Analyzing "The Yellow Wallpaper" from a Freudian perspective might cover several different areas, from husband-as-father to transference. However, the most important Freudian concept that applies to the story might be repression.
The narrator is literally repressed by her husband, who thinks of her almost as a child and keeps her from pursuing her passions. She then associates the wallpaper in her room with a fantasy designed to free her from the well-meaning isolation, and all-but represses the real world around her so she can inhabit her fantasy. In this sense, she is not repressing her memories or past, but repressing her total sensory input to become satisfied with a small space; since her husband limited her sensory input, she learns to live mentally inside an even more limited area, "repressing" all outside concepts. She seems to retain her mental faculties, as she is able to tell her husband where a key is, but applies unreasonable importance to the shape of a room and wallpaper.