If you're having that much trouble with this one, try formatting it more simply at first. This is a complex line of code the way you have it and you aren't able to spot the error.
Here's your code made more simple IMO. I left in your error, and moved the ternary stuff out of the array and into an if. Do you see the error now?
<?php
$src = 'assets/peach/img/sprites/userinfo/avatars/avatar.png';
if(!empty($this->session->userdata('avatar'))){
$src = 'assets/peach/img/sprites/userinfo/'.$this->session->userdata('avatar');
}
$image_properties = array(
'src' => $src,
'height' => '80px',
'width' => '80px',
'alt' => 'Avatar' )
);