  The shearlet transform from applied harmonic analysis is currently the state
of the art when analyzing multidimensional signals with anisotropic
singularities. Its optimal sparse approximation properties and its faithful
digitalization allow shearlets to be applied to different problems from imaging
science, such as image denoising, image inpainting, and singularities
detection. The shearlet transform has also be successfully utilized, for
instance, as a feature extractor. As such it has been shown to be well suited
for image preprocessing in combination with data-driven methods such as deep
neural networks. This requires in particular an implementation of the shearlet
transform in the current deep learning frameworks, such as TensorFlow. With
this motivation we developed a tensor shearlet transform aiming to provide a
faithful TensorFlow implementation. In addition to its usability in predictive
models, we also observed an significant improvement in the performance of the
transform, with a running time of almost 40 times the previous state-of-the-art
implementation. In this paper, we will also present several numerical
experiments such as image denoising and inpainting, where the TensorFlow
version can be shown to outperform previous libraries as well as the learned
primal-dual reconstruction method for low dose computed tomography in running
time.
