Numerical differentiation with regularization, allowing differentiation of noisy data without amplifying noise. Uses total variation and related penalty functions for regularization, allowing the derivative to be discontinuous.
This code implements the algorithm in the paper R. Chartrand, "Numerical differentiation of noisy, nonsmooth, multidimensional data," in IEEE Global Conference on Signal and Information Processing, 2017. A notebook reproducing the examples from this paper is in the examples directory. The implementation is in the function regularized_differentiation.regularized_gradient.tv_regularized_gradient.
The code was initially written and used in Python 2.7, but has been tested in Python 3.7.1.
To install, clone the repo, then run pip install -r requirements.txt from the top-level directory, then python setup.py develop. One of the dependencies is pyfftw, which requires that fftw3 be installed first (as in sudo apt-get install libfftw3-dev libfftw3-doc in Ubuntu). Soon it should be possible to instead just pip install regularized_differentiation (the bottleneck being pyfftw not managing its dependencies properly).