North Bay home prices continued to climb upwards in 2012, part of an overall 32 percent year-over-year boost for housing prices around the Bay Area and the fastest median price increase in more than 25 years, according to a monthly real estate market report released this week.

Combined with a continued decrease in foreclosure rates, as indicated by a separate monthly report by Irvine-based foreclosure tracker RealtyTrac, the trend points toward gradual but steady recovery for the region's housing market.

"Prices are in the midst of bouncing off bottom right now, and nobody really knows what the trajectory of this bounce will be at this point," said John Walsh, president of San Diego-based real estate data service DataQuick, in his company's report."So far, supply has been a bottleneck, but as prices go up, more homes will be put up for sale."

The North Bay median prices for the year rose most in Marin County, which had a 27.6 percent increase to $660,750 from 2011, according to San Diego-based real estate data service DataQuick.

Sonoma County's median increased 23.4 percent to $345,000; Solano County's, 19.6 percent to $218,000; and Napa County's, 10.2 percent to $350,000.

The median price for a home sold in the nine-county Bay Area was $442,750, up from a low of $290,000 in March 2009 but down from a high of $665,000 in summer 2007.

The price increase for homes sold around the Bay Area reflected, in part, a greater number of sales for medium- to high-priced homes. The number of homes sold for less than $500,000 decreased 12.6 percent year-over-year, while the number sold for more than that amount increased 61.2 percent.

The number of homes sold rose 4.5 percent across the Bay Area, but declined in two North Bay counties. Napa had 129 homes sold in December, down 2.3 percent, and Solano had 610 homes sold, down 14.6 percent.

Conversely, the number of homes sold in Marin rose 3.9 percent to 291 and in Sonoma, 3.2 percent to 555.

A shortage of inventory continues to slow the rate of sales, according to the report. In addition, mortgage lenders have been overwhelmed by purchase and refinance requests, further slowing the market.

Rising prices could mean more homes coming to the market in coming months, according to the report.December sales highest since 2006

While the number of homes sold across the Bay Area in December was the highest since 2006, the 7,832 homes sold was still 9 percent lower than the average number sold for all Decembers since DataQuick began gathering data in 1988.

Distressed property sales, which include foreclosure resales and short sales, made up 34.2 percent of the resale market. There were 18.2 percent fewer than in the same month in 2011.

Foreclosure resales, at 11.8 percent of sales, were at their lowest levels since accounting for 10.1 percent in November 2007.

Short sales made up 22.4 percent of Bay Area resales in December, down from 24.6 percent one year earlier.Investors, cash buyers dominate market

Investors purchased 25.8 percent of all Bay Area homes in December, an all-time high for the month since statistics began in January 1999. The level was up from 23.8 percent one year ago, and those investors paid a median price -- $315,000 -- 34 percent higher than a year prior.

Buyers appearing to pay all cash accounted for 29.3 percent of sales in December, up from 27.3 percent one year ago.

Government-insured Federal Housing Administration loans, popular with first-time buyers, accounted for 18.9 percent of all Bay Area home-purchase loans in December. That lending was down from a 22.9 percent share a year earlier.

A recent decrease in the program could show difficulty in qualifying for loans and increased competition with investors and other cash buyers, according to the report.Foreclosures fall, still higher than national average

The rate of new foreclosure filings continued to fall across the North Bay in December, with many counties beating the statewide rate but failing to beat the rate nationally, according to the RealtyTrac report.

Marin County had the lowest rate of new foreclosure filings -- one in every 1,087 homes. There were 819 foreclosure properties on the market, selling for an average of $660,000. The 100 new filings in December were down from 212 in January 2012, the earliest comparable data.

In Sonoma County, one in every 678 homes received a filing in December. There were 2,360 foreclosure homes on the market in the county, with an average sale price of $293,636. There were 296 new filings in December, and 657 in January.

In Napa County, one in every 667 homes was involved in a filing in December. There were 599 foreclosed homes on the market that month, with an average sale price of $289,139. 82 homes were involved in a filing that month, down from 172 in January.

Solano County had the highest foreclosure rate in the North Bay that month. One in every 264 homes was involved in a new foreclosure filing in Sonoma County in December, and there were 2,979 in some part of the foreclosure process that month. The average price for a foreclosed home was $236,975, with 572 new filings in December and 908 filings in January.

Mendocino County saw one filing for every 489 homes, with 79 new filings in December. There were 469 homes at some point in the foreclosure process that month, with an average sale price for a foreclosed home of $207,927.

In Lake County, one in every 382 homes were part of a foreclosure filing in December, and there were 879 homes at some point in the process. The average sale price for a foreclosed home was $102,733, and the new filings that month was down from 207 in January.

Statewide, one in every 457 homes was part of a filing, compared to a national average of one in every 810 homes.