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Titles can be used to clarify and enhance accessibility but can also impede accessibility when used for no reason e.g. duplicating link text.
Most users will visually scan a page, not hover over each item, so in all cases ease of use is enhanced by using clear link text, clear form element labels etc. Where an element needs additional clarification add a title element. But don't fall into the trap of using the title attribute just for the sake of using it.
By design a background image will not be "read" by screen reader software or search engine spiders, so unless the image is adding essential information to the page having neither an alt or title attribute directly/indirectly associated with a tables' background image is an entirely acceptable (and accessible) approach.