Aside from the JPEG compression in the posted image, part of the issue is the monochromatic nature of both the hair and the background that takes away some of the power of using color channels as the starting point for a good mask. However, the hair does contain red tones, so the contrast should be better in the green or blue channel.
Usually, this kind of exercise is shot on a green screen or similar backdrop - skin tones and most hair is light in the grayscale red channel and the green background is dark in the red channel, making this channel a nice place to start the construction of a mask.
In this image, you are relying on separation between the subject hair and the background based on luminosity, more or less. In this case, you can try to use the most contrasty channel as a starting point and then use the regular tricks - levels adjustment to increase contrast, painting in Overlay mode, etc. and also Refine Edge in the Mask Properties dialog.
If you do this kind of extraction a lot, consider shooting against a chromakey background or similar field that provides more channel separation.
kirk