allow non logged in user to upload images in media library

The hook wp_ajax_{action} is for logged-in users and wp_ajax_nopriv_{action} for non logged-in users.

For example in your functions.php file,

add_action( 'wp_ajax_your_ajax_action', 'your_ajax_function_callback' ); // logged-in users
add_action( 'wp_ajax_nopriv_your_ajax_action', 'your_ajax_function_callback' ); // logged-out users

function your_ajax_function_callback() {
    // handle ajax request
}