One way to reduce the visibility of the rosette structure is to move to a finer AM/XM screen which makes the rosette smaller and hence less visible. However, if that is not possible, then changing the separation method might be a viable option.
The majority of RGB to CMYK image conversions use "GCR" as the method (it is the default separation technique in Adobe PhotoShop). This ensures that wherever C, M, and Y inks are used black will be introduced. The result is a very visible rosette structure as seen in the left image below.
To reduce, and even eliminate most rosettes, a better strategy is to use the UCR separation method on problematic images. UCR separations (see image on right above) unlike GCR separations, primarily introduce black only in neutral and near neutral color areas. Since very little, if any, black is introduced in C and M screen tint areas – no rosettes are actually formed in those areas and hence no rosettes are visible. The result is smoother, less grainy appearing color.
While the UCR separation technique can reduce or even eliminate rosettes, there is a downside in that there will be a slight increase in ink usage as well as a slight reduction in color stability through the pressrun. That is why it should be used only for images with problematic colors - primarily dark blues and purples as well as dark skin colors/areas.