Atomic Norm Denoising for Complex Exponentials With Unknown Waveform Modulations
Atomic Norm Denoising for Complex Exponentials With Unknown Waveform Modulations
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DOI：
10.1109/tit.2019.2954452
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发表时间：
2019-02
影响因子：
2.5
通讯作者：
S. Li;M. Wakin;Gongguo Tang
中科院分区：
文献类型：
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作者：
S. Li;M. Wakin;Gongguo Tang
非平稳盲超分辨率是传统超分辨率问题的延伸，它处理从粗测量中恢复精细细节的问题。非平稳盲超分辨率问题出现在雷达成像、3D单分子显微镜、计算摄影等许多应用中。由于凸方法对噪声的鲁棒性和强大的理论保证，人们对用凸方法解决非平稳盲超分辨率任务越来越感兴趣。受最近关于盲逆问题中原子范数最小化的研究的推动，我们在这里重点关注非平稳盲超分辨率中的信号去噪问题。特别是，我们使用原子范数正则化最小二乘问题来对具有未知波形调制的复指数之和进行降噪。我们量化均方误差如何依赖于噪声方差和真实信号参数。还进行了数值实验来说明理论结果。
Non-stationary blind super-resolution is an extension of the traditional super-resolution problem, which deals with the problem of recovering fine details from coarse measurements. The non-stationary blind super-resolution problem appears in many applications including radar imaging, 3D single-molecule microscopy, computational photography, etc. There is a growing interest in solving non-stationary blind super-resolution task with convex methods due to their robustness to noise and strong theoretical guarantees. Motivated by the recent work on atomic norm minimization in blind inverse problems, we focus here on the signal denoising problem in non-stationary blind super-resolution. In particular, we use an atomic norm regularized least-squares problem to denoise a sum of complex exponentials with unknown waveform modulations. We quantify how the mean square error depends on the noise variance and the true signal parameters. Numerical experiments are also implemented to illustrate the theoretical result.