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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