Our goal is to obtain a noise-free, high resolution (HR) image, from an observed, noisy, low resolution (LR) image. The conventional approach of preprocessing the image with a denoising algorithm, followed by applying a super-resolution (SR) algorithm, has an important limitation: Along with noise, some high frequency content of the image (particularly textural detail) is invariably lost during the denoising step. This 'denoising loss' restricts the performance of the subsequent SR step, wherein the challenge is to synthesize such textural details. In this paper, we show that high frequency content in the noisy image (which is ordinarily removed by denoising algorithms) can be effectively used to obtain the missing textural details in the HR domain. To do so, we first obtain HR versions of both the noisy and the denoised images, using a patch-similarity based SR algorithm. We then show that by taking a convex combination of orientation and frequency selective bands of the noisy and the denoised HR images, we can obtain a desired HR image where (i) some of the textural signal lost in the denoising step is effectively recovered in the HR domain, and (ii) additional textures can be easily synthesized by appropriately constraining the parameters of the convex combination. We show that this part-recovery and part-synthesis of textures through our algorithm yields HR images that are visually more pleasing than those obtained using the conventional processing pipeline. Furthermore, our results show a consistent improvement in numerical metrics, further corroborating the ability of our algorithm to recover lost signal.