In order to overcome the effect of the atmosphere turbulence and reconstruct the high resolution image of the extended object, an improved speckle imaging algorithm based on bispectrum truncation method was proposed. There are two problems in phase recovery using the conventional algorithms: one is the enormous amount of the bispectrum data, and the other is the complicated computation. The improved algorithm combines phase recovery with the bispectrum computation by the Hermite symmetry of image and the look-up table technique. Only the bispectrum in neighbored domain of a spatial frequency below the cut-off frequency are calculated and some constraint is added to the bispectrum coordinates, therefor the improved algorithm makes a dramatic reduction in the bispectrum data. The coordinate look-up table, which is applicable to the two neighbored quadrants in Fourier domain, describes the computation sequence of the bispectrum and the phase recovery. The look-up table makes the phase recovery become simple, for the bispectrum and the object phase can be obtained just in order of the look-up table. The results on simulated demonstrate that the improved algorithm is able to recover the object phase correctly with a 24% reduction in the bispectrum data. The phase spectrum obtained by the improved algorithm displays the profile and structure of the object after inverse Fourier transform. The results on real world astronomical data demonstrate the improved algorithm can restore the image with higher resolution than the original image and it obtain almost the same final image as bispectrum truncation method with less computation time.