The problem of sparse multichannel blind deconvolution (S-MBD) arises frequently in many engineering applications such as radar/sonar/ultrasound imaging. To reduce its computational and implementation cost, we propose a compression method that enables blind recovery from much fewer measurements with respect to the full received signal in time. The proposed compression measures the signal through a filter followed by a subsampling, allowing for a significant reduction in implementation cost. We derive theoretical guarantees for the identifiability and recovery of a sparse filter from compressed measurements. Our results allow for the design of a wide class of compression filters. We, then, propose a data-driven unrolled learning framework to learn the compression filter and solve the S-MBD problem. The encoder is a recurrent inference network that maps compressed measurements into an estimate of sparse filters. We demonstrate that our unrolled learning method is more robust to choices of source shapes and has better recovery performance compared to optimization-based methods. Finally, in data-limited applications (fewshot learning), we highlight the superior generalization capability of unrolled learning compared to conventional deep learning.

翻译：稀疏多通道盲反卷积（S-MBD）问题频繁出现在许多工程应用中，例如雷达/声纳/超声成像。为降低其计算和实现成本，我们提出一种压缩方法，使得仅用远少于全接收信号时间样本的测量值即可实现盲恢复。所提压缩方法通过滤波器后接子采样测量信号，显著降低了实现成本。我们推导了从压缩测量值中识别与恢复稀疏滤波器的理论保证，该结果支持设计广泛类型的压缩滤波器。进而提出一种数据驱动的展开学习框架，用于学习压缩滤波器并求解S-MBD问题。其中编码器为循环推理网络，可将压缩测量值映射为稀疏滤波器的估计。实验表明，与基于优化的方法相比，我们的展开学习方法对源形状的选择更具鲁棒性，且恢复性能更优。最后，在数据受限的应用场景（小样本学习）中，我们突显了展开学习相较于传统深度学习的优越泛化能力。