There is enough information, should one be able to retain the phase; getting it from intensity is much more challenging. I'm familiar with the work of one of t

There is enough information, should one be able to retain the phase; getting it from intensity is much more challenging. I'm familiar with the work of one of the authors; he is a world expert on diffraction inverse problems in physical context. From a quick skim of the paper, it would appear that they're simply being careful and clever.