The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in fusion frames, we introduce a compressed sensing framework in which we split the dense information into sub-channel or local pieces and then fuse the local estimations. Each piece of information is measured by potentially low quality sensors, modeled by linear matrices and recovered via compressed sensing -- when necessary. Finally, by a fusion process within the fusion frames, we are able to recover accurately the original signal. Using our new method, we show, and illustrate on simple numerical examples, that it is possible, and sometimes necessary, to split a signal via local projections and / or filtering for accurate, stable, and robust estimation. In particular, we show that by increasing the size of the fusion frame, a certain robustness to noise can also be achieved. While the computational complexity remains relatively low, we achieve stronger recovery performance compared to usual single-device compressed sensing systems.

中文翻译：

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融合帧结构信号的局部稀疏与恢复

通过信号处理和谐波分析工具的组合，分析从低质量传感设备中恢复高复杂度信号的问题。通过使用融合帧的最新发展所提供的丰富结构，我们引入了一种压缩感知框架，在该框架中，我们将密集信息分成子通道或局部片段，然后融合局部估计。每条信息都由潜在的低质量传感器测量，由线性矩阵建模，并在必要时通过压缩感知恢复。最后，通过融合帧内的融合过程，我们能够准确地恢复原始信号。使用我们的新方法，我们展示并用简单的数值例子说明，这是可能的，有时是必要的，通过局部投影和/或过滤来分割信号以获得准确、稳定和稳健的估计。特别是，我们表明通过增加融合帧的大小，也可以实现一定的噪声鲁棒性。虽然计算复杂度仍然相对较低，但与通常的单设备压缩感知系统相比，我们实现了更强的恢复性能。