Abstract: 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.

Key words: Euclidean space, Deconvolution, Generalized l_p-norm criterion, Criterion function