First - lets dispell a little confusion:
a title tag is what you use in the head of the html page to describe the page
a title attribute is what you would use on a href link as a tooltip to describe where the link is taking you
an alt attribute is used for accesibility reasons to describe what an image is for visually impaired or for browsers that dont display images well
OK thats the original uses of those elements
As far as SE's go - no one has ever proved to me whether an image using a title attribute is any help or hindrence - however - it is very possible to prove that using an image alt attribute does help - as a matter of fact Ive done it myself with two test sites and img alt attributes definitely help if written concisely and to the point without looking like spam - although there is a 100 character limit to the alt text originally - the SEs seem to think that anything over about 4 words is pretty much overdoing it
a proper way to use both attributes would be:
<a href="file.html" title="short description of linked page"><img src="file.jpg" alt="describe the image">
Hope that helps and of course this is just my opinion based on a lot of testing and previous experiences - others may have different results
