CBS News correspondent Kimberly Dozier, who was wounded by a car bomb in Iraq that killed four other people, is expected to return to the United States on Wednesday, the network said.

Dozier, 39, was critically wounded May 29 in an attack that killed her camera crew — Britons Paul Douglas and James Brolan — as well as a U.S. soldier and an Iraqi translator.

CountryWatch: Iraq

She underwent two emergency operations in Iraq before being flown the next day to the U.S. military's Landstuhl Regional Medical Center in southern Germany. She suffered head and lower body injuries, and her family said she would need rods in her legs.

A CBS News statement said Tuesday that Dozier was making progress, adding that "the swelling of her face has decreased significantly, she had the first physical therapy session on her legs, and she had her hair washed."

The network said Dozier was in good spirits. She was initially scheduled to be flown home Sunday, but the plane expected to carry her was full.