Power-Constrained Sparse Gaussian Linear Dimensionality Reduction Over Noisy Channels
Power-Constrained Sparse Gaussian Linear Dimensionality Reduction Over Noisy Channels
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DOI：
10.1109/tsp.2015.2455521
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发表时间：
2014-10
影响因子：
5.4
通讯作者：
A. Shirazinia;S. Dey
中科院分区：
文献类型：
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作者：
A. Shirazinia;S. Dey
在本文中，我们研究了稀疏高斯线性降维框架下的功率约束传感矩阵设计。我们的研究是在一个单终端设置，以及在多终端设置组成的正交或相干多址接入信道（MAC）。在源到传感器通道和传感器到解码器通信通道有噪声的系统中，我们采用均方误差（MSE）性能标准进行稀疏源重建。我们提出的传感矩阵设计过程依赖于最大限度地减少在单终端和多终端设置的MSE的下限。我们提出了一个三阶段的传感矩阵优化方案，结合半定松弛（SDR）规划，低秩近似问题和功率重新缩放。在一定条件下，我们推导出封闭形式的解决方案，建议的优化过程。通过数值实验，应用实际的稀疏重建算法，与其他相关方法进行比较，显示了该方案的优越性。这种性能的提高是以更高的计算复杂度为代价的。因此，为了解决的复杂性负担，我们提出了一个等效的随机优化方法的兴趣，可以近似解决的问题，同时仍然提供了一个上级性能超过流行的方法。
In this paper, we investigate power-constrained sensing matrix design in a sparse Gaussian linear dimensionality reduction framework. Our study is carried out in a single-terminal setup as well as in a multi-terminal setup consisting of orthogonal or coherent multiple access channels (MAC). We adopt the mean square error (MSE) performance criterion for sparse source reconstruction in a system where source-to-sensor channel(s) and sensor-to-decoder communication channel(s) are noisy. Our proposed sensing matrix design procedure relies upon minimizing a lower-bound on the MSE in single- and multiple-terminal setups. We propose a three-stage sensing matrix optimization scheme that combines semi-definite relaxation (SDR) programming, a low-rank approximation problem and power-rescaling. Under certain conditions, we derive closed-form solutions to the proposed optimization procedure. Through numerical experiments, by applying practical sparse reconstruction algorithms, we show the superiority of the proposed scheme by comparing it with other relevant methods. This performance improvement is achieved at the price of higher computational complexity. Hence, in order to address the complexity burden, we present an equivalent stochastic optimization method to the problem of interest that can be solved approximately, while still providing a superior performance over the popular methods.