[2006.09534] Discriminative reconstruction via simultaneous dense and sparse coding

Computer Science > Information Theory arXiv:2006.09534 (cs) [Submitted on 16 Jun 2020 (v1), last revised 26 Mar 2026 (this version, v4)] Title:Discriminative reconstruction via simultaneous dense and sparse coding Authors:Abiy Tasissa, Emmanouil Theodosis, Bahareh Tolooshams, Demba Ba View a PDF of the paper titled Discriminative reconstruction via simultaneous dense and sparse coding, by Abiy Tasissa and 3 other authors View PDF HTML (experimental) Abstract:Discriminative features extracted from the sparse coding model have been shown to perform well for classification. Recent deep learning architectures have further improved reconstruction in inverse problems by considering new dense priors learned from data. We propose a novel dense and sparse coding model that integrates both representation capability and discriminative features. The model studies the problem of recovering a dense vector $\mathbf{x}$ and a sparse vector $\mathbf{u}$ given measurements of the form $\mathbf{y} = \mathbf{A}\mathbf{x}+\mathbf{B}\mathbf{u}$. Our first analysis relies on a geometric condition, specifically the minimal angle between the spanning subspaces of matrices $\mathbf{A}$ and $\mathbf{B}$, which ensures a unique solution to the model. The second analysis shows that, under some conditions on $\mathbf{A}$ and $\mathbf{B}$, a convex program recovers the dense and sparse components. We validate the effectiveness of the model on simulated data and propose a dense and sparse autoencoder (De...