In this paper, we propose a new wavelet denoising method with edge preservation for digital images. Traditionally, most denoising methods assume additive Gaussian white noise or statistical models; however, we do not make such an assumption here. Briefly, the proposed method consists of a combination of dyadic lifting schemes and edge-preserving wavelet thresholding. The dyadic lifting schemes have free parameters, enabling us to construct filters that preserve important image features. Our method involves learning such free parameters based on some training images with and without noise. The learnt wavelet filters preserve important features of the original training image while removing noise from noisy images. We describe how to determine these parameters and the edge-preserving denoising algorithm in detail. Numerical image denoising experiments demonstrate the high performance of our method.