We propose an image restoration technique that uses multiple image integration. The detail of the dark area when acquiring a dark scene is often deteriorated by sensor noise. Simple image integration inherently has the capability of reducing random noises, but it is especially insufficient in scenes that have a dark area. We introduce a novel image integration technique that optimizes the weights for the integration. We find the optimal weight map by solving a convex optimization problem for the weight optimization. Additionally, we apply the proposed weight optimization scheme to a single-image super-resolution problem, where we slightly modify the weight optimization problem to estimate the high-resolution image from a single low-resolution one. We use some of our experimental results to show that the weight optimization significantly improves the denoising and super-resolution performances.