Underwater images are degraded due to scatters and absorption, resulting in low contrast and color distortion. In this paper, a novel self-similarity-based method for descattering and super resolution (SR) of underwater images is proposed. The traditional approach of preprocessing the image using a descattering algorithm, followed by application of an SR method, has the limitation that most of the high-frequency information is lost during descattering. Consequently, we propose a novel high turbidity underwater image SR algorithm. We first obtain a high resolution (HR) image of scattered and descattered images by using a self-similarity-based SR algorithm. Next, we apply a convex fusion rule for recovering the final HR image. The super-resolved images have a reasonable noise level after descattering and demonstrate visually more pleasing results than conventional approaches. Furthermore, numerical metrics demonstrate that the proposed algorithm shows a consistent improvement and that edges are significantly enhanced.