A one-year-old Federal Housing Administration program to help otherwise responsible homeowners who lost everything in the housing crash is starting to help these boomerang buyers, according to a new report from CNBC.

After renting for three years, [Linda] Van Doren bought a home last summer, using a loan insured by the Federal Housing Administration (FHA).

Since the housing crash began, 7.2 million homes have been lost to foreclosure or short sale, according to Black Knight Financial Services. Most of those former owners became renters and still are, but some are slowly, carefully moving back into homeownership. A new government program is making that happen faster than ever before.

"We see a lot of boomerang buyers. I'd say about 20% of my current clientele has either suffered a short sale or a foreclosure in the past and are now re-buying back into the marketplace," said Matt Weaver, a lender with PMAC Lending Services in Florida.

"It's mine, I can do what I want to do. I love it. I come home from work and I know what I'm working for."

The bulk of those borrowers are using a new program launched last summer by the FHA, the government's insurer of home loans. The program requires that applicants show they lost at least 20 percent of their income for at least six months and that that caused them to lose their home. They then must show they recovered from that hardship and have had clean credit for at least one year. The loans are fully documented, with all the borrowers finances considered.