Rails Permission denied @ dir_s_mkdir
We need to grant permission to access the required directory for the system root user
sudo chmod 777 -R your_project_directory_to_be_access
In your case you can use:
sudo chmod 777 -R /var/www/noise/public
For security reasons, just keep in your mind:
chmod 777
gives everybody read, write and execute rights which for most problems is definitively too much.