Fourier transform artifacts
The cross pattern is typically a border effect, due to the periodicity induced by the standard implementation and hypotheses behind the Fast Fourier transform, when the image lacks periodicity from the right to the left, and the bottom to the top. In other words: if two opposite borders lacks continuity in values (when glued together), artifacts show.


The easiest way out is to multiply your image by an apodizing window, that goes smoothly to $0$ on the border (imagine for instance a 2D Hamming window). 
A mirror extension is a second option. 
More involved, you can try the Periodic plus smooth image decomposition, that has been used in random texture synthesis. Some Python versions have been offered:


Periodic plus smooth image decomposition, as described by Moisan
Python implementation of Moisan's periodic-plus-smooth decomposition of an image, with an improvement described in a series of blog posts, like: On the periodic-plus-smooth decomposition of an image, part 7: improved implementation of Moisan’s algorithm.