Sentinel-1 is a synthetic aperture radar (SAR) platform with an operational mode called extra wide (EW) that offers large regions of ocean areas to be observed. A major issue with EW images is that the cross-polarized HV and VH channels have prominent additive noise patterns relative to low backscatter intensity, which disrupts tasks that require manual or automated interpretation. The European Space Agency (ESA) provides a method for removing the additive noise pattern by means of lookup tables, but applying them directly produces unsatisfactory results because characteristics of the noise still remain. Furthermore, evidence suggests that the magnitude of the additive noise dynamically depends on factors that are not considered by the ESA estimated noise field. To address these issues we propose a quadratic objective function to model the mis-scale of the provided noise field on an image. We consider a linear denoising model that re-scales the noise field for each subswath, whose parameters are found from a least-squares solution over the objective function. This method greatly reduces the presence of additive noise while not requiring a set of training images, is robust to heterogeneity in images, dynamically estimates parameters for each image, and finds parameters using a closed-form solution. Two experiments were performed to validate the proposed method. The first experiment simulated noise removal on a set of RADARSAT-2 images with noise fields artificially imposed on them. The second experiment conducted noise removal on a set of Sentinel-1 images taken over the five oceans. Afterwards, quality of the noise removal was evaluated based on the appearance of open-water. The two experiments indicate that the proposed method marks an improvement both visually and through numerical measures.