Nigella Lawson, the celebrity food writer and TV personality behind
Lawson "has left the house" she shares with her husband, her rep told E! News on Monday, giving no further details.
Saatchi, however, had comments aplenty Monday to explain the images.
"About a week ago, we were sitting outside a restaurant having an intense debate about the children, and I held Nigella's neck repeatedly while attempting to emphasize my point," the 70-year-old art collector told London's Evening Standard.
It was, he said, a "playful tiff" with "no grip."
According to the Mirror, the "tiff" included angry words and Nigella's tears, with Saatchi putting one or both of his hands around 53-year-old Lawson's neck a total of four times.
"It was utterly shocking to watch," an alleged onlooker told the paper. "I have no doubt she was scared. It was horrific, really. She was very tearful and was constantly dabbing her eyes."
"Nigella's tears were because we both hate arguing, not because she had been hurt," Saatchi told the Standard.
He also told the paper he'd told his wife to take off with the kids Sunday because paparazzi were congregated outside their home after the news broke.
Lawson has a son and a daughter, 17 and 19, from her first marriage. Her first husband, John Diamond, died in 2001, and she married Saatchi in 2003. Saatchi has a daughter, 18, from a previous relationship.