@ Esther, the attached file may be useful to you.

If the silica and alumina impurities are mostly in separate grains or on the surface of the titania (as opposed to solid solution in titania), which is likely, you can treat the impure titania with concentrated NaOH (30-40%), preferably hot. Silica and alumina will dissolve selectively. It may take a while - depends a lot on sample thermal history, grain size of the impurities, crystallographic phase or lack of crystallinity etc. (quartz and sapphire in particular are very slow to dissolve). Then rinse the powder with deionized water, with dilute acid, and finally with water again.