基于傅里叶基的自适应压缩感知重构算法

在压缩感知中，为了提高含噪信号的重构精度，提出了基于傅里叶基的稀疏度自适应匹配追踪算法.该算法在重构过程中采用相关系数作为匹配准则的基础上，创新性地利用傅里叶变换的共轭对称性，进一步严格控制索引值加入支撑集的过程；同时利用余量能量和余量能量变化率双门限作为停止迭代的依据；最后将估计的傅里叶域中的信号逆变换得到时域的重构信号.仿真实验表明，在同等噪声污染的情况下，该算法与同类算法相比有较高的重构精度. 

Adaptive recovery algorithm for compressive sensing based on Fourier basis

In order to improve the recovery accuracy of compressive sampling, an algorithm of modified sparsity adaptive matching pursuit based on discrete Fourier transform (MSAMP-DFT) was proposed. In the course of reconstruction, not only the correlation, but also the conjugate symmetry on discrete Fourier transform was used to control the process of adding the index value into support set. The double threshold, residual energy and changing rate of residual energy were used to stop loop iteration. Lastly, the reconstructed signal was obtained by inverse discrete Fourier transform. The experiment results verify that, the method introduced can converge to the signal sparsity without any prior information and the recovery accuracy of the arithmetic introduced is better than others under the same rate of signal to noise.