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Synthetic aperture radar (SAR) images offer crucial information for studying and monitoring sea ice in the Arctic. Sentinel-1 captures images of the area using an extremely wide swath for reduced revisit time. The backscattered signal from sea ice and open water is often very weak, making it difficult to distinguish from the sensor thermal noise floor. Thermal noise impacts the images by generating a bias and increasing the fluctuations related to the speckle phenomenon. Analyzing these images requires both correcting this bias and reducing fluctuations without blurring out the image content. The acquisition of several subswaths in a single pass using Terrain Observation with Progressive Scans (TOPS) produces images that exhibit, after compensation for antenna gains, a nonuniform thermal noise floor and strong discontinuities between subswaths. Denoising techniques must take these specificities into account to restore the images. This article introduces a joint approach to remove the thermal noise offset and suppress fluctuations due to speckle and thermal noise. Compensating at once for all these effects largely reduces artifacts at the boundary between subswaths. We demonstrate using both numerical simulations and actual Sentinel-1 images that debiased polarimetric reflectivities can be recovered and fluctuations strongly reduced while preserving fine spatial structures.