At the core of many sensing and imaging applications, the signal of interest can be modeled as a linear superposition of translated or modulated versions of some template [e.g., a point spread function (PSF) or a Green's function] and the fundamental problem is to estimate the translation or modulation parameters (e.g., delays, locations, or Dopplers) from noisy measurements. This problem is centrally important to not only target localization in radar and sonar, channel estimation in wireless communications, and direction-of-arrival estimation in array signal processing, but also modern imaging modalities such as superresolution single-molecule fluorescence microscopy, nuclear magnetic resonance imaging, and spike localization in neural recordings, among others.

中文翻译：

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利用连续体上的稀疏性：超分辨率的原子范数最小化

在许多传感和成像应用的核心中，感兴趣的信号可以建模为某个模板的平移或调制版本的线性叠加[例如，点扩散函数 (PSF) 或格林函数]，基本问题是从噪声测量中估计平移或调制参数（例如，延迟、位置或多普勒）。这个问题不仅对雷达和声纳中的目标定位、无线通信中的信道估计和阵列信号处理中的到达方向估计都很重要，而且对现代成像模式如超分辨率单分子荧光显微镜、核磁共振也很重要。成像和神经记录中的尖峰定位等。