  In the past decade, sparsity-driven regularization has led to advancement of
image reconstruction algorithms. Traditionally, such regularizers rely on
analytical models of sparsity (e.g. total variation (TV)). However, more recent
methods are increasingly centered around data-driven arguments inspired by deep
learning. In this letter, we propose to generalize TV regularization by
replacing the l1-penalty with an alternative prior that is trainable.
Specifically, our method learns the prior via extending the recently proposed
fast parallel proximal algorithm (FPPA) to incorporate data-adaptive proximal
operators. The proposed framework does not require additional inner iterations
for evaluating the proximal mappings of the corresponding learned prior.
Moreover, our formalism ensures that the training and reconstruction processes
share the same algorithmic structure, making the end-to-end implementation
intuitive. As an example, we demonstrate our algorithm on the problem of
deconvolution in a fluorescence microscope.
