Synthetic test that shows the application of the 2D discrete Fourier transform and the 2D wavelet transform to denoise white noise

I have great interest in signal processing, so I decided to learn more along my PhD. Unfortunately, this was a part of my PhD that did not worked as I expected but it took me to other works. This is part of the extended abstract 2D discrete wavelet transform for denoising aeromagnetic data that I presented in 2018 at the SEG conference in Anaheim, CA - USA, with some things that I presented in my PhD qualifying exam. Here are the slides of the presentation. For contextualization, there is a Disneyland in Anaheim. These techniques can be applied to any kind of data, although I applied in magnetic data, on that time. The discrete wavelet transform is used to denoise white noise and also defines the edges of an image. In this work, the filtering in Fourier domain is performed with a Buterworth filter and in wavelet domain with the hard threshold with cycle spinning.