Aiming at image reconstruction problem

an image reconstruction method based on weighting function with statistic is proposed. Regarding as degraded images not only have Gaussian noise but also have Laplacian noise

the idea of the maximum likelihood estimation is adopted to estimate the variance of Gaussian noise and Laplacian noise; Because

in reconstruction process

the distribution of noise change

the weighting function of Gussian and Laplace is constructed based on statistic

which integrates L

1

and L

2

norm

and design an adaptive weighting function. Combine with bilateral total variation（ BTV） regularization algorithm

an adaptive image restoration method is

designed by weighting function. Experimental results show that in comparision with hybrid errors model（ HEM） based on L

1

-L

2

norm

peak signal to noise ratio（ PSNR） and structural similarity（ SSIM） are increased by an average of about 2. 07 d B

0. 02

for degraded image with different noise

can achieve more satisfied result.