I want to build an iOS 10 app that lets you shoot a RAW (.dng) image, edit it, and then saved the edited .dng file to the camera roll. By combining code from Apple's 2016 "AVCamManual" and "RawExpose" sample apps, I've gotten to the point where I have a CIFilter containing the RAW image along with the edits.
However, I can't figure out how to save the resulting CIImage to the camera roll as a .dng file. Is this possible?
A RAW file is "raw" output direct from a camera sensor, so the only way to get it is directly from a camera. Once you've processed a RAW file, what you have is by definition no longer "raw", so you can't go back to RAW.
To extend the metaphor presented at WWDC where they introduced RAW photography... a RAW file is like the ingredients for a cake. When you use Core Image to create a viewable image from the RAW file, you're baking the cake. (And as noted, there are many different ways to bake a cake from the same ingredients, corresponding to the possible options for processing RAW.) But you can't un-bake a cake — there's no going back to original ingredients, much less a way that somehow preserves the result of your processing.
Thus, the only way to store an image processed from a RAW original is to save the processed image in a bitmap image format. (Use JPEG if you don't mind lossy compression, PNG or TIFF if you need lossless, etc.)
If you're writing the results of an edit to PHPhotoLibrary, use JPEG (high quality / less compressed if you prefer), and Photos will store your edit as a derived result, allowing the user to revert to the RAW original. You can also describe the set of filters you applied in PHAdjustmentData saved with your edit — with adjustment data, another instance of your app (or Photos app extension) can reconstruct the edit using the original RAW data plus the filter settings you save, then allow a user to alter the filter parameters to create a different processed image.
Note: There is a version of the DNG format called Linear DNG that supports non-RAW (or "not quite RAW") images, but it's rather rare in practice, and Apple's imaging stack doesn't support it.