A question about Wolverine's memory loss?

In X-Men (the original movie), Wolverine (aka Logan) does not remember his history. He recovers bits and pieces of it, but never seems to fully recover his memory.
In X-Men Origins: Wolverine it appears that he lost his memory due to an adamantium bullet fired into Logan’s skull, which happened some time in the 1970’s, based on events in the movie.
So, in The Wolverine, why does he remember Yashida, who he saved from an atomic bomb during World War II?