Sorry to bump an old thread, but I came here looking for a similar answer. Unfortunately both of the answers listed here are not best practices for accessibility, so I want to be sure that's noted.
Alt text is limited to about 100 characters, less than a Tweet, and unlikely to fully describe a complex image. The Poet Training Tool is a great resource for learning how to properly describe complex images.
Using a table for the purpose of layout is generally discouraged for accessibility reasons. Tables primarily should be used for tabular information, generally rows and columns of text and numbers, and only when following accessibility standards such as including a caption and identifying row and column headers. Tables generally should not be used for layout or positioning, as in placing an image and a caption together, without taking into consideration how screen readers interact with tables, such as reading order. See Webaim's article Creating Accessible Tables offers a good explanation.
Right now I'm opting for a paragraph of text immediately above or below the image, where the paragraph begins with something like "Caption: ..."
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