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 the deep neural networks and the 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; and 3) an image boosting procedure using a deep neural network to improve the contrast and to recover the lost details of the combined images. Experimental results show that CsNet can consistently improve the denoising performance for both deterministic and neural network denoisers.