With the help of Picsmize - Image Optimizer app available on Shopify app store,

You can compress Shopify products and Store assets images manually as well as automatically.

See how,

Step 1 : 

Install the "Picsmize - Image Optimizer" App from Shopify app store. Jump to step 2 if app is already installed on your store.

Step 2 :

Go to the Apps section in Shopify Admin > Open Picsmize app.

Step 3:

On Dashboard, you will see a list of all images available in your Shopify store,

To manually compress or process the image, click the option (three dots) button and Click compress.

That's it. You are done. :)

Same way, You can compress product as well as asset images available in your store.