摘要
为求解欠定噪声方程组,需要从噪声和抽样不足的数据中重建高维离散信号。压缩感知矩阵的零空间特性保证了可以通过l_(1)最小化来恢复信号的稀疏表示。文章在Kalman滤波l_(1)模算法(KML1算法)的基础上通过采用基于Aitken的delta-squared过程外推法对其进行改进,提出了一种改进的Kalman滤波l_(1)模加速算法(加速算法),并运用于语音信号重构中。实验结果表明:在高维情况下,KML1算法经过500次迭代后,重构的解基本接近真实值,而加速算法经过100次迭代后,重构的解与真实值基本一致;与传统的正交匹配追踪(OMP)算法相比,加速算法的恢复时间比OMP算法缩减了将近20倍。具有外部阈值的l1最小化Kalman滤波器为x重构提供了更短的时间和更高的精确度。
To solve the underdetermined noise equations,high-dimensional discrete signals need to be reconstructed from noisy and sampled data.The zero-space characteristics of the perception matrix of compressed sensing theory ensure that the sparse representation can be restored through l_(1) minimization,which can be achieved by convex optimization methods or estimation theories.On the basis of Kalman filtering mode algorithm(KML1 algorithm),the external threshold method with Aitken-based delta-squared is used to improve it.An improved Kalman filter mode acceleration algorithm(acceleration algorithm)was proposed.It can be used in speech signal reconstruction.Experimental results show that after 500 iterations,the solution reconstructed by the KML1 algorithm is basically consistent with the true value,and after 100 iterations,the solution reconstructed by acceleration algorithm is basically consistent with the true value.And compared with the traditional orthogonal matching tracking(OMP)algorithm,and the recovery time of the acceleration algorithm is nearly 20 times smaller than that of the OMP algorithm.The Kalman filter through l_(1) minimization with external thresholds provides x shorter time and higher accuracy for reconstruction.
作者
马春
汪庆
李亚
李芳芳
MA Chun;WANG Qing;LI Ya;LI Fangfang(School of Medical Information Engineering,Anhui University of Chinese Medicine,Hefei 230012 China)
出处
《西华大学学报（自然科学版）》
CAS
2021年第4期27-34,共8页
Journal of Xihua University:Natural Science Edition
基金
国家自然基金面上项目(61672035)
安徽省高校人文研究重点项目(SK2019A0243)
安徽省高校自然科学重点项目(KJ2019A0437)。
