CIF: Small: Blind Perfect Signal Reconstruction in Subsampled Multi-Channel Systems

当信号在多个地点被接收或发送到多个地点时，就出现了多信道系统。它们在成像和传感、数据通信和存储以及所有音频、语音或图像处理数字技术中无处不在。它们的应用范围从超声或MRI诊断扫描仪到射电天文学。多通道系统的丰富理论解决了两种情况：当整个系统，包括通道，可以自由设计时;或者当通道可能是固定的和未知的，但每个通道的输出端的数据是完全采集的。然而，在许多重要的应用中，情况并非如此。通道的特性通常由控制感测过程的物理决定，由于传感器与环境的相互作用或其误校准，这些特性是未知的。此外，由于物理或成本限制，仅部分（二次采样）信道数据可用。本项目的目标是发展、评估和展示解决这类重要问题的基本理论和设计工具，本项目旨在扩展盲多通道反卷积方法，目前仅限于非二次采样系统，以提供盲完美信号重建。 本项目的具体目标是：（1）发展下采样多通道系统的盲辨识理论;（2）提出利用完善的（或接近完美的）重建滤波器组;（3）提供分析工具来研究和量化调节之间的各种权衡（噪声性能）、信号失真、鲁棒性和计算成本;以及（4）证明在真实的应用上的性能增益，特别是在高加速的多通道磁共振成像（MRI）和鲁棒的图像超分辨率中。

Multi-channel systems arise whenever a signal is picked up in or sent to more than one location. They are ubiquitous in imaging and sensing, data communication and storage, and in all audio, speech, or image processing digital technologies. Their applications range from ultrasound or MRI diagnostic scanners, to radio astronomy. The rich theory of multi-channel systems addresses two scenarios: when the entire system, including the channels, can be freely designed; or when the channels may be fixed and unknown, but data at the output of each channel is fully acquired. However, in many important applications this is not the case. The characteristics of the channels are often dictated by the physics governing the sensing process, which are unknown because of interaction of the sensors with the environment or their miss-calibration. Furthermore, because of physical or cost constraints only partial (subsampled) channel data is available. The goal of this project is to develop, evaluate and demonstrate the fundamental theory and design tools to address this important class of problems.This project aims to extend the methods of blind multi-channel deconvolution, which are currently limited to non-subsampled systems , to provide blind perfect signal reconstruction from subsampled data. The specific aims of this project are to: (1) develop the theory of blind identification of subsampled multi-channel systems; (2) propose practical methods for blind identification of such systems using perfect (or near perfect) reconstruction filter banks; (3) provide analytical tools to study and quantify various tradeoffs between conditioning (noise performance), signal distortion, robustness, and computational cost; and (4) to demonstrate performance gains on real applications, and in particular in highly-accelerated multi-channel magnetic resonance imaging (MRI), and robust image super-resolution.