ROCHESTER, N.Y.—Eastman Kodak Co. has obtained a bankruptcy judge’s approval to borrow an initial $650 million from Citigroup Inc. to keep operations running while it peddles a trove of digital-imaging patents.

The ailing photography pioneer filed for bankruptcy protection on Thursday, and is required under the financing terms to produce a reorganization plan by Feb. 15, 2013.

U.S. Bankruptcy Judge Allan Gropper in New York also set a June 30 deadline for Kodak to seek his approval of bidding procedures for the sale of 1,100 patents that analysts estimate could fetch at least $2 billion.

After years of struggles to transform itself into a printing powerhouse, Kodak ran short of cash and sought protection from its creditors. It has been trying to sell its patents since July.