Image upload failure may have various reasons and so, becomes difficult to know that whom to approach for its solution! Before you actually approach someone, just try to troubleshoot it as mentioned below,

How to know that problem really is of image?

Apart from the obvious thing that you can see on your site that images are failing to load, this kind of problem often creates some fatal error like PHP Fatal error: Call to undefined function imagecreatefromjpeg()or a completely blank screen ( blank screen is a result of fatal error only. you can print this error on your screen.).

Troubleshoot

Considering the above error and situation, this problem lies in your php that runs on your web space. So,

• Check whether GD Library is installed in it or not? If not then install it.
• If it is installed then make sure its JPEG extension (library) is installed and enabled.

But how will I know and do that?

Generally, these things are looked into by your web hosts. So, for these checking and installation, you should ask your web host to install and configure that on your site to solve your problem.

Still if you want to know it by yourself then you can try out php function,

• Go to your active WordPress directory and open the functions.php file (of your active theme) located in ../wp-content/themes/../functions.php
• Now, write this code echo phpinfo();  in it to know all the information of your php and save it
• Now refresh your site to see the effect.

On using php function, you will be having a whole page of information where you can check out GD information as shown below,

PHP Reference

If you really want to get into the roots then you can read this php tutorial http://www.php.net/manual/en/function.imagecreatefromjpeg.php#70832