论文标题
盲二维超级分辨率（扩展版本）中原子规范的数学理论
Mathematical Theory of Atomic Norm Denoising In Blind Two-Dimensional Super-Resolution (Extended Version)
论文作者
论文摘要
本文在使用原子规范后开发了一个新的数学框架，用于在盲二维（2D）超分辨率中降解。该框架将信号授予一个信号，该信号由从其嘈杂测量值中的未知数量和频率偏移的未知波形组成的信号组成。此外，该框架还提供了一种估计信号中未知参数的方法。我们证明，当观察到的样品的数量满足系统参数函数的某些下限时，我们可以在解决正则化最小二乘原子原子范围最小化问题后以非常高的精度估算无噪声信号。我们得出了估计器的理论于点于点，我们表明它取决于噪声方差，未知波形的数量，样本数量以及未知波形所在的低维空间的尺寸。最后，我们通过使用广泛的模拟实验来验证论文的理论发现。
This paper develops a new mathematical framework for denoising in blind two-dimensional (2D) super-resolution upon using the atomic norm. The framework denoises a signal that consists of a weighted sum of an unknown number of time-delayed and frequency-shifted unknown waveforms from its noisy measurements. Moreover, the framework also provides an approach for estimating the unknown parameters in the signal. We prove that when the number of the observed samples satisfies certain lower bound that is a function of the system parameters, we can estimate the noise-free signal, with very high accuracy, upon solving a regularized least-squares atomic norm minimization problem. We derive the theoretical mean-squared error of the estimator, and we show that it depends on the noise variance, the number of unknown waveforms, the number of samples, and the dimension of the low-dimensional space where the unknown waveforms lie. Finally, we verify the theoretical findings of the paper by using extensive simulation experiments.
