Updated

TEMPE, Ariz. -- The Arizona Cardinals returned to practice Tuesday after a long bye weekend off and the biggest news was Tyrann Mathieu's rapid recovery from a shoulder injury.

Coach Bruce Arians said he "really has" been surprised by how quickly Mathieu is coming back. The do-everything All-Pro defensive back was projected to be out three to six weeks after he sustained a shoulder subluxation in the team's Oct. 30 loss at Carolina.

Arians described Mathieu as "real close" but didn't know if that meant he could play Sunday when the Cardinals are home against the San Francisco 49ers.

Mathieu is coming off an offseason knee surgery and was getting closer to being his old self when the shoulder injury hit. His absence could mean another chance for rookie Brandon Williams, a starter at cornerback when the season began. Williams lost his job to Marc us Cooper after struggling mightily and has been inactive in recent weeks.

"I thought Brandon has gotten better and better," Arians said. "He had a nice interception today. He is more than ready if he is needed."

Arians said tight end Darren Fells (ankle) and outside linebacker Alex Okafor (calf) were ahead of schedule in their return from injury. There was no official injury report because Tuesday's workout was a bonus practice due to the bye week.

"We actually should get a few guys back that might be able to play in this ball game that I didn't think we would," Arians said.

The Cardinals entered the bye with a disappointing 3-4-1 record midway through their season. They fell two games behind first-place Seattle in the NFC West when the Seahawks beat Buffalo on Monday night.

The schedule gets tougher after the 49er game, with five of the Arizona's final seven games on the road, including trips to Minnesota, Atlanta and Seattle.

"There is no doubt" the bye week did the Cardinals a lot of good, Arians said, "a lot of rest and a lot of guys that wouldn't have been able to play last week that are healthy and practicing now."

He insisted the season is still salvageable.

"Just go to work every day," Arians said. "Everything that we set our goals for in April is obtainable. We just have to play better."

During the bye weekend, the coach and his staff spent "a bunch" of time reviewing film of the team's first-half games.

What was discovered?

"I wouldn't care to share that part," Arians said, "but there were a lot of things we learned about ourselves."