Many tools are available for checking whether or not your images need to be optimized, in addition to other performance metrics. To list a few:
It is important to bear in mind that most available tools simply check whether or not an image contains unnecessary metadata in the form of EXIF elements. They do not an can not test how a site might benefit from more drastic image recompression and re-encoding such as that which Kraken.io performs, which is often a source of misunderstanding for many users.
For example, let's take an imaginary image and call it example.jpg. example.jpg might contain 12KB of EXIF headers and have a total file weight of 1012KB.
Typical performance scanning tools will claim a 12KB reduction in size when analyzing that image. However, using sophisticated image recompression (such as that which Kraken.io offers) the file weight can be reduced by up to 90% - we have even seen savings of up to 92%.
Now let's take the resulting image, which is say 100KB in size, and re-apply the EXIF metadata. The performance scanning tool will still complain about the 12KB of EXIF metadata, because that is the only factor which is analyzed. But wait, we have reduced the image's weight by 90%, and the tool is still complaining? What is going on? It is simple: as previously stated, the tools we are aware of will simply check the opportunity for metadata stripping.
The more sophisticated tools might additionally look at opportunities for resizing images to match the dimensions in which they are presented on the page by its CSS and HTML. In some cases they might even check that the image (when a JPG) has been progressively encoded. With that said, do be aware that pagespeed analysis tools do not paint the full picture, particularly when it comes to images on your site.