Complex-valued Reed-Solomon Codes for Deterministic Compressed Sensing

用于确定性压缩感知的复值 Reed-Solomon 码

• 批准号: 273209895
• 负责人: Professor Dr.-Ing. Martin Bossert
• 金额: --
• 依托单位: Institut für Nachrichtentechnik (NT)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/273209895?language=en
• 关键词: Complex; valued; Reed; Solomon; Codes

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.

本文研究了复数域上的Reed-Solomon码在确定性压缩感知中的应用。近年来在有限域和复数域上的RS码译码的研究成果可以用于CS中。确定性CS方案通过利用嵌入到确定性感测矩阵中的结构来提供（非概率）重构保证、降低的存储要求或较不复杂的计算。然而，现有的RS码的译码算法需要适应所产生的问题与使用的复数域和有限精度的实现。特别是算法对非稀疏失真的鲁棒性是需要考虑的重要附加因素。基于CRS的CS方案的第一个结果是有希望的。