You're effectively doing signal analysis. It's neither quantum mechanics nor a semi-classical approximation. Signal processing is (very) often not stochastic (random), unless thermal noise is an issue for accurate modeling of the apparatus. It's often easier to find a way to eliminate the effects of thermal noise than to calculate the effects of thermal noise. If quantum noise has a significant effect, then one has to use quantum mechanics.
The mathematics of signal processing can almost always be presented in terms of Hilbert spaces, just because Fourier analysis of the signals is so important, even when the signals being processed are noise-free, which gives a specific mathematical link between deterministic signal processing and quantum mechanics, however the interpretation of the observables is generally quite different. I would say that the ideas that the "Wigner function is claimed to be a representation of the photon flux density in the radiation", and that negative values are unphysical, are not helpful, that it's better to see the negativity as a consequence of attempting to measure the frequency of a signal over a very small time period, whereas measuring the frequency of a signal precisely in principle requires the signal to be measured as a function of time for all time, because the Fourier analysis of a signal requires us to take the integral over all time, $\int_{-\infty}^\infty f(t)\mathrm{e}^{\mathrm{i}t\omega}\mathrm{d}t$.
A good reference for Wigner functions is Leon Cohen, "Time-Frequency Distributions-A Review", PROCEEDINGS OF THE IEEE, VOL. 77, NO. 7, JULY 1989, DOI: 10.1109/5.30749. Alternatively, a book by the same author, Leon Cohen, "Time Frequency Analysis: Theory and Applications". Sorry to say that either of these will need access to an academic library or cash. I didn't know of any on-line references before I searched for them now --- the Wikipedia page you want is cited on the page cited by Kostya, http://en.wikipedia.org/wiki/Cohen%27s_class_distribution_function; you should certainly read it as well because it is much more relevant to your application. There is a fairly strong sense in which this is well understood, but quantum mechanics, and particularly quantum field theory, is not so well-understood, which makes it correspondingly difficult to say that the relationship between classical signal processing and quantum mechanics is well-understood.
