14,596 research outputs found
Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration
Image restoration is a long-standing problem in low-level computer vision
with many interesting applications. We describe a flexible learning framework
based on the concept of nonlinear reaction diffusion models for various image
restoration problems. By embodying recent improvements in nonlinear diffusion
models, we propose a dynamic nonlinear reaction diffusion model with
time-dependent parameters (\ie, linear filters and influence functions). In
contrast to previous nonlinear diffusion models, all the parameters, including
the filters and the influence functions, are simultaneously learned from
training data through a loss based approach. We call this approach TNRD --
\textit{Trainable Nonlinear Reaction Diffusion}. The TNRD approach is
applicable for a variety of image restoration tasks by incorporating
appropriate reaction force. We demonstrate its capabilities with three
representative applications, Gaussian image denoising, single image super
resolution and JPEG deblocking. Experiments show that our trained nonlinear
diffusion models largely benefit from the training of the parameters and
finally lead to the best reported performance on common test datasets for the
tested applications. Our trained models preserve the structural simplicity of
diffusion models and take only a small number of diffusion steps, thus are
highly efficient. Moreover, they are also well-suited for parallel computation
on GPUs, which makes the inference procedure extremely fast.Comment: 14 pages, 13 figures, to appear in IEEE Transactions on Pattern
Analysis and Machine Intelligence (TPAMI
IMEXnet: A Forward Stable Deep Neural Network
Deep convolutional neural networks have revolutionized many machine learning
and computer vision tasks, however, some remaining key challenges limit their
wider use. These challenges include improving the network's robustness to
perturbations of the input image and the limited ``field of view'' of
convolution operators. We introduce the IMEXnet that addresses these challenges
by adapting semi-implicit methods for partial differential equations. Compared
to similar explicit networks, such as residual networks, our network is more
stable, which has recently shown to reduce the sensitivity to small changes in
the input features and improve generalization. The addition of an implicit step
connects all pixels in each channel of the image and therefore addresses the
field of view problem while still being comparable to standard convolutions in
terms of the number of parameters and computational complexity. We also present
a new dataset for semantic segmentation and demonstrate the effectiveness of
our architecture using the NYU Depth dataset
The Neural Network Approach to Inverse Problems in Differential Equations
We proposed a framework for solving inverse problems in differential
equations based on neural networks and automatic differentiation. Neural
networks are used to approximate hidden fields. We analyze the source of errors
in the framework and derive an error estimate for a model diffusion equation
problem. Besides, we propose a way for sensitivity analysis, utilizing the
automatic differentiation mechanism embedded in the framework. It frees people
from the tedious and error-prone process of deriving the gradients. Numerical
examples exhibit consistency with the convergence analysis and error saturation
is noteworthily predicted. We also demonstrate the unique benefits neural
networks offer at the same time: universal approximation ability, regularizing
the solution, bypassing the curse of dimensionality and leveraging efficient
computing frameworks.Comment: 32 pages, 9 figure
A network partition method for solving large-scale complex nonlinear processes
A numerical framework based on network partition and operator splitting is
developed to solve nonlinear differential equations of large-scale dynamic
processes encountered in physics, chemistry and biology. Under the assumption
that those dynamic processes can be characterized by sparse networks, we
minimize the number of splitting for constructing subproblems by network
partition. Then the numerical simulation of the original system is simplified
by solving a small number of subproblems, with each containing uncorrelated
elementary processes. In this way, numerical difficulties of conventional
methods encountered in large-scale systems such as numerical instability,
negative solutions, and convergence issue are avoided. In addition, parallel
simulations for each subproblem can be achieved, which is beneficial for
large-scale systems. Examples with complex underlying nonlinear processes,
including chemical reactions and reaction-diffusion on networks, demonstrate
that this method generates convergent solution in a efficient and robust way
Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data
We present hidden fluid mechanics (HFM), a physics informed deep learning
framework capable of encoding an important class of physical laws governing
fluid motions, namely the Navier-Stokes equations. In particular, we seek to
leverage the underlying conservation laws (i.e., for mass, momentum, and
energy) to infer hidden quantities of interest such as velocity and pressure
fields merely from spatio-temporal visualizations of a passive scaler (e.g.,
dye or smoke), transported in arbitrarily complex domains (e.g., in human
arteries or brain aneurysms). Our approach towards solving the aforementioned
data assimilation problem is unique as we design an algorithm that is agnostic
to the geometry or the initial and boundary conditions. This makes HFM highly
flexible in choosing the spatio-temporal domain of interest for data
acquisition as well as subsequent training and predictions. Consequently, the
predictions made by HFM are among those cases where a pure machine learning
strategy or a mere scientific computing approach simply cannot reproduce. The
proposed algorithm achieves accurate predictions of the pressure and velocity
fields in both two and three dimensional flows for several benchmark problems
motivated by real-world applications. Our results demonstrate that this
