Image denoising aims to restore a clean image from an observed noisy one. Model based image
denoising approaches can achieve good generalization ability over different noise levels and
are with high interpretability. Learning-based approaches are able to achieve better results, but
usually with weaker generalization ability and interpretability. In this paper, we pro pose a
wavelet-inspired invertible network (WINNet) to combine the merits of the wavelet-based
approaches and learning based approaches. The proposed WINNet consists of K-scale of lifting
inspired invertible neural networks (LINNs) and sparsity-driven denoising networks together
with a noise estimation network. The network architecture of LINNs is inspired by the lifting
scheme in wavelets. LINNs are used to learn a non-linear redundant transform with perfect
reconstruction property to facilitate noise removal. The denoising network implements a sparse
coding process for denoising. The noise estimation network estimates the noise level from the
input image which will be used to adaptively adjust the soft-thresholds in LINNs. The forward
transform of LINNs produces a redundant multi-scale representation for denoising. The
denoised image is reconstructed using the inverse transform of LINNs with the denoised detail
channels and the original coarse channel. The simulation results show that the proposed
WINNet method is highly interpretable and has strong generalization ability to unseen noise
levels.