This paper does further research for the lifted Donoho wavelets.Through the computing of regularity and the wavelets sampling approximation theory

we explain it has better approximation capability when N=N~=4(denoted as SWE13/7)

and it precedes D9/7 wavelets in sampling approximation.The lifting coefficients of SWE13/7 are all simple fractions

so wavelets transform only with integer shift and adder operations can be obtained in computing process

the computing complexity is efficiently lower than D9/7

and the result is equivalent to those using floating number in computing process.The line-based lifting scheme can efficiently decrease the memory usage

and increase the speed at parallel computing case.This paper has realized the line-based lifting scheme of SWE13/7

it has lower complexity than D9/7 in evidence.Numerical experiments indicate that the image compression performance of SWE13/7 precedes that of D9/7 when using EZW coding

and its computing complexity is much less.