Adaptive signal denoising with provable guarantees via first-order algorithms ---- Dmitrii Ostrovskii

We consider the problem of recovering the signal observed in Gaussian noise. In this problem, classical linear estimators are known to be quasi-optimal provided that the set of possible signals is convex, compact, and known a priori. However, when this set is unknown, designing an estimator that does not “know” the underlying structure of the signal, yet has favorable theoretical guarantees of statistical performance, remains a challenging problem.

We study a family of estimators for statistical recovery of signals satisfying certain time-invariance properties. Such signals are characterized by their harmonic structure, which is usually unknown in practice. Our estimators are capable of exploiting this unknown structure without estimating it directly. In particular, we demonstrate that these estimators admit theoretical performance guarantees, in the form of oracle inequalities, in a variety of settings. We provide efficient algorithmic implementation of these estimators via first-order optimization algorithms with non-Euclidean geometry, and evaluate them on a synthetic data benchmark as well as some real-world signals and images.

 

Dmitrii Ostrovskii is a postdoc at SIERRA team of INRIA Paris, hosted by Francis Bach.