Police have identified 75 suspects; most are from North Africa and entered Germany illegally or sought asylum.
A 23-year-old Moroccan man given a suspended sentence for theft has become the first person to be convicted in connection with the assaults.
The man, named only as Younis A, was handed a six-month suspended sentence for stealing a mobile phone.
"The CCTV footage is not good enough to clearly identify sexual assaults. We can see some thefts but that`s all. We are relying on witness accounts and victims identifying their attackers," said Mr Mathies.
Another Moroccan and a Tunisian were also due to face trial for theft.
They are among 13 men who have been arrested for stealing. Only one person, a 26-year-old Algerian asylum seeker, has been arrested on suspicion of sexual assault.
Mr Mathies` predecessor Wolfgang Albers was fired over his handling of the wave of assaults and robberies.
An official report found that Cologne police made "serious mistakes" in not calling in reinforcements and in the way they informed the public.
About 1,000 men of North African and Arab origin gathered near Cologne`s main station on 31 December.
Smaller groups formed, first surrounding women and then threatening and attacking them, the report said.
Chancellor Angela Merkel`s immigration policy has since come under mounting criticism. About 1.1 million asylum seekers arrived in Germany in 2015.
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