基于L_infty误差度量的混合高斯信号估计
Mixture Gaussian Signal Estimation with L_infty Error Metric
摘要：
我们考虑的问题，估计输入信号的噪声测量并行标量高斯信道和线性混合系统。估计过程的性能由$\ell_\infty$范数误差度量量化。首先研究了并行标量高斯信道中的最小均值$\ell_\infty$误差估计器，并证明了当输入是独立同分布（i.i.d.）混合高斯，维纳滤波器是渐近最优的概率为1。对于具有i.i.d.的线性混合系统稀疏高斯或混合高斯输入，在松弛置信传播（BP）算法匹配Tanaka的不动点方程的假设下，将维纳滤波器应用于松弛BP的输出也是概率为1的渐近最优的。然而，为了解决实际问题的信号维数是有限的，我们申请的估计算法，已经提出了在我们以前的工作，并说明了一个$\ell_\infty$误差最小化可以近似由一个$\ell_p$误差最小化提供的值$p$是适当的选择。
英文摘要：
We consider the problem of estimating an input signal from noisy measurements in both parallel scalar Gaussian channels and linear mixing systems. The performance of the estimation process is quantified by the $\ell_\infty$ norm error metric. We first study the minimum mean $\ell_\infty$ error estimator in parallel scalar Gaussian channels, and verify that, when the input is independent and identically distributed (i.i.d.) mixture Gaussian, the Wiener filter is asymptotically optimal with probability 1. For linear mixing systems with i.i.d. sparse Gaussian or mixture Gaussian inputs, under the assumption that the relaxed belief propagation (BP) algorithm matches Tanaka's fixed point equation, applying the Wiener filter to the output of relaxed BP is also asymptotically optimal with probability 1. However, in order to solve the practical problem where the signal dimension is finite, we apply an estimation algorithm that has been proposed in our previous work, and illustrate that an $\ell_\infty$ error minimizer can be approximated by an $\ell_p$ error minimizer provided the value of $p$ is properly chosen.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
