Thanks to lowering costs, sensors of all kinds have increasingly been used in a wide variety of disciplines and fields, facilitating the rapid development of new technologies and applications. The information of interest (e.g. source location, refractive index, etc.) gets encoded in the measured sensor data, and the key problem is then to decode this information from the sensor measurements. In many cases, sensor data exhibit sparse features—“innovations”—that typically take the form of a finite sum of sinusoids. In practice, the robust retrieval of such encoded information from multi-sensors data (array or network) is difficult due to the non-uniformity of instrument precision and noise (i.e. different across sensors). This motivates the development of a joint sparse (“vector Finite Rate of Innovation”) recovery strategy for multi-sensor data: by fitting the data to a joint parametric model, an accurate sparse recovery can be achieved, even if the noise of the sensors is non-homogenous and correlated. Although developed for one-dimensional sensor data, we show that our method is easily extended to multi-dimensional sensor measurements, e.g. direction-of-arrival data of 2D planar array and interference fringes of underwater acoustics, which provides a generic solution to these applications. A very robust and efficient algorithm is proposed, which we validate in various conditions (simulations, multiple types of real data).

中文翻译：

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多传感器测量的 Vector-FRI 恢复


随着成本的降低，各类传感器越来越多地应用于各个学科和领域，促进了新技术和新应用的快速发展。感兴趣的信息（例如源位置、折射率等）被编码在测量的传感器数据中，然后关键问题是从传感器测量中解码该信息。在许多情况下，传感器数据表现出稀疏特征（“创新”），通常采用正弦曲线有限和的形式。在实践中，由于仪器精度和噪声的不均匀性（即传感器之间的差异），从多传感器数据（阵列或网络）中稳健地检索此类编码信息是困难的。这促使开发多传感器数据的联合稀疏（“向量有限创新率”）恢复策略：通过将数据拟合到联合参数模型，即使传感器的噪声存在，也可以实现精确的稀疏恢复是非同质且相关的。尽管是针对一维传感器数据开发的，但我们表明我们的方法可以轻松扩展到多维传感器测量，例如二维平面阵列的到达方向数据和水声学的干涉条纹，这为这些应用提供了通用解决方案。提出了一种非常稳健且高效的算法，我们在各种条件（模拟、多种类型的真实数据）下对其进行了验证。