Belvin Perry and Casey Anthony
Red Huber/Reuters/Landov (2)
09/29/2011 at 11:00 AM EDT
A week after her psychological treatment
began, Casey Anthony is doing "well," according to a source close to her, who adds, "She hopes she will someday redeem herself and live a productive life."
The public, meanwhile, may get to see another side of the infamous Florida resident
. In court on Wednesday, a media organization argued for the release of a jailhouse video of Casey
watching TV news reports saying police found remains, which turned out to be her missing daughter, 2-year-old Caylee.
According to detectives, Anthony doubled over and hyperventilated before asking for a sedative in the video.
Her reaction is striking because the remains had not yet been identified. Did she know the remains belonged to Caylee?
The tape was sealed by a judge in 2009, after he said it would be "inflammatory" and prejudicial to a jury. Now that the trial is over – and Anthony has been acquitted of murder
– several media outlets say that the video should become public record.
is expected to rule on the matter this week.
For more on Casey Anthony's true-crime drama, based on PEOPLE's unparalleled access at key moments of the case, buy PEOPLE's book Outrage
, available now at people.com/caseyanthony