A computation technique, known as inverse perturbation-fractional norm regularization (IP-FNR), is proposed in this wok for a sparse signal recovery problem. The objective function of this method is derived using a general ${\ell }_p$ norm, when $p$ is a positive fractional number. Numerical examples are conducted for both noiseless and noisy cases. Performance of the proposed approach in terms of root-mean-square relative error (RMSRE), mean normalized squared error, standard deviation mean, occupied memory during the computation, and computational time is compared to several previous methods. It is found that in the noiseless case, the IP-FNR method significantly outperforms the former fixed-point algorithms for a certain range of the norm exponent $p$, provided that the perturbation parameter and the regularization multiplier are properly chosen. In the noisy case, at the expense of computational time, the IP-FNR approach provides noticeably lower RMSRE when the signal-to-noise ratio or the sparsity ratio is high and the compression ratio is quite low.

本文针对稀疏信号恢复问题提出了一种称为逆扰动-分数范数正则化 (IP-FNR) 的计算技术。该方法的目标函数是使用一般的${\ell }_p$规范，当$p$是正小数。针对无噪声和噪声情况进行了数值示例。将所提出的方法在均方根相对误差 (RMSRE)、平均归一化平方误差、标准偏差平均值、计算期间占用的内存和计算时间方面的性能与以前的几种方法进行了比较。结果发现，在无噪声情况下，IP-FNR 方法在范数指数的一定范围内明显优于以前的定点算法$p$，前提是正确选择了扰动参数和正则化乘数。在嘈杂的情况下，以计算时间为代价，当信噪比或稀疏比很高且压缩比很低时，IP-FNR 方法提供明显较低的 RMSRE。