a linear deterministic operator from its response to a given probing signal. For a large class of linear operators, we show that stable identifiability is possible if the total support area of the operator's spreading function satisfies Δ ≤ 1/2. This result holds for an arbitrary (possibly fragmented) support region of the spreading function, does not impose limitations on the total extent of the support region, and, most importantly, does not require the support region to be known prior to identification. Furthermore, we prove that stable identifiability of almost all operators is possible if Δ <; 1. This result is surprising as it says that there is no penalty for not knowing the support region of the spreading function prior to identification. Algorithms that provably recover all operators with Δ ≤ 1/2, and almost all operators with Δ <; 1 are presented.
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影响因子：
1.2
作者：
G. E. Pfander.
通讯作者：
G. E. Pfander.
影响因子：
2.5
作者：
Davies, Mike E.;Eldar, Yonina C.
通讯作者：
Eldar, Yonina C.