Convolutional Compressed Sensing Using Deterministic Sequences
Convolutional Compressed Sensing Using Deterministic Sequences
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DOI：
10.1109/tsp.2012.2229994
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发表时间：
2013-02-01
影响因子：
5.4
通讯作者：
Ling, Cong
中科院分区：
文献类型：
--
作者：
Li, Kezhi;Gan, Lu;Ling, Cong
在本文中，针对基于卷积的压缩感知（CS），提出了一类由确定性序列构建的新型正交循环矩阵。与随机卷积不同，基础滤波器的系数由具有良好自相关特性的确定性序列的离散傅里叶变换给出。基于所提出的感知矩阵的相干性参数，研究了稀疏信号的均匀恢复和非均匀恢复。对许多序列示例进行了研究，特别是弗兰克 - 扎多夫 - 朱（FZC）序列、[此处缺失序列名称]序列和戈莱序列。所提出的感知矩阵的一个显著特征是它们不仅能够处理时域中的稀疏信号，还能处理频域和/或离散余弦变换（DCT）域中的稀疏信号。
In this paper, a new class of orthogonal circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the - sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain.