非负矩阵分解下的稀疏基构建

摘要

当信号在某个变换域是稀疏的或可压缩的,可以利用与变换矩阵非相干的测量矩阵将变换系数投影为低维向量,同时这种投影保持了重建信号所需的信息.压缩感知技术以较少的投影数据实现信号的精确或高概率重构.而信号重建能力很大程度上取决于信号的稀疏性,以及采样矩阵和变换矩阵的非相干性.提出用非负矩阵分解(NMF)对原始信号进行稀疏变化,构建稀疏变换基矩阵Ψ,并与离散傅里叶变换(DFT)和离散小波变换(DWT)构建变换矩阵进行对比研究,对相干度,稀疏度进行测量,并采用正交匹配追踪(OMP)进行信号还原能力分析,表明在同等测量次数下NMF还原能力优于DFT和DWT.%When the signal in a transform domain is sparse or compressible, it could be projected to low-dimensional vector utilizing measurement matrix. Usually the measurement matrix is incoherence with transform matrix. Compressive sensing theory could precisely or high probability reconstruct signal from far fewer samples or measurements than traditional methods, to make this possible, reconstruction of signal relies on two principles: sparsity of signal, and incoherence between sampling matrix and transform matrix. NMF is used to structure transform matrix tp for origin signal, then compare with DFT and DWT about coherence and sparsity, finally analyze ability of reconstruction through introducing OMP to recover signal. Experiment result show that NMF' s performance is superior to DFT and DWT.