Grampian Police said they are following a number of leads after the 22-year-old was attacked in the Powis area of Aberdeen on Saturday morning.
They have released a description of the man who struck in Bedford Avenue at around 7.30am.
He is around 30 years old, white, about 6ft, of medium build and has an unkempt appearance, as if he had been sleeping rough.
The man is thought to have been wearing a black hooded top, a red, white and blue scarf, and grey or black hiking boots with thick laces.
Detective Chief Inspector Martin Dunn said: "We have received a number of calls from members of the public with information relating to Saturday morning's incident. We also have a number of lines of enquiry which we have picked up from door-to-door enquiries and officers are following up on those.
"I am grateful to those people for coming forward but I would also like to urge anyone who saw anything suspicious at all, no matter how small or insignificant they believe it to be, to contact us as soon as possible. It may be the vital link we are looking for."
Police have also released a description of the victim to help jog people's memory.
She is around 5ft 6in, slightly built and was wearing a dark jacket and dark jeans. She also wore a black and white woollen hat and was carrying a green and blue handbag with tan straps.
DCI Dunn said: "This was a particularly nasty attack and we have increased police patrols in the area. As always, I would also remind members of the public to take all reasonable precautions to protect their personal safety."