Los Angeles private equity firm the Gores Group LLC is buying Healthsouth Corp.’s diagnostic division for $47.5 million, the troubled Birmingham healthcare company said.

The sale announced Thursday is part of corporate restructuring that will shift Healthsouth’s focus to inpatient rehabilitation and reduce debt in the wake of an multibillion-dollar accounting scandal.

The diagnostic division includes 54 freestanding diagnostic imaging centers in 19 states and Washington, D.C. Gores officials said in a statement they plan to keep division operations headquartered in Birmingham. The deal should be completed by the end of June, the companies said.