11,545 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
Deep learning approach to Fourier ptychographic microscopy
Convolutional neural networks (CNNs) have gained tremendous success in
solving complex inverse problems. The aim of this work is to develop a novel
CNN framework to reconstruct video sequence of dynamic live cells captured
using a computational microscopy technique, Fourier ptychographic microscopy
(FPM). The unique feature of the FPM is its capability to reconstruct images
with both wide field-of-view (FOV) and high resolution, i.e. a large
space-bandwidth-product (SBP), by taking a series of low resolution intensity
images. For live cell imaging, a single FPM frame contains thousands of cell
samples with different morphological features. Our idea is to fully exploit the
statistical information provided by this large spatial ensemble so as to make
predictions in a sequential measurement, without using any additional temporal
dataset. Specifically, we show that it is possible to reconstruct high-SBP
dynamic cell videos by a CNN trained only on the first FPM dataset captured at
the beginning of a time-series experiment. Our CNN approach reconstructs a
12800X10800 pixels phase image using only ~25 seconds, a 50X speedup compared
to the model-based FPM algorithm. In addition, the CNN further reduces the
required number of images in each time frame by ~6X. Overall, this
significantly improves the imaging throughput by reducing both the acquisition
and computational times. The proposed CNN is based on the conditional
generative adversarial network (cGAN) framework. Additionally, we also exploit
transfer learning so that our pre-trained CNN can be further optimized to image
other cell types. Our technique demonstrates a promising deep learning approach
to continuously monitor large live-cell populations over an extended time and
gather useful spatial and temporal information with sub-cellular resolution
Deep learning approach to Fourier ptychographic microscopy
Convolutional neural networks (CNNs) have gained tremendous success in solving complex inverse problems. The aim of this work is to develop a novel CNN framework to reconstruct video sequences of dynamic live cells captured using a computational microscopy technique, Fourier ptychographic microscopy (FPM). The unique feature of the FPM is its capability to reconstruct images with both wide field-of-view (FOV) and high resolution, i.e. a large space-bandwidth-product (SBP), by taking a series of low resolution intensity images. For live cell imaging, a single FPM frame contains thousands of cell samples with different morphological features. Our idea is to fully exploit the statistical information provided by these large spatial ensembles so as to make predictions in a sequential measurement, without using any additional temporal dataset. Specifically, we show that it is possible to reconstruct high-SBP dynamic cell videos by a CNN trained only on the first FPM dataset captured at the beginning of a time-series experiment. Our CNN approach reconstructs a 12800×10800 pixel phase image using only ∼25 seconds, a 50× speedup compared to the model-based FPM algorithm. In addition, the CNN further reduces the required number of images in each time frame by ∼ 6×. Overall, this significantly improves the imaging throughput by reducing both the acquisition and computational times. The proposed CNN is based on the conditional generative adversarial network (cGAN) framework. We further propose a mixed loss function that combines the standard image domain loss and a weighted Fourier domain loss, which leads to improved reconstruction of the high frequency information. Additionally, we also exploit transfer learning so that our pre-trained CNN can be further optimized to image other cell types. Our technique demonstrates a promising deep learning approach to continuously monitor large live-cell populations over an extended time and gather useful spatial and temporal information with sub-cellular resolution.We would like to thank NVIDIA Corporation for supporting us with the GeForce Titan Xp through the GPU Grant Program. (NVIDIA Corporation; GeForce Titan Xp through the GPU Grant Program)First author draf
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
Plug-and-Play Methods Provably Converge with Properly Trained Denoisers
Plug-and-play (PnP) is a non-convex framework that integrates modern
denoising priors, such as BM3D or deep learning-based denoisers, into ADMM or
other proximal algorithms. An advantage of PnP is that one can use pre-trained
denoisers when there is not sufficient data for end-to-end training. Although
PnP has been recently studied extensively with great empirical success,
theoretical analysis addressing even the most basic question of convergence has
been insufficient. In this paper, we theoretically establish convergence of
PnP-FBS and PnP-ADMM, without using diminishing stepsizes, under a certain
Lipschitz condition on the denoisers. We then propose real spectral
normalization, a technique for training deep learning-based denoisers to
satisfy the proposed Lipschitz condition. Finally, we present experimental
results validating the theory.Comment: Published in the International Conference on Machine Learning, 201
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