In theory, a perfectly clean signal fed through a perfect low-pass filter would eliminate all of the information above the cutoff frequency. However there is no implementable perfect low-pass filter. Instead, the high-frequency information can be attenuated, but not eliminated. In truth, there may be total information loss at certain specific notch frequencies, but that can happen only at an infinitesimally small subset of the band, so you won't miss it. So an appropriately-designed reversing filter could recover effectively all of the useful information.
In practice, this breaks down because noise enters the picture. The quantization of the output of the low-pass filter will introduce noise in the signal. Now if done right, the noise will be low enough that you won't notice it if you leave the filtering alone. But if you try to reverse the filtering, then those places that were severely attenuated will now be severely noisy.
So what I think all of this means from a practical standpoint is that you can do a limited amount of reversal, but if you try to be too aggressive with it you'll just end up with a lot of noise and you'll quickly see that it's not worth it.
I'd start by designing the theoretically near-perfect reversing filter, and follow it with a new lowpass filter. By adjusting the cutoff of the new lowpass filter, you can trade noise for high frequency content to your liking.
(Edit) Oops, I forgot one important wrinkle. Sometimes the low-pass filtering will be accompanied by some sort of upsampling or downsampling (interpolation, chroma resampling, etc.) In those cases, thanks to aliasing effects, it's much harder (and sometimes impossible) to reverse the filtering process. For example, in a downsampling stage, high-frequency information is actually folded back into the low-frequencies as aliasing noise, and cannot be separated out.
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