Distribution of the Fisher information loss due to random compressed sensing
Distribution of the Fisher information loss due to random compressed sensing
复制标题
随机压缩感知导致的 Fisher 信息损失的分布
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
S. Howard
中科院分区：
文献类型：
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作者：
Pooria Pakrooh;A. Pezeshki;L. Scharf;D. Cochran;S. Howard
在这项工作中，我们研究了随机矩阵压缩采样对Fisher信息和复杂多元正态测量模型中非线性参数估计的Crame 'r-Rao界（CRB）的影响。本文考虑一类分布对右酉变换不变的随机压缩矩阵。对于这类随机压缩矩阵，我们证明了压缩后的归一化Fisher信息矩阵具有复杂的矩阵变量beta分布，这是独立于压缩前的Fisher信息矩阵和参数的值。我们还得到了CRB的分布。我们的研究结果可以用来量化的损失量的Fisher信息和增加CRB由于随机压缩。
In this work, we study the impact of compressive sampling with random matrices on Fisher information and the Cramér-Rao bound (CRB) for nonlinear parameter estimation in a complex multivariate normal measurement model. We consider the class of random compression matrices whose distribution is invariant to right-unitary transformations. For this class of random compression matrices, we show that the normalized Fisher information matrix after compression has a complex matrix-variate beta distribution, which is independent of the Fisher information matrix before compression and the values of the parameters. We also derive the distribution of CRB. Our results can be used to quantify the amount of loss in Fisher information and the increase in CRB due to random compression.