Background you can remove in the conventional way: add background points manually, then make a polynomial fit for them, subtract the fitting curve from the data. Noise could be removed pretty nicely by FFT smoothing or you may try any other smoothing functions available, just keep comparing initial picture to the smoothed, to avoid artifacts.

It is not necessary to remove the background noise from the graph as it may be caused due the instrument or sample or it might be due to amorphous nature of the sample. moreover smoothing the graph using any software alters your original data, just for the sake to make your figure look beautiful. So it is recommended to avoid such practice.