Though the image quality degradation caused by atmospheric turbulent noise can be overcome and the diffraction-limited resolution image reconstruction of telescope can be achieved with speckle masking, there are many kinds of noise in a real speckle detector, which introduce noise bias terms into the average power spectrum and bi-spectrum of speckle images and distort the recovery of module and phase. The noise problem was discussed and a positive restriction method to correct the noise bias terms in bi-spectrum was presented. The high resolution image reconstruction observation of binary star ADS16800 and triple star Hld171 (ADS16648) was reported.
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