Complex-valued Reed-Solomon Codes for Deterministic Compressed Sensing

我们提出研究Reed-Solomon码在复数（CRS）上作为确定性压缩感知（CS）方案的应用。在有限域和复数上解码RS码的最新研究成果可用于计算机科学。确定性CS方案通过利用嵌入到确定性感知矩阵中的结构提供（非概率）重建保证，减少存储需求或减少复杂的计算。但是，现有的RS码译码算法需要适应复杂域的使用和有限精度的实现所带来的问题。特别是算法对非稀疏失真的鲁棒性是需要考虑的一个重要附加因素。基于crs的CS方案的初步结果是有希望的。

We propose to investigate the application of Reed-Solomon codes over the complex numbers (CRS) as deterministic Compressed Sensing (CS) schemes. Recent research results in decoding RS codes over finite fields and complex numbers can be studied for their usage in CS. Deterministic CS schemes offer (non-probabilistic) reconstruction guarantees, reduced storage requirements or less complex computation by utilizing the structure embedded into the deterministic sensing matrix. However, the existing decoding algorithms for RS codes need to be adapted to the problems arising with the usage of the complex field and the implementation with finite precision. Especially the robustness of the algorithms against non-sparse distortions is an important additional factor which needs to be considered. First results on CRS-based CS schemes are promising.