Parallel acquisition systems are employed successfully in a variety of different sensing applications when a single sensor cannot provide enough measurements for a high-quality reconstruction. In this paper, we consider compressed sensing (CS) for parallel acquisition systems when the individual sensors use subgaussian random sampling. Our main results are a series of uniform recovery guarantees which relate the number of measurements required to the basis in which the solution is sparse and certain characteristics of the multi-sensor system, known as sensor profile matrices. In particular, we derive sufficient conditions for optimal recovery, in the sense that the number of measurements required per sensor decreases linearly with the total number of sensors, and demonstrate explicit examples of multi-sensor systems for which this holds. We establish these results by proving the so-called Asymmetric Restricted Isometry Property (ARIP) for the sensing system and use this to derive both nonuniversal and universal recovery guarantees. Compared to existing work, our results not only lead to better stability and robustness estimates but also provide simpler and sharper constants in the measurement conditions. Finally, we show how the problem of CS with block-diagonal sensing matrices can be viewed as a particular case of our multi-sensor framework. Specializing our results to this setting leads to a recovery guarantee that is at least as good as existing results.

当单个传感器无法为高质量重建提供足够的测量值时，并行采集系统已成功应用于各种不同的传感应用中。在本文中，当单个传感器使用亚高斯随机采样时，我们将并行搜索系统考虑为压缩传感（CS）。我们的主要结果是一系列一致的恢复保证，这些保证将所需的测量数量与解决方案稀疏的基础以及多传感器系统的某些特征（称为传感器轮廓矩阵）相关联。特别是，在每个传感器所需的测量数量随传感器总数线性减少的意义上，我们得出了可实现最佳恢复的充分条件，并展示了对此适用的多传感器系统的显式示例。我们通过证明传感系统的所谓非对称受限等距特性（ARIP）来建立这些结果，并以此得出非通用和通用恢复保证。与现有工作相比，我们的结果不仅可以带来更好的稳定性和鲁棒性估计，还可以在测量条件下提供更简单，更清晰的常数。最后，我们展示了如何将块对角线传感矩阵的CS问题视为我们的多传感器框架的特殊情况。将我们的结果专门用于此设置，可以确保恢复结果至少与现有结果一样好。我们的结果不仅可以带来更好的稳定性和鲁棒性估计，还可以在测量条件下提供更简单，更清晰的常数。最后，我们展示了如何将块对角线传感矩阵的CS问题视为我们的多传感器框架的特殊情况。将我们的结果专门用于此设置，可以确保恢复结果至少与现有结果一样好。我们的结果不仅可以带来更好的稳定性和鲁棒性估计，还可以在测量条件下提供更简单，更清晰的常数。最后，我们展示了如何将块对角线传感矩阵的CS问题视为我们的多传感器框架的特殊情况。将我们的结果专门用于此设置，可以确保恢复结果至少与现有结果一样好。