Proximal gradient-based optimization is one of the most common strategies for
solving image inverse problems as well as easy to implement. However, these
techniques often generate heavy artifacts in image reconstruction. One of the
most popular refinement methods is to fine-tune the regularization parameter to
alleviate such artifacts, but it may not always be sufficient or applicable due
to increased computational costs. In this work, we propose a deep geometric
incremental learning framework based on second Nesterov proximal gradient
optimization. The proposed end-to-end network not only has the powerful
learning ability for high/low frequency image features,but also can
theoretically guarantee that geometric texture details will be reconstructed
from preliminary linear reconstruction.Furthermore, it can avoid the risk of
intermediate reconstruction results falling outside the geometric decomposition
domains and achieve fast convergence. Our reconstruction framework is
decomposed into four modules including general linear reconstruction, cascade
geometric incremental restoration, Nesterov acceleration and post-processing.
In the image restoration step,a cascade geometric incremental learning module
is designed to compensate for the missing texture information from different
geometric spectral decomposition domains. Inspired by overlap-tile strategy, we
also develop a post-processing module to remove the block-effect in
patch-wise-based natural image reconstruction. All parameters in the proposed
model are learnable,an adaptive initialization technique of physical-parameters
is also employed to make model flexibility and ensure converging smoothly. We
compare the reconstruction performance of the proposed method with existing
state-of-the-art methods to demonstrate its superiority. Our source codes are
available at this https URL

在这项研究中，我们提出了一种基于二阶 Nesterov 近端梯度优化的深度几何增量学习框架，该框架能够高效地解决图像逆问题并降低图像重建中的伪影。我们的重建方案包括线性重建、级联几何增量修复、Nesterov 加速和后处理四个模块，并通过与现有技术的比较表明其优越性。