4 research outputs found
An Algorithm Unrolling Approach to Deep Image Deblurring
While neural networks have achieved vastly enhanced performance over
traditional iterative methods in many cases, they are generally empirically
designed and the underlying structures are difficult to interpret. The
algorithm unrolling approach has helped connect iterative algorithms to neural
network architectures. However, such connections have not been made yet for
blind image deblurring. In this paper, we propose a neural network architecture
that advances this idea. We first present an iterative algorithm that may be
considered a generalization of the traditional total-variation regularization
method on the gradient domain, and subsequently unroll the half-quadratic
splitting algorithm to construct a neural network. Our proposed deep network
achieves significant practical performance gains while enjoying
interpretability at the same time. Experimental results show that our approach
outperforms many state-of-the-art methods.Comment: IEEE International Conference on Acoustics, Speech, and Signal
Processing (ICASSP
Deep Algorithm Unrolling for Blind Image Deblurring
Blind image deblurring remains a topic of enduring interest. Learning based
approaches, especially those that employ neural networks have emerged to
complement traditional model based methods and in many cases achieve vastly
enhanced performance. That said, neural network approaches are generally
empirically designed and the underlying structures are difficult to interpret.
In recent years, a promising technique called algorithm unrolling has been
developed that has helped connect iterative algorithms such as those for sparse
coding to neural network architectures. However, such connections have not been
made yet for blind image deblurring. In this paper, we propose a neural network
architecture based on this idea. We first present an iterative algorithm that
may be considered as a generalization of the traditional total-variation
regularization method in the gradient domain. We then unroll the algorithm to
construct a neural network for image deblurring which we refer to as Deep
Unrolling for Blind Deblurring (DUBLID). Key algorithm parameters are learned
with the help of training images. Our proposed deep network DUBLID achieves
significant practical performance gains while enjoying interpretability at the
same time. Extensive experimental results show that DUBLID outperforms many
state-of-the-art methods and in addition is computationally faster
Graph Unrolling Networks: Interpretable Neural Networks for Graph Signal Denoising
We propose an interpretable graph neural network framework to denoise single
or multiple noisy graph signals. The proposed graph unrolling networks expand
algorithm unrolling to the graph domain and provide an interpretation of the
architecture design from a signal processing perspective. We unroll an
iterative denoising algorithm by mapping each iteration into a single network
layer where the feed-forward process is equivalent to iteratively denoising
graph signals. We train the graph unrolling networks through unsupervised
learning, where the input noisy graph signals are used to supervise the
networks. By leveraging the learning ability of neural networks, we adaptively
capture appropriate priors from input noisy graph signals, instead of manually
choosing signal priors. A core component of graph unrolling networks is the
edge-weight-sharing graph convolution operation, which parameterizes each edge
weight by a trainable kernel function where the trainable parameters are shared
by all the edges. The proposed convolution is permutation-equivariant and can
flexibly adjust the edge weights to various graph signals. We then consider two
special cases of this class of networks, graph unrolling sparse coding (GUSC)
and graph unrolling trend filtering (GUTF), by unrolling sparse coding and
trend filtering, respectively. To validate the proposed methods, we conduct
extensive experiments on both real-world datasets and simulated datasets, and
demonstrate that our methods have smaller denoising errors than conventional
denoising algorithms and state-of-the-art graph neural networks. For denoising
a single smooth graph signal, the normalized mean square error of the proposed
networks is around 40% and 60% lower than that of graph Laplacian denoising and
graph wavelets, respectively
Unfolding WMMSE using Graph Neural Networks for Efficient Power Allocation
We study the problem of optimal power allocation in a single-hop ad hoc
wireless network. In solving this problem, we depart from classical purely
model-based approaches and propose a hybrid method that retains key modeling
elements in conjunction with data-driven components. More precisely, we put
forth a neural network architecture inspired by the algorithmic unfolding of
the iterative weighted minimum mean squared error (WMMSE) method, that we
denote by unfolded WMMSE (UWMMSE). The learnable weights within UWMMSE are
parameterized using graph neural networks (GNNs), where the time-varying
underlying graphs are given by the fading interference coefficients in the
wireless network. These GNNs are trained through a gradient descent approach
based on multiple instances of the power allocation problem. We show that the
proposed architecture is permutation equivariant, thus facilitating
generalizability across network topologies. Comprehensive numerical experiments
illustrate the performance attained by UWMMSE along with its robustness to
hyper-parameter selection and generalizability to unseen scenarios such as
different network densities and network sizes.Comment: Accepted at IEEE Transactions on Wireless Communication