Sparse synthesis regularization with deep neural networks
arXiv:1902.00390
The paper introduces a sparse reconstruction framework for inverse problems that trains an encoder‑decoder network with an ℓ¹ penalty, enabling sparse signal recovery via thresholded encoded coefficients and an ℓ¹‑Tikhonov regularization functional.
Abstract
We propose a sparse reconstruction framework for solving inverse problems. Opposed to existing sparse regularization techniques that are based on frame representations, we train an encoder-decoder network by including an $\ell^1$-penalty. We demonstrate that the trained decoder network allows sparse signal reconstruction using thresholded encoded coefficients without losing much quality of the original image. Using the sparse synthesis prior, we propose minimizing the $\ell^1$-Tikhonov functional, which is the sum of a data fitting term and the $\ell^1$-norm of the synthesis coefficients, and show that it provides a regularization method.
Presented at the SAMPTA 2019 conference