基于压缩感知稀疏信号重建的迭代硬阀值算法

Nyquist采样速率条件下的信号采样，采样系统表现良好并且信号可以被稀疏向量近似表示时，信号可以被有效而精确地重构。针对无噪声信号，利用确定的稀疏基和随机的观测矩阵，研究迭代硬阀值算法的有效性。若观测矩阵满足有限等距性质（RIP），且稀疏基与随机观测矩阵不相干时，通过该算法，原始信号的稀疏投影可以被高概率重构。最后，利用哈达码正交矩阵作为稀疏基，高斯随机矩阵作为观测矩阵，对原始信号的稀疏投影进行重构，结果验证了该算法的有效性。

Iterative hard threshold algorithm for sparse signal reconstruction based on compressive sensing

For the signal sampling under the Nyquist rate,the signal can be reconstructed efficiently and accurately when the sampling system is well behaved and the signal is approximately expressed by a sparse vector.For no noise signal,the effectiveness of iterative hard thresholding(IHT) algorithm is investigated by using the fixed sparse basis and random observable matrix.If observable matrix satisfies RIP,and sparse basis is incoherent with random observable matrix,sparse projection of original signal can be reconstructed with high probability by the algorithm.Taking Hadamard orthonormal matrix as sparse basis and Gaussian random matrix as observable matrix,the sparse projection of the original signal was reconstructed.The effectiveness of the algorithm is verified by reconstructing result.