First it uses the double line interposition and the minimum summation of grey value in differential coefficient image to extract the direction of motion blurred image then uses traveling wave equation to restore the blurred image which is caused by uniform linear motion .
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New method of calculating summation of series is constructed by using a set of suitable wave functions in an infinite square potential well of one dimension .
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In terms of the Kirchhoff summation method of wave equation an approximate calculation formula for 3-D synthetic seismograms of a single layered interface is established in this paper .
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The general summation formulas and the rule for finding the suitable wave functions are given .
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