This is the most mind-blowing finding I have made playing with channels!
YOU CAN NOT!
And here comes a long explanation why.
My first reaction was like the other two posts. Invert the image will invert the values (layer 1), then just re-reverse the hue (layer2, orange elipse) and voila!
The Hue is in fact reversed but not the saturation and brightness.
I was wondering why, and I remembered that that is not how those HSB channels work.
When you invert a saturated color, the saturation remains the same. Let's see why.
Here is an almost red color. If we invert the values on an RGB file, the channels are in fact inverted but the overall saturation, which is the difference between the maximum value and the minimum one is, in this case, the same. The same saturation.
Now I made more complex tests.
1. The test sample
Here is a color table with HUE+Saturation circles organized in groups with the exact same brightness.
And here is the separated channels. (Photoshop cannot separate the channels like this, but PhotoPaint can)
The result is clear on each H+S+B Channel and they are as expected.
2. Inverting the RGB file
And now let's just invert the RGB file. The result is obvious on the HUE Channel, but funny things start to appear on the Saturation and Brightness channels. They are simply NOT the opposite of what we got earlier.
Now let's play with the S and B channels... And we are starting to mess things up.
3. Inverting saturation
By actually inverting the saturation channel we start to simply loose information.
We told every outer color in circles "You all guys are NOT saturated" so they all turned white or gray.
4. Inverting Brightness
This is even worst. We are telling all the first circle. "You guys do not have any light. You are all black".
5. Taken to the extreme
Here I am inverting both.
Notice the red dots at the center. We will address that later(1).
As shown a color is dependant on the other values to actually be a color. If you remove for example the Brightness of all colors you simply turn off the lights. By removing saturation you do not only remove saturation, but also Hue.
(1) The explanation about the red is when you remove the color information, removing either the saturation or the brightness, any original value the color had is irrelevant, so the hue is reset to 0, which is the value of the red hue.
You can not
You can not by using RGB channels because the 3D geometry of the space is different.
An RGB file which is normally how you work on most digital images is a cube with linear coordinates. But the HSB is a Cone with radial and polar coordinates. And as far as I know, Photoshop cannot work in HSB mode.
Use PhotoPaint that can work in HSB channels as I have shown here.
Prepare an Exel table that can be used to generate an HTM+CSS file to show you the colors.