Learning Deep $\ell_0$ Encoders
This addresses sparse approximation for theoretical and application cases, presenting a hybrid deep learning approach that is incremental in methodology.
The paper tackles the nonconvex ℓ₀ sparse approximation problem by proposing Deep ℓ₀ Encoders, which model iterative algorithms as neural networks with novel neurons and pooling functions, achieving faster inference, larger learning capacity, and better scalability compared to conventional sparse coding.
Despite its nonconvex nature, $\ell_0$ sparse approximation is desirable in many theoretical and application cases. We study the $\ell_0$ sparse approximation problem with the tool of deep learning, by proposing Deep $\ell_0$ Encoders. Two typical forms, the $\ell_0$ regularized problem and the $M$-sparse problem, are investigated. Based on solid iterative algorithms, we model them as feed-forward neural networks, through introducing novel neurons and pooling functions. Enforcing such structural priors acts as an effective network regularization. The deep encoders also enjoy faster inference, larger learning capacity, and better scalability compared to conventional sparse coding solutions. Furthermore, under task-driven losses, the models can be conveniently optimized from end to end. Numerical results demonstrate the impressive performances of the proposed encoders.