filter_file_names.php

<?php
$file_names = array('GOPR1772.jpg', 'GOPR1955.jpg', 'IMG_2393.jpg',
  'IMG_2393_big.jpg', 'national-seismic-trace.png', 'foo_BIG.jpg');

$filtered_file_names = array_filter($file_names, function($value) {
  return stripos(strtolower($value), '_big.') === FALSE;
});

var_dump($filtered_file_names);
?>

gistfile1.txt

$ php -f filter_file_names.php 
array(4) {
  [0]=>
  string(12) "GOPR1772.jpg"
  [1]=>
  string(12) "GOPR1955.jpg"
  [2]=>
  string(12) "IMG_2393.jpg"
  [4]=>
  string(26) "national-seismic-trace.png"
}