BranchHull: Convex bilinear inversion from the entrywise product of signals with known signs
BranchHull: Convex bilinear inversion from the entrywise product of signals with known signs
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DOI：
10.1016/j.acha.2019.03.002
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发表时间：
2020-09-01
影响因子：
2.5
通讯作者：
Joshi, Babhru
中科院分区：
文献类型：
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作者：
Aghasi, Alireza;Ahmed, Ali;Joshi, Babhru
我们考虑从R-L中的两个向量x和w的乘积恢复它们的双线性逆问题。对于向量具有已知符号且属于已知子空间的情况，我们引入凸程序BranchHull，其在自然参数空间中提出，不需要近似解或初始化以便陈述或求解。在结构性假设下，x和ware成员已知的K和N维随机子空间，我们提出了一个恢复保证的无噪声的情况下，有噪声的情况下。在无噪声的情况下，我们证明了当L >> 2（K+ N）时，BranchHull以高概率恢复向量到固有的缩放模糊度。分析提供了一个精确的上限的系数为样本的复杂性。在有噪声的情况下，我们表明，高概率的BranchHull是强大的小密集噪声时，L = Ω（K+ N）。(C)2019爱思唯尔公司All rights reserved.
We consider the bilinear inverse problem of recovering two vectors, x and w, in R-L from their entrywise product. For the case where the vectors have known signs and belong to known subspaces, we introduce the convex program BranchHull, which is posed in the natural parameter space that does not require an approximate solution or initialization in order to be stated or solved. Under the structural assumptions that x and ware members of known K and N dimensional random subspaces, we present a recovery guarantee for the noiseless case and a noisy case. In the noiseless case, we prove that the BranchHull recovers the vectors up to the inherent scaling ambiguity with high probability when L >> 2(K+ N). The analysis provides a precise upper bound on the coefficient for the sample complexity. In a noisy case, we show that with high probability the BranchHull is robust to small dense noise when L = Omega(K+ N). (C) 2019 Elsevier Inc. All rights reserved.