  Given a set of image denoisers, each having a different denoising capability,
is there a provably optimal way of combining these denoisers to produce an
overall better result? An answer to this question is fundamental to designing
an ensemble of weak estimators for complex scenes. In this paper, we present an
optimal combination scheme by leveraging deep neural networks and convex
optimization. The proposed framework, called the Consensus Neural Network
(CsNet), introduces three new concepts in image denoising: (1) A provably
optimal procedure to combine the denoised outputs via convex optimization; (2)
A deep neural network to estimate the mean squared error (MSE) of denoised
images without needing the ground truths; (3) An image boosting procedure using
a deep neural network to improve contrast and to recover lost details of the
combined images. Experimental results show that CsNet can consistently improve
denoising performance for both deterministic and neural network denoisers.
