CIF: Small: Non-Linear Processing and Coding for Compressive Sensing with Applications in Imaging

“该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。“最近，压缩传感的新领域已经出现，并有望广泛地革新数字处理。其关键思想是使用非自适应线性投影，只需几次测量即可直接获取信号或图像的高效、降维表示。令人惊讶的是，自数字处理起源以来，奈奎斯特采样率一直主导着科学和技术中信号的采集和处理方式，而压缩感知理论可以跨越奈奎斯特采样率。这样的结果可能会产生深远的影响广泛，包括光谱学，成像，通信，以及消费电子产品中的应用。在这项研究中，压缩感知框架是"扩展”，使其成为离散时间全模拟处理通信系统的一个组成部分，完全跳过了数字域，并显示出良好的鲁棒性对噪声。关键思想是使用非线性映射作为模拟信道编码器，处理来自模拟源的样本或压缩感知测量，并产生直接通过噪声信道传输的连续幅度样本。因此，通信系统中的所有处理都在模拟域中进行。 除了其理论上的兴趣，这种方法在实际系统中的潜力是巨大的。例如，所提出的框架很容易应用于实际系统，如成像，其中它呈现出非常接近理论极限的性能，并且明显优于基于标准压缩感知的系统。此外，完全避免数字域的想法不仅可以应用于点对点通信系统，还可以应用于更复杂的通信问题，如传感器网络中的分布式编码。

"This award is funded under the American Recovery and Reinvestment Act of 2009(Public Law 111-5)."Recently, the new field of compressive sensing has emerged with the promise to revolutionize digital processing broadly. The key idea is the use of nonadaptive linear projections to acquire an efficient, dimensionally reduced representation of a signal or image directly using just a few measurements. Surprisingly, Nyquist-rate sampling, which has dominated how signals are acquired and processed in science and technology since the origin of digital processing, can be leaped over through compressive sensing theory. Such results may have a profound impact broadly, including applications in spectroscopy, imaging, communications, as well as consumer electronics.In this research, the compressive sensing framework is ``extended" to make it an integral part of a discrete-time all-analog-processing communications system that completely skips the digital domain and shows an excellent robustness against noise. The key idea is the use of non-linear mappings that act as analog channel encoders, processing the samples or compressive sensing measurements proceeding from an analog source and producing continuous amplitude samples that are transmitted directly through the noisy channel. Thus, all the processing in the communications system is made in the analog domain. In addition to its theoretical interest, the potential of this approach in practical systems is substantial. For instance, the proposed framework is readily applicable in practical systems such as imaging, where it presents a performance that is very close to the theoretical limits and clearly outperforms systems based on standard compressive sensing. Furthermore, the idea of completely avoiding the digital domain can be applied not just in point-to-point communications systems, but also in more complex communications problems such as distributed coding in sensor networks.