Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction

TL;DR

This paper introduces a learnable descent algorithm for nonsmooth, nonconvex image reconstruction that combines deep learning with convergence guarantees, improving performance and efficiency over existing methods.

Contribution

It presents a novel, provably convergent descent algorithm that integrates deep neural networks into nonsmooth nonconvex image reconstruction, enabling flexible and efficient regularization.

Findings

The method achieves competitive results on various image reconstruction tasks.

The network inherits convergence guarantees from the algorithm.

It demonstrates parameter efficiency and superior performance compared to state-of-the-art methods.

Abstract

We propose a general learning based framework for solving nonsmooth and nonconvex image reconstruction problems. We model the regularization function as the composition of the $l_{2,1}$ norm and a smooth but nonconvex feature mapping parametrized as a deep convolutional neural network. We develop a provably convergent descent-type algorithm to solve the nonsmooth nonconvex minimization problem by leveraging the Nesterov's smoothing technique and the idea of residual learning, and learn the network parameters such that the outputs of the algorithm match the references in training data. Our method is versatile as one can employ various modern network structures into the regularization, and the resulting network inherits the guaranteed convergence of the algorithm. We also show that the proposed network is parameter-efficient and its performance compares favorably to the state-of-the-art methods in a variety of image reconstruction problems in practice.