Robust wavelet denoising

For extracting a signal from noisy data, waveshrink and basis pursuit are p owerful tools both from an empirical and asymptotic point of view. They are especially efficient at estimating spatially inhomogeneous signals when th e noise is Gaussian, Their performance is altered when the noise has a long tail distribution, for instance, when outliers are present. We propose a robust wavelet-based estimator using a robust loss function. T his entails solving a nontrivial optimization problem and appropriately cho osing the smoothing and robustness parameters, We illustrate the advantage of the robust wavelet denoising procedure on simulated and real data.