The deficiency of the existing level-set-based denoising techniques is that they are sensitive to noise. This is due to that fact that the curvature and gradient measurements in the partial differential equation are very sensitive to noise, and the denoising performance is affected. This work proposes to perform the level-set-based curve evolution on the dyadic wavelet transform domain. The main advantage is that in the dyadic wavelet transform domain, noise has less influence on curvature and gradient measurements as the scale increases. Thus, the edge indicator function value can be directly calculated from the dyadic wavelet coefficients rather than from an external force field by convolving the noisy image with a Gaussian filter. For further reducing the noise at the finest scale where noise is dominant, minimum mean-squared-error (MMSE)-based filtering is performed as the first pass of denoising, followed by performing the level-set curve evolution as the second pass of further denoising and enhancement. Experimental results demonstrate that the proposed algorithm generates state of the art denoising results.