Official Prestashop documentation regarding the images http://doc.prestashop.com/display/PS15/Understanding+The+Preferences#UnderstandingThePreferences-Images
By default Prestashop uses only .jpg (transparent background supports only .gif and .png image types). But if you need transparent background for logo here you can find the solution:
1.1) Change image format in the Back-office. Back office > Preferences > Images and check the “Image Quality” as seen below.
1.2) Now if you go to Preferences > Themes and upload your png file as the header image, it will have transparency even though it'll say logo.jpg in the source code.
However if you'd prefer to hard-code your logo to be logo.png, you can do it via the file header.tpl in your theme.
For example Alysum theme \your_site\theme\alysum\header.tpl
On line ~77 change
to point to the image you wish to use. For example