Fourier deconvolution is a good tool to remove the blurring of images with a very high SNR. However it suffers under severe noise degradation and becomes impracticable at a SNR of 20dB. If the convolution width is very high this happens even earlier. The analysis of the frequency spectrum brings information on the data, especially on the periodicity of certain features. Furthermore it can be used to better understand other processing tools. Gaussian blur and smoothing can be used with the goal to enhance image structures at different scales. They have the effect of reducing high frequency information, corresponding to high pixel to pixel variation and usually a characteristic of noise. However it also reduces detail. In 2D better resultsmay be obtained, because diagonal pixels can be used in addition. Gaussian smoothing is certainly a useful tool in the analysis of ARPES data and it should be well integrated in other measures of data recovery. If the blurring of the signal is high it is beneficial apply some Gaussian blur before proceeding to other measures. If the blurring of the signal is low, it is better to apply Gaussian smoothing only after de-convolution measures in order to not loose information on the signal.