It was my understanding that the type of compression used was equivalent to taking the square root of the amplitude at each pixel.
The idea is to retain almost all bit level detail at low levels and to discard fine tonality in highlights.
<edit > : Here is a link to the details behind the scheme
"out of 16 bits.....the finest gradations are contaminated by noise....simply crossed out....The processor of the M8 now multiplies the 14 bit number of every pixel with 4 and extracts the integral square root from that sum.The resulting values are somewhere between 0 and 255 and can be written with 8 bits. By squaring them and dividing them by 4 we again achieve the values of the 14 bit tonal spectrum"