Total-variation regularization

tvreg_smoothed_series solves the one-dimensional ROF objective 0.5 ||x-y||² + lambda ||D x||₁ with deterministic ADMM iterations, a fixed rho = 1, and a residual tolerance of 1e-9. tvreg_series differentiates the resulting signal with the finite-difference estimator.

lambda must be positive and finite and the iteration count nonzero. The penalty is on adjacent index differences, not elapsed time, so uneven sampling changes its physical interpretation. No convergence status, adaptive penalty, weighted observations, or higher-order TV model is exposed.