Plug-and-Play methods constitute a class of iterative algorithms for imaging
problems where regularization is performed by an off-the-shelf denoiser.
Although Plug-and-Play methods can lead to tremendous visual performance for
various image problems, the few existing convergence guarantees are based on
unrealistic (or suboptimal) hypotheses on the denoiser, or limited to strongly
convex data terms. In this work, we propose a new type of Plug-and-Play
methods, based on half-quadratic splitting, for which the denoiser is realized
as a gradient descent step on a functional parameterized by a deep neural
network. Exploiting convergence results for proximal gradient descent
algorithms in the non-convex setting, we show that the proposed Plug-and-Play
algorithm is a convergent iterative scheme that targets stationary points of an
explicit global functional. Besides, experiments show that it is possible to
learn such a deep denoiser while not compromising the performance in comparison
to other state-of-the-art deep denoisers used in Plug-and-Play schemes. We
apply our proximal gradient algorithm to various ill-posed inverse problems,
e.g. deblurring, super-resolution and inpainting. For all these applications,
numerical results empirically confirm the convergence results. Experiments also
show that this new algorithm reaches state-of-the-art performance, both
quantitatively and qualitatively.

本文提出了一种新型的 Plug-and-Play 方法，使用半二次分裂作为正则器，将梯度下降步骤实现为由深度神经网络参数化的功能。作者证明了该算法是一个收敛的迭代方案，可应用于各种形式的逆问题，比如去模糊、超分辨率和修复等，达到与最先进的方法相当的性能。

梯度步长去噪器用于插拔式收敛

Gradient Step Denoiser for convergent Plug-and-Play

Snapshot compressive imaging (SCI) aims to record three-dimensional signals
via a two-dimensional camera. For the sake of building a fast and accurate SCI
recovery algorithm, we incorporate the interpretability of model-based methods
and the speed of learning-based ones and present a novel dense deep unfolding
network (DUN) with 3D-CNN prior for SCI, where each phase is unrolled from an
iteration of Half-Quadratic Splitting (HQS). To better exploit the
spatial-temporal correlation among frames and address the problem of
information loss between adjacent phases in existing DUNs, we propose to adopt
the 3D-CNN prior in our proximal mapping module and develop a novel dense
feature map (DFM) strategy, respectively. Besides, in order to promote network
robustness, we further propose a dense feature map adaption (DFMA) module to
allow inter-phase information to fuse adaptively. All the parameters are
learned in an end-to-end fashion. Extensive experiments on simulation data and
real data verify the superiority of our method. The source code is available at
this https URL

本文提出了一种基于 DUN 的快速高效的快照压缩成像算法，采用 3D-CNN 先验和新型密集特征映射（DFM）策略来更好地利用帧间的时空相关性和解决现有 DUN 中相邻相位信息丢失的问题，同时为了提高网络鲁棒性，还提出了密集特征映射适应（DFMA）模块。最终的实验结果验证了我们方法的优越性。

具有三维卷积神经网络先验的密集深度展开网络用于快照压缩成像

Dense Deep Unfolding Network with 3D-CNN Prior for Snapshot Compressive  Imaging

Non-blind image deblurring is typically formulated as a linear least-squares
problem regularized by natural priors on the corresponding sharp picture's
gradients, which can be solved, for example, using a half-quadratic splitting
method with Richardson fixed-point iterations for its least-squares updates and
a proximal operator for the auxiliary variable updates. We propose to
precondition the Richardson solver using approximate inverse filters of the
(known) blur and natural image prior kernels. Using convolutions instead of a
generic linear preconditioner allows extremely efficient parameter sharing
across the image, and leads to significant gains in accuracy and/or speed
compared to classical FFT and conjugate-gradient methods. More importantly, the
proposed architecture is easily adapted to learning both the preconditioner and
the proximal operator using CNN embeddings. This yields a simple and efficient
algorithm for non-blind image deblurring which is fully interpretable, can be
learned end to end, and whose accuracy matches or exceeds the state of the art,
quite significantly, in the non-uniform case.

本篇论文提出了一种用于图像去模糊的简单而高效的算法，其通过预处理 Richardson 解算器，使用模糊核和自然图像先验核的近似逆滤波器，以卷积的形式代替通用的线性预处理器，可以实现图像间高效的参数共享；同时利用 CNN 嵌入学习预处理器与辅助变量的 proximal operator，进一步提高了算法的鲁棒性与准确性，使其成为非盲目图像去模糊领域中性能更出色的算法。