We present a novel approach to compensate coherence effect via combining the transport of intensity equation (TIE) with look-up table phase compensation (LUT-PC) method. It is the better version of the Speckle-TIE method we demonstrated before on the basis of the quantitative phase imaging camera with a weak diffuser (QPICWD). With the phase gradient ratio theory and the look-up table method, the phase blurring caused by underestimation of phase gradient will be compensated correctly by reasonable rescaling. The LUT-PC SpeckleTIE method has the evident predominance of speediness since it only needs one slightly defocused speckle image in one time owing to that the reference speckle image can be captured beforehand. The deblurring achieved by this method improves the imaging resolution to the theoretical partial coherence limit with good robustness, reducing artifacts and improving the accuracy and contrast. The experimental results show the effectiveness of the technique.