Americans are back to eating out at Cheesecake Factory and Texas Roadhouse, putting the restaurant industry on track for its best showing in more than three years as the recovery broadens.

Sales at full-service eateries, where customers pay after a meal rather than before, will rise 0.7 percent in 2011 after adjusting for inflation, the first year-over-year increase since 2007, according to a National Restaurant Association forecast by Malcolm Knapp, a New York-based consultant who has monitored the industry since 1970.

The pickup may help jump-start a restaurant rebound after a record stretch of sales declines, and also reinforces growing strength in household spending, which accounts for 70 percent of the economy.

“Consumers are finding some retail therapy in things like eating out,” said John Herrmann of State Street Global Markets in Boston.