论文标题
散射介质中成像的通用界限
Universal bounds for imaging in scattering media
论文作者
论文摘要
在这项工作中，我们建立了通用集合的独立界限，以通过复杂介质成像的相互信息和通道能力的均值和方差。上限和下限都是派生的，仅取决于培养基的平均透射率和自由度的$ n $。在大$ n $的渐近极限中，通道容量上的上限被证明与具有独立的Bernoulli分布式传输特征值的双峰通道的近似值相近。还考虑了基于反射的成像方式，并在定义的传输反射信息平面中允许区域。从圆形和DMPK随机矩阵集合中绘制的数值示例用于说明衍生边界的有效性。最后，尽管相互信息和通道容量被证明是传输特征值的非线性统计数据，但表明并讨论了中心极限定理的存在。
In this work we establish universal ensemble independent bounds on the mean and variance of the mutual information and channel capacity for imaging through a complex medium. Both upper and lower bounds are derived and are solely dependent on the mean transmittance of the medium and the number of degrees of freedom $N$. In the asymptotic limit of large $N$, upper bounds on the channel capacity are shown to be well approximated by that of a bimodal channel with independent identically Bernoulli distributed transmission eigenvalues. Reflection based imaging modalities are also considered and permitted regions in the transmission-reflection information plane defined. Numerical examples drawn from the circular and DMPK random matrix ensembles are used to illustrate the validity of the derived bounds. Finally, although the mutual information and channel capacity are shown to be non-linear statistics of the transmission eigenvalues, the existence of central limit theorems is demonstrated and discussed.
