If you also want to remove the background from your render in Cycles, in the render options you will find a similar panel to that in Eevee. There, you can turn on Transparency in the Film settings, as shown here:
And your render will have a transparent background. Just remember to save your files as a PNG, with the RGBA option checked, to keep that transparency in the final image.
To apply a filter to your render and reduce the amount of noise, you can turn on the Denoising option in your Viewport tab in the properties window, shown in the following screenshot. Using the default settings of the filter will ...
