Learning Plug-And-Play Proximal Quasi-Newton Denoisers

Plug-and-play (PnP) denoising for solving inverse problems has received significant attention recently thanks to its state of the art signal reconstruction performance. However, the performance improvement hinges on carefully choosing the noise level of the Gaus-sian denoiser and the descent step size in every iteration. We propose a strategy for training a Gaussian denoiser inspired by an unfolded proximal quasi-Newton algorithm, where the noise level of the input signal to the denoiser is estimated in each iteration and at every entry in the signal. Our scheme deploys a small convolutional neural network (mini-CNN) to estimate an element-wise noise level, mimicking a diagonal approximation of the Hessian matrix in quasi-Newton methods. Empirical simulation results on image deblurring demonstrate that our proposed approach achieves approximately 1dB improvement over state of the art methods, such as, BM3D-PnP and proximal gradient descent-PnP that are supplied with the true noise level, as well as over an end-to-end retrained FFDNet architecture that was trained to estimate the noise level and recover the deblurred images.