You said:

...this yields Cartesian results, creating duplicate values for Image records when there's no match in the Images table for values in the joined ones.

I'm not sure I understand what you mean there, but it sounds like you don't understand what "Cartesian" means in this context. You are querying for all columns from a set of joined tables, and when table A has two or more rows related to a single row of table B, the values from that row of B will have to be repeated for each matching row in A. That's the Cartesian product you get from doing that sort of join.

If you only want one row of output for each row in the Images table, you either don't want to join with tables that contain multiple matches to a given Images row, or else you want to select some sort of grouped or aggregate value from those other tables, so that there is only one value from each table to be returned for each row of Images -- e.g.:

SELECT
 ImageID,ImageName,
 Regio.RegioID,RegioName,
 Insula.InsulaID,InsulaName,
 Sources.SourceID,SourceName,
 (etc...),
 COUNT(ThemeID)
  FROM Images
    LEFT JOIN Regio ON Images.RegioID = Regio.RegioID
    LEFT JOIN Insula ON Images.InsulaID = Insula.InsulaID
    LEFT JOIN ImgThemes ON Images.ImageID = ImgThemes.ImageID
    LEFT JOIN Sources ON Images.SourceID = Sources.SourceID
    GROUP BY ImgThemes.ImageID
    ORDER BY ImageName LIMIT $start,$numrows"
[download]

Note the addition of the "GROUP BY" clause, and the use of the "COUNT()" function for returning a single value for all rows in the ImgThemes table that match a given Image row.

(update: fixed typo in field list of select statement)