Construction of Incoherent Unit Norm Tight Frames With Application to Compressed Sensing
Construction of Incoherent Unit Norm Tight Frames With Application to Compressed Sensing
复制标题
DOI：
10.1109/tit.2014.2308171
复制
发表时间：
2014-04
影响因子：
2.5
通讯作者：
Evaggelia Tsiligianni;L. Kondi;A. Katsaggelos
中科院分区：
文献类型：
--
作者：
Evaggelia Tsiligianni;L. Kondi;A. Katsaggelos
尽管单位范数紧框架（UNTF）和等角紧框架（ETFs）具有重要的性质，但它们的构造已被证明是极其困难的。少数已知的技术仅产生少量的这种帧，同时对帧尺寸施加某些限制。受压缩感知（CS）中非相干紧帧的应用启发，我们提出了一种构造非相干UNTF的方法。当帧冗余度不是很高时，所实现的最大列相关性变得接近于最低可能界限。所提出的方法可以构建任何维度的框架。在CS中采用所获得的帧以产生优化的投影矩阵。实验结果表明，所提出的优化技术改善了CS信号恢复，提高了重建精度。考虑到UNTF和ETFs在稀疏表示、信道编码和通信中的重要性，我们期望所提出的构造在CS之外的其他应用中也是有用的。
Despite the important properties of unit norm tight frames (UNTFs) and equiangular tight frames (ETFs), their construction has been proven extremely difficult. The few known techniques produce only a small number of such frames while imposing certain restrictions on frame dimensions. Motivated by the application of incoherent tight frames in compressed sensing (CS), we propose a methodology to construct incoherent UNTFs. When frame redundancy is not very high, the achieved maximal column correlation becomes close to the lowest possible bound. The proposed methodology may construct frames of any dimensions. The obtained frames are employed in CS to produce optimized projection matrices. Experimental results show that the proposed optimization technique improves CS signal recovery, increasing the reconstruction accuracy. Considering that the UNTFs and ETFs are important in sparse representations, channel coding, and communications, we expect that the proposed construction will be useful in other applications, besides the CS.