16,242 research outputs found
Solving ill-posed inverse problems using iterative deep neural networks
We propose a partially learned approach for the solution of ill posed inverse
problems with not necessarily linear forward operators. The method builds on
ideas from classical regularization theory and recent advances in deep learning
to perform learning while making use of prior information about the inverse
problem encoded in the forward operator, noise model and a regularizing
functional. The method results in a gradient-like iterative scheme, where the
"gradient" component is learned using a convolutional network that includes the
gradients of the data discrepancy and regularizer as input in each iteration.
We present results of such a partially learned gradient scheme on a non-linear
tomographic inversion problem with simulated data from both the Sheep-Logan
phantom as well as a head CT. The outcome is compared against FBP and TV
reconstruction and the proposed method provides a 5.4 dB PSNR improvement over
the TV reconstruction while being significantly faster, giving reconstructions
of 512 x 512 volumes in about 0.4 seconds using a single GPU
Artificial Neural Network Approach to the Analytic Continuation Problem
Inverse problems are encountered in many domains of physics, with analytic
continuation of the imaginary Green's function into the real frequency domain
being a particularly important example. However, the analytic continuation
problem is ill defined and currently no analytic transformation for solving it
is known. We present a general framework for building an artificial neural
network (ANN) that solves this task with a supervised learning approach.
Application of the ANN approach to quantum Monte Carlo calculations and
simulated Green's function data demonstrates its high accuracy. By comparing
with the commonly used maximum entropy approach, we show that our method can
reach the same level of accuracy for low-noise input data, while performing
significantly better when the noise strength increases. The computational cost
of the proposed neural network approach is reduced by almost three orders of
magnitude compared to the maximum entropy methodComment: 6 pages, 4 figures, supplementary material available as ancillary
fil
Task adapted reconstruction for inverse problems
The paper considers the problem of performing a task defined on a model
parameter that is only observed indirectly through noisy data in an ill-posed
inverse problem. A key aspect is to formalize the steps of reconstruction and
task as appropriate estimators (non-randomized decision rules) in statistical
estimation problems. The implementation makes use of (deep) neural networks to
provide a differentiable parametrization of the family of estimators for both
steps. These networks are combined and jointly trained against suitable
supervised training data in order to minimize a joint differentiable loss
function, resulting in an end-to-end task adapted reconstruction method. The
suggested framework is generic, yet adaptable, with a plug-and-play structure
for adjusting both the inverse problem and the task at hand. More precisely,
the data model (forward operator and statistical model of the noise) associated
with the inverse problem is exchangeable, e.g., by using neural network
architecture given by a learned iterative method. Furthermore, any task that is
encodable as a trainable neural network can be used. The approach is
demonstrated on joint tomographic image reconstruction, classification and
joint tomographic image reconstruction segmentation
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