This may sound tangential, but I think it's the best way to address what you want to do. this is as close as I can think of without discussing what you're doing in more detail.

Consider reading the output of a spectrometer using a linear CCD array. The objective is to measure the light intensity at different points along the array. With this model you have a number of noise sources in addition to the statistical nature of light. Their are losses in the charge transfers in the shift register, random ionizing radiation and EMI from the device.

Conventionally, you have resolution equal to the number of pixels in your array. However, courtesy of work by David Donoho and Emmanuel Candes of Stanford, you can do 5-10x better using compressive sensing.

If rather than sample each pixel individually, you instead sample sets of pixels with a random set turned off in each sample, you can then increase both your spatial and amplitude resolution by solving an L1 problem using linear programming or one of several other algorithms with very exotic names which accomplish the same thing.

The extreme example is the single pixel camera devised by a team at Rice led by Richard Baraniuk. Here's a link:

http://www.wisdom.weizmann.ac.il/~vision/courses/2010_2/papers/csCamera-SPMag-web.pdfTI does this in their near infrared photospectrometer product:

https://www.element14.com/community/roadTestReviews/2302/l/dlp-nirscan-nano-evaluation-module-reviewThe mathematics are nothing short of agonizing to read. However, actually doing it is quite easy. You only have to suffer if you want the proof it works.

The first monograph to come out was:

"A Mathematical Introduction to Compressive Sensing"

Foucar & Rauhut 2013

There are others now, but I've only read Foucart & Rauhut.

Aside from improving the resolution, you can also reduce the data acquisition time. This is being done for MRI scanners. I'm sure there are already other commercial applications. The mathematics is very general and in addition to compressive sensing, solves matrix completion, commonly called the" Netflix problem", solves inverse problems in physics and blind source separation which selects a single conversation out of a room full of people talking using a very small number of microphones placed at random locations in the room.

To apply this to your problem requires being able to explicitly describe all instances of the desired signal. That is all the possible answers. Finding a sparse L1 solution finds the optimal L0 solution if and only if the solution is sparse. In matrix notation, we're solving Ax=y where y is the measured data, x is the desired result and A is a matrix in which all the columns are uncorrelated. I usually call this L1 basis pursuit as that seems to me the most general name, but there are plenty of others. To use the language of Mallat in "A Wavelet Tour of Signal Processing" the A matrix is a dictionary containing all the possible answers and x is a sparse vector which selects the combination of columns of A which best fit y. If an L1 (least summed absolute error) solution for x exists which is a sparse vector it is unique and is the optimal L0 solution. The proof of this was done by David Donoho of Stanford in 2004.

To continue with the spectrometer example, A would be a matrix in which each column described the amplitude of the light at different positions along the array for a particular element. x would be the amount of that element present and y would be the CCD array output.

I've glossed over an immense amount of stuff, so I'm not sure what I've written makes sense. The links are much longer and more thorough, though even those don't explain why it works.