Title: Signal denoising by maximum likelihood estimation with l_1-penalty

We consider an approach to signal denoising whereby a linear combination of wavelet bases is fitted to the noisy signal by maximizing the likelihood function minus an l_1-penalty on the coefficients of combination. The l_1-penalty induces parsimony of the coefficients while avoiding oversmoothing the fine scale features. For Gaussian noise, the maximization problem can be solved efficiently using a block coordinate relaxation method. For more general noise, the maximization problem can be solved using an interior point method. If the set of optimal coefficients is nonunique and unbounded, Tikhonov regularization can be used to ensure uniqueness of the coefficients. [This is joint work with Sylvain Sardy, EPFL, Switzerland.]