A simple simulation to show the effect of the positivity constraint in Richardson-Lucy deconvolution.
Originally written in MATLAB, this code can be successfully run in Octave after installing and loading the statistics package from Octave Forge.
Support for GPU acceleration is provided through the USE_GPU flag, but is overkill for the example ground truth provided by default.
The image above shows results of the simulation when run using the following parameters:
max_photons = 100;
num_iter = 100;
pixel_size = 20;
spacing_px = 4;
n = 512;
lambda = 510;
numerical_aperture = 1.4;
background_level = 0;
left_bg = 0;
mid_bg = 0.05;
right_bg = 0.25;
As the RNG seed is not set before each run, the results will vary slightly in noise profile every time the simulation is repeated. Here, the line-pair spacing is 80 nm, while the resolution limit of the imaging system is ~180 nm. Despite this, RL produces an output with a distinctly resolved line pair in the region with zero background. The line pair remains an unresolved 'block' in regions with a higher background level.