Recovery from a halftone image

I need to recover a B&W, fairly high-res image made up of only black and white pixels (a halftone, but individual pixels, not circular patterns for printing). The goal is to make it look more or less like a regular greyscale, so it loses that grainy look when printed. The detail is there, it's just muddled by this.

The best solution I've found so far is a gaussian blur to mix everything together. Sadly, this leaves everything rather noisy. Is there a better way than just blue + noise removal + unsharp mask? Or is this the standard prescription for such an image.

Filter > Noise > Median

Copy your layer, run this filter on it, probably around 2-5 and then lower the opacity of the layer so it fades into the image nicely. I like to make multiple layers, run the filter on a low setting and build it up. Works wonders.

I had to do the same thing on a poorly scanned image that had a moire pattern. It got 95% of the moire out, which made the client quite happy.

Hope this helps.