This image was originally shot in RAW. Like I said there was no posterization in the original before it was converted to JPG for the web gallery. I haven't yet had a chance to go back and take a look for the quality settings (which I never noticed or modified, so that is the likely culprit).
Yes ironing would help reduce the wrinkles in the backdrop, it takes about 15 minutes to iron those things. I'm gonna buy a steamer this weekend, and hopefully find a better backdrop. For now I'll have to iron out the wrinkles in photoshop. The two muslin sheets I have are just too thin, definitely the weakest pieces of my kit.
One interesting thing to note is that I'm currently working on a different computer right now and looking at that image as I'm typing this reply, and I can't see the posterization at all. I'm currently on a notebook computer, is this maybe some sort of colorspace/monitor calibration issue? I didn't do anything to convert the colorspace of those images to sRGB before the creation of the LR gallery.
To clearly see the source of posterization, I loaded the image in PS, added a curve adjustment layer to it and moved the top right corner of the line to the left, until Input 25, Output 255 or so.
What I see is
1. the posterisation (at least that, what is visible on my monitor) comes from the shadow on the cloth (you should iron the cloth to eliminate the strong lines of folding :-).
2. there are quite large chunks of identical pixels. 90 kilobytes for a 600x900 JPEG image is not much, i.e. the degree of lossiness is high (compared to this background). Higher quality setting makes the chunks smaller, i.e. the transitions appear smoother.
If you created this image from a larger, higher quality JPEG, take a look at that one the same way. Was that quality high enough? If you have the image in TIFF (i.e. in raw converted in TIFF), then create the Web version from that one, not from an intermediate JPEG.
If it is raw based, then perhaps increasing the black level would eliminate this issue all together by making the background pure black.