TV2_interpolation

Matlab and Python implementation of a regression method for noisy 1D data that minimizes second-order total-variation regularization with the minimum number of piecewise-linear regions. The Matlab implementation uses the GlobalBioIm library as a dependency. The Python version uses a custom implementation of the Alternating Direction Method of Multipliers (ADMM) algorithm; its only dependencies are Numpy and Scipy.

Getting started

Matlab:

• gBLASSO_sol.m solves the (g-BLASSO) regression problem for a fixed regularization parameter
• user_interface.m does so with a GUI that allows to user to vary the regularization parameter manually
• main_example.m gives an example of how these functions are applied

Python:

• denoise_y() in denoising.py computes the denoised data points (with adjustable noise level) using ADMM
• sparsest_interpolant() in sparsification.py computes the linear spline that connects the noisy data points with the fewest possible knots using Algorithm 1 in Debarre et al. 2022
• main_example.py gives an example of how these functions are applied

References

Sparsest Piecewise-Linear Regression of One-Dimensional Data
Journal of Computational and Applied Mathematics, vol. 406, p. 114044, May 2022.
T. Debarre, Q. Denoyelle, M. Unser, and J. Fageot.

Pocket Guide to Solve Inverse Problems with GlobalBioIm
Inverse Problems, vol. 35, no. 10, pp. 10-20, October 2019.
E. Soubies, F. Soulez, M. McCann, T-a. Pham, L. Donati, T. Debarre, D. Sage, and M. Unser.

Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers.
Foundations and Trends® in Machine learning, vol. 3, no. 1, p. 1-122, 2011.
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein.