How to sync albums on my iPhone on to my computer?

I accidentally permanently deleted and misplaced all the folders of pictures I had on my laptop. I have a few folders on my iPhone from when I synced them on to my phone and I wanna know how I could place them on to my computer… It's just that those folders on my computer are deleted but they are on my iPhone still. I just want to transfer them on to my computer. I need help on how to do this because these pictures are VERY important to me. So if anyone knows how I could do this, any help will be greatly appreciated. Thank you.

Added (1). I already know how to sync photos from my camera roll, I just want to sync the other albums on my iPhone on to my computer.

If you have a windows computer, I'd try CopyTrans Manager. They have an app called Copy Trans Photo that says it's $19.99.

http://www.copytrans.net/support/gettingstarted-copytrans-photo/

I have a Mac and I use iExplorer by Macroplant. Http://www.macroplant.com/iexplorer/
Just to test your problem, I made a folder on my computer and put some pictures in it, then I synched them to my phone. I deleted them from my computer and was able to use iExplorer to return them to my computer.

In this picture, you can see the test folder I made and you can see the folder on my iPhone. I can simply drag and drop the folder back onto my computer.