denoising floor function
The problem is a bit more complicated that mere denoising, since a highly non-linear operator affects the original signal. Restoration or recovery would be more appropriate.

The floor function acts as an instance of data quantization (and possibly saturation or clipping). And adding noise is also known as dithering, a method to  reduce sensitive quantization effects (dequantization).
Those are keywords you can use along with: restoration, recovery, inference... Without more information on the signal's dynamics, models, and the noise, a couple of pointers that I am aware of (to be updated):


Wavelet denoising of coarsely quantized signals
quantized compressing sensing
piecewise regular approximations