Fourier and Wavelet domain based on deconvolution algorithm has a massive superiority over others when the noise level of blurred image is low. However, this kind of method will lead to a bad result when the blurred image is noisy. In this paper, to solve this problem, two constrained terms were introduced into Fourier domain filter and Wavelet domain filter correspondingly. In Fourier domain, the objective function was performed in a matric form and was added with Laplacian regularization. The parameter of this regularization term was computed from the noise power and the power of high frequencies. Similarly, the objective function in Wavelet domain was equipped with power constrain and the parameter of power constrain term was a function of the parameter of Laplacian regularization term. The Laplacian regularization term reduced the power of error caused by Fourier domain and the power constrain enhanced the anti-noise ability of Wavelet domain filter. Experiments showed that the improved algorithm led to a better results with stronger robustness. The peak signal to noise ratio of the improved algorithm was averagely 1 more than the number of initial algorithm, when the standard deviation of noise ranged from 0.01 to 0.1. And the robustness to point spread function was shown. Even when the variance of Gaussian point spread function deviated about 0.4 away from the ground truth, the peak signal to noise ratio of the improved algorithm was higher than the number of initial algorithm.