Effective '0,1' sparse signal compressed sensing reconstruction method
专利类型：发明专利
语 言：中文
申 请 号：CN201410058106.7
申 请 日：20140220
申 请 人：重庆大学
申请人地址：400030 重庆市沙坪坝区沙正街174号
公 开 日：20170208
公 开 号：CN103825621B
代 理 人：康海燕
代理机构：重庆华科专利事务所 50123
摘 要：Abstract：The invention discloses an effective '0,1' sparse signal compressed sensing reconstruction method. The method mainly comprises a sparse and uniform measurement matrix construction part and an iteration reconstruction order part based on a bipartite graph. According to the method, a bipartite graph model in a graph theory is ingeniously introduced, the minimum cover characteristic of the bipartite graph is closely combined, a constraint condition is appropriately added, and the sparse, uniform and minimally-covered measurement matrix is constructed. Based on the special structure that the '0,1' sparse signals are fully utilized in an iteration reconstruction algorithm based on the bipartite, the connecting line phi ij of the bipartite graph is deleted and a measurement value y is updated through an iteration method, and an original signal reconstruction method is achieved finally. According to the method, the bipartite graph model in the graph theory is introduced in compressed sensing sampling and reconstruction, compared with an l1 norm minimization method, reconstruction errors do not exist, the method can be applied to compressive sampling of neutron pulse sequences, earthquake signals, wireless sensor networks, binary images and the like.
主 权 项：一种有效的“0,1”稀疏信号的压缩感知重构方法，包括稀疏均匀的观测矩阵的构建和基于二分图的迭代重构；其特征在于：(1)所述稀疏均匀的观测矩阵的构建步骤如下：(1.1)压缩采样的二分图表示针对本身具有K?稀疏特性的N×1中子脉冲序列，即原始信号x，其压缩采样表示为y＝Φx；其中，Φ为M×N的观测矩阵，y为M×1的测量值；根据二分图的定义，将原始信号x和观测值y看作两个集合，即二分图的两个顶点，观测矩阵Φ看作是二分图的边，压缩采样过程即可以通过二分图进行直观表示；(1.2)添加约束条件(1.2a)二分图中共有l＝ML条边；(1.2b)观测值y的每个顶点有且仅有ly＝L条边，即观测矩阵Φ的每行的零范数均为||Φ(i，:)||0＝L；(1.2c)与原始信号x连接的边数即观测矩阵Φ的每列的零范数
(1.3)构建观测矩阵依据上述约束条件，结合原始信号x特殊的“0,1”稀疏结构，观测矩阵Φ(M×N)需要满足以下三个特征：A.||Φ(i，：)||0＝L；B.i(Φ(i，：)≠0)≠j(Φ(j，：)≠0)；C.ΣiΦ(i，:)≠∑jΦ(j，：)，(i，j∈(1，2，...M)，i≠j)；即Φ的每一行中有且仅有L个非零元素，非零元素所在位置点每一行不重复，?Φ的每一行元素的和值唯一；满足上述特性的观测矩阵Φ通过以下算法构建：(1.3a)生成随机位置点矩阵θ(M×L)，1≤θij≤N，Θi表示θ的第i行元素集合；(1.3b)构造高斯矩阵G(M×N)；(1.3c)产生观测矩阵
对于K?稀疏原始信号x，压缩感知重构需要的观测值数量为：M＝O(K·logN)；若K?稀疏原始信号x的所有元素均被观测，那么二分图边的数量l至少为N·logN；因此，
其中S为稀疏比；(2)基于二分图的迭代重构：针对观测值y＝φx，本方法涉及的信号重构算法如下：(2.1)如果
(2.2)如果
(2.3)对于已重构的xi
令φij＝0，j∈θj；Φkj＝0，k≠j，k＝1，2，...，M；(2.4)迭代(2.1)、(2.2)、(2.3)至没有xi可以重构，将已重构的xi的位置点存入Γ，i∈Γ；(2.5)最终得到重构信号
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法律状态：公开
IPC专利分类号：H03M7/30