relatively simple methodology can be used in physical and biomedical problems
to extract valuable quantitative information (e.g., lift and drag forces or
wall shear stresses in arteries) for which direct measurements may not be
possible
Dynamically Unfolding Recurrent Restorer: A Moving Endpoint Control Method for Image Restoration
In this paper, we propose a new control framework called the moving endpoint
control to restore images corrupted by different degradation levels in one
model. The proposed control problem contains a restoration dynamics which is
modeled by an RNN. The moving endpoint, which is essentially the terminal time
of the associated dynamics, is determined by a policy network. We call the
proposed model the dynamically unfolding recurrent restorer (DURR). Numerical
experiments show that DURR is able to achieve state-of-the-art performances on
blind image denoising and JPEG image deblocking. Furthermore, DURR can well
generalize to images with higher degradation levels that are not included in
the training stage.Comment: The first two authors contributed equall
Multitask Diffusion Adaptation over Networks
Adaptive networks are suitable for decentralized inference tasks, e.g., to
monitor complex natural phenomena. Recent research works have intensively
studied distributed optimization problems in the case where the nodes have to
estimate a single optimum parameter vector collaboratively. However, there are
many important applications that are multitask-oriented in the sense that there
are multiple optimum parameter vectors to be inferred simultaneously, in a
collaborative manner, over the area covered by the network. In this paper, we
employ diffusion strategies to develop distributed algorithms that address
multitask problems by minimizing an appropriate mean-square error criterion
with -regularization. The stability and convergence of the algorithm in
the mean and in the mean-square sense is analyzed. Simulations are conducted to
verify the theoretical findings, and to illustrate how the distributed strategy
can be used in several useful applications related to spectral sensing, target
localization, and hyperspectral data unmixing.Comment: 29 pages, 11 figures, submitted for publicatio
Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction
Following the success of deep learning in a wide range of applications,
neural network-based machine learning techniques have received interest as a
means of accelerating magnetic resonance imaging (MRI). A number of ideas
inspired by deep learning techniques from computer vision and image processing
have been successfully applied to non-linear image reconstruction in the spirit
of compressed sensing for both low dose computed tomography and accelerated
MRI. The additional integration of multi-coil information to recover missing
k-space lines in the MRI reconstruction process, is still studied less
frequently, even though it is the de-facto standard for currently used
accelerated MR acquisitions. This manuscript provides an overview of the recent
machine learning approaches that have been proposed specifically for improving
parallel imaging. A general background introduction to parallel MRI is given
that is structured around the classical view of image space and k-space based
methods. Both linear and non-linear methods are covered, followed by a
discussion of recent efforts to further improve parallel imaging using machine
learning, and specifically using artificial neural networks. Image-domain based
techniques that introduce improved regularizers are covered as well as k-space
based methods, where the focus is on better interpolation strategies using
neural networks. Issues and open problems are discussed as well as recent
efforts for producing open datasets and benchmarks for the community.Comment: 14 pages, 7 figure
Inverse Halftoning Through Structure-Aware Deep Convolutional Neural Networks
The primary issue in inverse halftoning is removing noisy dots on flat areas
and restoring image structures (e.g., lines, patterns) on textured areas.
Hence, a new structure-aware deep convolutional neural network that
incorporates two subnetworks is proposed in this paper. One subnetwork is for
image structure prediction while the other is for continuous-tone image
reconstruction. First, to predict image structures, patch pairs comprising
continuous-tone patches and the corresponding halftoned patches generated
through digital halftoning are trained. Subsequently, gradient patches are
generated by convolving gradient filters with the continuous-tone patches. The
subnetwork for the image structure prediction is trained using the mini-batch
gradient descent algorithm given the halftoned patches and gradient patches,
which are fed into the input and loss layers of the subnetwork, respectively.
Next, the predicted map including the image structures is stacked on the top of
the input halftoned image through a fusion layer and fed into the image
reconstruction subnetwork such that the entire network is trained adaptively to
the image structures. The experimental results confirm that the proposed
structure-aware network can remove noisy dot-patterns well on flat areas and
restore details clearly on textured areas. Furthermore, it is demonstrated that
the proposed method surpasses the conventional state-of-the-art methods based
on deep convolutional neural networks and locally learned dictionaries
When an attacker meets a cipher-image in 2018: A Year in Review
This paper aims to review the encountered technical contradictions when an
attacker meets the cipher-images encrypted by the image encryption schemes
(algorithms) proposed in 2018 from the viewpoint of an image cryptanalyst. The
most representative works among them are selected and classified according to
their essential structures. Almost all image cryptanalysis works published in
2018 are surveyed due to their small number. The challenging problems on design
and analysis of image encryption schemes are summarized to receive the
attentions of both designers and attackers (cryptanalysts) of image encryption
schemes, which may promote solving scenario-oriented image security problems
with new technologies.Comment: 12 page
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