NEW YORK — Sponsors who stuck by Tiger Woods are ramping up to profit from his return to the golf course.

Upper Deck Co. will sell memorabilia like signed red shirts with price tags upward of $1,800. Electronic Arts Inc. has a new browser-based version of its Tiger-themed video game coming out next week. And Nike Inc. reportedly has a TV commercial featuring Woods in the works, though it won’t confirm that.

The big question is whether his tarnished image can work anything close to its old magic for them and the golf industry, which has been going through tough times of its own because of the weak economy.

It could be that all publicity is good publicity — as time passes since his admissions to extramarital affairs and he returns to golf after four months at the Masters, starting next Thursday.

Woods’ value as a pitchman who embodied professional perfection may have suffered. He became sports’ first $1 billion earner, but lost top endorsements from companies such as Accenture LLP and AT&T Inc. as the scandal unfolded.

But it’s hard to see much falloff in sales of some Woods-branded wares.

Golfsmith, the nation’s biggest chain of golf stores, and sports card and memorabilia maker Upper Deck Co. say Woods’ scandal that erupted in late November didn’t dampen demand for his products.

Golfsmith International Holdings Inc. says sales of Woods-branded hats, shirts and belts (all made by Nike) grew 8 percent from October through mid-March this year compared with last year. Most of that period came after word spread that the quiet, clean-cut golfer had a sex addiction and partook in serial infidelities.

The company sold 9,564 Woods-branded hats, belts, shirts and other products made by Nike from October through mid-March, compared with 8,855 in the same period the previous year.

Woods’ leave from golf will end in about a week at the Masters, the season’s first major tournament. It’s about time for an industry that has seen its retail sales drop as its main participants trim their tee times and spending habits in the recession.

“The tour wants him back. The players want him back. His endorsers want him back and like anybody with an economic interest in him, we want him back,” said Golfsmith CEO Marty Hanaka.

Tiger has been good for golf. He’s brought more interest to the game from even casual players, and boosted television ratings and sponsorships — which has translated into higher payouts for Woods and his fellow golfers. In 1995, the year before Woods turned pro, the Masters’ total prize payout was $2.1 million. Last year, it reached $7.5 million.

The sport is in need of a boost again. The industry has seen an unprecedented slump because of the weak economy and unseasonably wet weather, which also depresses playing, said Tom Stine, co-founder of Golf Datatech LLC, a market research firm.

Total revenue for the golf industry was $2.4 billion last year, down 11.6 percent from $2.8 billion in 2008, the firm said. People are delaying equipment purchases but they’re still playing golf, said Stine, who expected minimal effect from Woods’ return.

EA is releasing the browser version of “Tiger Woods PGA Tour” on Tuesday. The timing is good, though coincidental: the video game maker announced the launch date a day before Woods announced his return and now figures his return will just add exposure for its sites for the game and its Woods franchise.

“Sometimes you just get lucky,” said Craig Evans, marketing director of the game, who added visits to the company’s Woods sites have risen “significantly” since Woods said he’d return.