褶积反演中的脉冲压缩准则

通过分析基于脉冲压缩原理的反褶积方法,提出了具有广泛用途的广义L_p模准则,像脉冲反褶积、极小熵反褶积、L₁模反褶积和D模反褶积等都为其特例。根据有限维欧氏空间的L。模性质和高维欧氏空间的几何性质,分析了广义L_p模方法中的参数影响。为了比较不同反褶积方法的脉冲压缩效果,给出了一类判别函数,从理论上证明了,为什么对非小相位信号L₁模法的脉冲压缩效果优于脉冲反褶积;D模反褶积要比常规极小熵法更具有"简单性"。广义L_p模准则为构造、分析新的反褶积方法和进一步研究最优脉冲压缩准则提供了必要的理论基础。

THE PULSE COMPRESSION CRITERION IN DECONVOLUTION

Deconvolution methods based on the pulse compression principle are analyzed,and a more generalized l_p-norm criterion for wide use is proposed,which in cludes as special cases pulse deconvolution,minimum-entropy deconvolution l_t-norm deconvolution and D-norm deconvolution.According to the p-norm properties of the finite-dimensional space and the geometric properties of the higher-dimensional space,an analysis is made on the effect of the parameters in the generalized l_p-norm method,and a criterion function is designed to compare pulse compression of different methods.It is also theoretically proved why for nonminimum-phase signals the l₁-norm approach yields better pulse compression than pulse deconvolution,and why the D-norm approach has more "simplicity" than general minimum-entropy methods.New deconvolution methods can be readily constructed,and analyzed,by use of this generalized l_p-norm criterion.The results provide a better understanding of the role these deconvolution methods play in enhancing the resolution and the theoretical basis for further study of the optimal pulse compression criterion and the algorithms to find its optimal solution in deconvolution.