Alberti was born in Langon, France. At the age of 19 in 1973, Alberti traveled to New York City planning to see Jimi Hendrix in concert, but only discovered of his death after her arrival. Instead of returning to France, she hitchhiked around the US for three years before she settled in New York City. There, she began a job as an au pair before turning to film.

In a podcast interview with Movie Geeks United!, Alberti states that she never attended film school. She first landed in the film industry as a still Photographer for porn films. In 1982, after having worked on enough film sets and getting to know people within the industry, she persuaded the filmmakers of the small punk film-noir film Vortex (1982) to let her be an assistant to the Cinematographer. At the time, she had known nothing about film-making and was trained by the film's Cinematographer, Steven Fierberg.

Alberti began her cinematography career working for the film company, Apparatus, run by short-film Director Christine Vachon. The first full-length documentary she shot was Stephanie Black's H-2 Worker (1990). She won her first Sundance Film Festival award as a Cinematographer for this film. She secured her career after being hired for Todd Haynes' controversial pseudo-documentary feature film Poison (1991).

Alberti's first big budget film was Haynes' Velvet Goldmine (1998) with a spending allowance of $8 million. Working on this film also consisted of her first time having to use a camera operator.

In June 2006, Alberti traveled to Germany to film portions of the FIFA World Cup for scenes to be shown in Michael Apted's soccer documentary The Power of the Game (2007).

A more recent work includes Darren Aronofsky's wrestling drama, The Wrestler (2008), starring Mickey Rourke. Aronofsky hired Alberti as the Cinematographer due to her documentary background. Prior to working on this film, Alberti had no knowledge or experience with wrestling so she would study the sport by attending wrestling matches with members of the crew every Saturday night for a period of time. She revealed that viewing the sport in person was helpful to see the world of wrestling. The Director and her decided on a "naturalist look"; her aim was to "make [the film style] work for the drama of the film and keep it as natural as possible" in order to let the viewer feel like they were in a "real [wrestling] place". Important film elements, styles, and techniques were decided between Alberti and the Director including an aspect ratio of 2.4:1 in order to capture the wrestling ring, fans, and the arena which they decided were very valuable to the sport. Alberti also used a handheld camera for the action scenes and shot in 16mm film to, as she states in an interview with MovieMaker, "[embrace] a slightly grainy, edgier look". She used the Arriflex 416 camera and Kodak Vision3 500T color negative film 7219.

In 2013, her photography series called The Pool Series was featured in the gallery 'Show Room' located in Brookyln, New York. Alberti has stated that she could not see what she was photographing and could "only anticipate what the next fragment of time might look like" and thus aimed to create an "artistic anticipation".