论文标题
在一位量化上
On One-Bit Quantization
论文作者
论文摘要
我们考虑了一种一位量化器，可最大程度地减少生活在真正希尔伯特空间中的源的平方误差。最佳量化器是一个投影，然后是阈值操作，我们提供了识别沿沿线投影的最佳方向的方法。作为我们方法的应用，我们表征了最佳的一位量化器，用于表现出低维结构的连续时间随机过程。我们从数值上表明，通过随机梯度下降训练的基于神经网络的压缩机可以找到此最佳量化器。
We consider the one-bit quantizer that minimizes the mean squared error for a source living in a real Hilbert space. The optimal quantizer is a projection followed by a thresholding operation, and we provide methods for identifying the optimal direction along which to project. As an application of our methods, we characterize the optimal one-bit quantizer for a continuous-time random process that exhibits low-dimensional structure. We numerically show that this optimal quantizer is found by a neural-network-based compressor trained via stochastic gradient descent.
