In this article, we investigate the privacy issues that arise from a new frame-based kernel analysis approach to reconstruct from frame coefficient erasures. We show that while an erasure recovery matrix is needed in addition to a decoding frame for a receiver to recover the erasures, the erasure recovery matrix can be designed in such a way that it protects the encoding frame. The set of such erasure recovery matrices is shown to be an open and dense subset of a certain matrix space. We present algorithms to construct concrete examples of encoding frame and erasure recovery matrix pairs for which the erasure reconstruction process is robust to additive channel noise. Using the Restricted Isometry Property, we also provide quantitative bounds on the amplification of sparse additive channel noise. Numerical experiments are presented on the amplification of additive normally distributed random channel noise. In both cases, the amplification factors are demonstrated to be quite small.

在本文中，我们研究了一种新的基于帧的内核分析方法从帧系数擦除中重建所引起的隐私问题。我们表明，尽管除了解码帧之外还需要擦除恢复矩阵以使接收机恢复擦除，但是擦除恢复矩阵可以以保护编码帧的方式进行设计。这种擦除恢复矩阵的集合显示为某个矩阵空间的开放且密集的子集。我们提出了一些算法来构造编码帧和擦除恢复矩阵对的具体示例，对于这些示例，擦除重建过程对于加性信道噪声具有鲁棒性。使用受限等轴测特性，我们还提供了稀疏加性通道噪声放大的定量界限。数值实验表明了加法正态分布随机信道噪声的放大。在两种情况下，放大因子都被证明很小。