Using multiple transparency effects on top of images within Indesign will cause problems when offset printing.
Pixilation occurs when the underlying image has multiple transparency effects applied.
The solution is to create the ‘underlay’ in Photoshop as an image. Import the ‘underlay’ Photoshop file (do not to apply any effects in InDesign). 
Now you can create the InDesign transparency ‘overlay’ on top of the placed image. The end printed result will not pixilate. 
To check, use Distiller to create the final PDF for printing from the postscript file.