Sparse representations in nested non-linear models

Following recent contributions in non-linear sparse representations, this work focuses on a particular non-linear model, defined as the nested composition of functions. Recalling that most linear sparse representation algorithms can be straightforwardly extended to non-linear models, we emphasize that their performance highly relies on an efficient computation of the gradient of the objective function. In the particular case of interest, we propose to resort to a well-known technique from the theory of optimal control to evaluate the gradient. This computation is then implemented into the “ℓ₁-reweighted” procedure proposed by Candès et al., leading to a non-linear extension of it.