Foreclosures remain a problem, but two recent developments showing they are a lessoning one.

Two developments in the foreclosure market this week, one involving completions and the other construction, have shown that housing is slowly but surely working its way through the distressed inventories that have long plagued the industry.

First, LPS has reported that “foreclosure sales,” the period when a foreclosure process is completed and a property becomes an REO, increased by 29 percent from December to January and by 15 percent from a year ago.

Foreclosure sales have been on a bit of a roller coaster ride the last three years. After rising and falling through 2008, sales rose steadily from mid-2009 to late 2010, exceeding 80,000 every month of that period; moreover, sales exceeded 100,000 eight times and 120,000 twice.

That trend collapsed in the last coupled months of 2010, when the robo signing scandal froze the vast majority of foreclosures by the nation’s largest banks. With the mortgage settlement behind us, though, banks are resuming their foreclosure activities and working their way through the extensive backlog of properties that developed during the big freeze in 2011.

But an uptick in foreclosures does not mean an absence of new construction, ironically. A recent HousingWire article highlighted that Census Bureau data compiled by the Federal Deposit Insurance Corp. found that in the latter half of 2011, building permit activity increased in states hardest hit by foreclosures,

In Nevada, for instance, which has been the poster child for foreclosures since 2007, single-family home permits were up by 16.1 percent year-over-year in 2011’s fourth quarter; Georgia, the most bank-failure-prone state in the country, saw permits rise 16 percent in the quarter; and Florida, where the average foreclosure takes nearly 900 days to complete, permits were up 22 percent in the third quarter and 26 percent in the fourth quarter, year-over-year.

The story was even more dramatic for the multifamily sector, undoubtedly the jewel of the construction industry the last few months. Nationally, multifamily starts were up 21 percent in February (they were down 1.1 percent for all of housing), and in Georgia, they were up 160 percent year-over-year in the fourth quarter.

Paul Diggie, property economist for Capital Economics, said in HousingWire’s article that 2012 should be a solid year for starts.

“The slight fall in housing starts in February leaves the recent upward trend broadly intact,” Diggie said. “Housing starts should rise further later this year on the back of continued employment growth and an improvement in housing demand.”