tfShearlab: The TensorFlow Digital Shearlet Transform for Deep Learning

Abstract: 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.