Elizabeth Edwards Finds Inspiration in Sandra Bullock

06/30/2010 AT 09:15 AM EDT

Though they've never met, Elizabeth Edwards says she is inspired by Sandra Bullock's story and can relate to the actress's struggle to deal with a very public breakdown of a marriage with dignity and grace.

Asked in a Today show interview Wednesday whether she's bitter about the end of her marriage to John Edwards, Elizabeth said the hardest part now is being defined simply as a cuckolded wife.

"I think about Sandra Bullock, who I don't know at all, but what an incredible year she's had," Edwards said. "She won the Academy Award for an incredible performance … and yet the stories you hear are not about all of those great successes but about the failure of her marriage. And I thought, that's not who she is."

Like Bullock, Edwards – who also speaks out in PEOPLE's new issue, on newsstands Friday – says she is now trying to overcome a "media-imposed image" the public has of her. "In a sense – and I don't know her – but I assume [Bullock] wants to reclaim who she is in the same way that I want to reclaim who I am," Edwards said.

She adds: "I hope the next time I'm on television, it's to talk about some policy I really care about and not about this part of my life, of which I'm hoping maybe this chapter will close the door."

The chapter she's referring to is a new section of her book Resilience, added for the paperback version, in which Edwards addresses the finality of her breakup with her husband of more than 30 years following his affair with Rielle Hunter.

Edwards said Wednesday that her husband's affair still baffles her – "It's hard to believe the same person could marry me and be attracted to that woman as well," she said – and that John is "no longer the person who I married."

Yet she still wants a positive relationship with John for the sake of their children, particularly the younger two – Emma Clair, 12, and Jack, 10. (They have an older daughter, Cate, who is 28. Their son Wade was killed in a car accident in 1996 at age 16.)

"I have three living children for whom this is a father who I want them to love and on whom they're going to have to rely if my disease takes a bad turn," said Edwards, who has battled cancer since 2004. "It's really important to me that they see him in a positive light."

For much more of what Elizabeth Edwards has to say about her post-scandal life and how her children now treat their father, pick up this week's new issue of PEOPLE, on newsstands Friday

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