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astra-toolbox requires cuda 10.2: conda install -c astra-toolbox/label/dev astra-toolbox | ||
# Fourier Image Transformer | ||
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conda install pytorch torchvision torchaudio cudatoolkit=10.2 -c pytorch | ||
Tim-Oliver Buchholz<sup>1</sup> and Florian Jug<sup>2</sup></br> | ||
<sup>1</sup>[email protected], <sup>2</sup>[email protected] | ||
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Build Python package: | ||
`python setup.py bdist_wheel` | ||
Transformer architectures show spectacular performance on NLP tasks and have recently also been used for tasks such as | ||
image completion or image classification. Here we propose to use a sequential image representation, where each prefix of | ||
the complete sequence describes the whole image at reduced resolution. Using such Fourier Domain Encodings (FDEs), an | ||
auto-regressive image completion task is equivalent to predicting a higher resolution output given a low-resolution | ||
input. Additionally, we show that an encoder-decoder setup can be used to query arbitrary Fourier coefficients given a | ||
set of Fourier domain observations. We demonstrate the practicality of this approach in the context of computed | ||
tomography (CT) image reconstruction. In summary, we show that Fourier Image Transformer (FIT) can be used to solve | ||
relevant image analysis tasks in Fourier space, a domain inherently inaccessible to convolutional architectures. | ||
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Build singularity recipe: | ||
`neurodocker generate singularity -b nvidia/cuda:10.2-cudnn7-devel-ubuntu18.04 -p apt --copy /home/tibuch/Gitrepos/FourierImageTransformer/dist/fourier_image_transformers-0.1.24_zero-py3-none-any.whl /fourier_image_transformers-0.1.24_zero-py3-none-any.whl --miniconda create_env=fit conda_install='python=3.7 astra-toolbox pytorch torchvision torchaudio cudatoolkit=10.2 -c pytorch -c astra-toolbox/label/dev' pip_install='/fourier_image_transformers-0.1.24_zero-py3-none-any.whl' activate=true --entrypoint "/neurodocker/startup.sh python" > v0.1.24_zero.Singularity` | ||
Preprint: [arXiv](arXiv) | ||
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Build singularity container: | ||
`sudo singularity build fit_v0.1.24_zero.simg v0.1.24_zero.Singularity` | ||
## FIT for Super-Resolution | ||
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![SRes](figs/SRes.png) | ||
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__FIT for super-resolution.__ Low-resolution input images are first transformed into Fourier space and then unrolled | ||
into an FDE sequence, as described in Section 3.1 of the paper. This FDE sequence can now be fed to a FIT, that, | ||
conditioned on this input, extends the FDE sequence to represent a higher resolution image. This setup is trained using | ||
an FC-Loss that enforces consistency between predicted and ground truth Fourier coefficients. During inference, the FIT | ||
is conditioned on the first 39 entries of the FDE, corresponding to (a,d) 3x Fourier binned input images. Panels (b,e) | ||
show the inverse Fourier transform of the predicted output, and panels (c,f) depict the corresponding ground truth. | ||
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## FIT for Tomography | ||
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![TRec](figs/TRec.png) | ||
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__FIT for computed tomography.__ We propose an encoder-decoder based Fourier Image Transformer setup for tomographic | ||
reconstruction. In 2D computed tomography, 1D projections of an imaged sample (i.e. the columns of a sinogram) are | ||
back-transformed into a 2D image. A common method for this transformationis the filtered backprojection (FBP). Since | ||
each projection maps to a line of coefficients in 2D Fourier space, a limited number of projections in a sinogram leads | ||
to visible streaking artefacts due to missing/unobserved Fourier coefficients. The idea of our FIT setup is to encode | ||
all information of a given sinogram and use the decoder to predict missing Fourier coefficients. The reconstructed image | ||
is then computed via an inverse Fourier transform (iFFT) of these predictions. In order to reduce high frequency | ||
fluctuations in this result, we introduce a shallow conv-block after the iFFT (shown in black). We train this setup | ||
combining the FC-Loss, see Section 3.2 in the paper, and a conventional MSE-loss between prediction and ground truth. | ||
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## Installation | ||
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We use [fast-transformers](https://github.com/idiap/fast-transformers) as underlying transformer implementation. In our super-resolution experiments we use their | ||
`causal-linear` implementation, which uses custom CUDA code (prediction works without this custom code). This code is | ||
compiled during the installation of fast-transformers and it is necessary that CUDA and NVIDIA driver versions match. | ||
For our experiments we used CUDA 10.2 and NVIDIA driver 440.118.02. | ||
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We recommend to install Fast Image Transformer into a new [conda](https://docs.conda.io/en/latest/miniconda.html) | ||
environment: | ||
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`conda create -n fit python=3.7` | ||
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Next activate the new environment.: | ||
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`conda activate fit` | ||
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Then we install PyTorch for CUDA 10.2: | ||
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`conda install pytorch torchvision torchaudio cudatoolkit=10.2 -c pytorch` | ||
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Followed by installing fast-transformers: | ||
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`pip install --user pytorch-fast-transformers` | ||
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Now we have to install the `astra-toolbox`: | ||
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`conda install -c astra-toolbox/label/dev astra-toolbox` | ||
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And finally we install Fourier Image Transformer: | ||
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`pip install fourier-image-transformer` | ||
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Start the jupyter server: | ||
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`jupyter notebook` | ||
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## Cite | ||
``` | ||
@{} | ||
``` |
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