In recent years it has turned out that shearlets have the potential to retrieve directional
information so that they became interesting for many applications. Moreover the continuous …

A large number of imaging problems reduce to the optimization of a cost function, with
typical structural properties. The aim of this paper is to describe the state of the art in …

Deep convolutional neural networks (DCNNs) have led to breakthrough results in numerous
practical machine learning tasks, such as classification of images in the ImageNet data set …

We derive fundamental lower bounds on the connectivity and the memory requirements of
deep neural networks guaranteeing uniform approximation rates for arbitrary function …

This paper develops fundamental limits of deep neural network learning by characterizing
what is possible if no constraints are imposed on the learning algorithm and on the amount …

In spite of their remarkable success in signal processing applications, it is now widely
acknowledged that traditional wavelets are not very effective in dealing multidimensional …

In this paper we show that shearlets, an affine-like system of functions recently introduced by
the authors and their collaborators, are essentially optimal in representing 2-dimensional …

As a rapidly growing, multidisciplinary field of mathematics, wavelet theory provides the
major mathematical multiscale representation for analyzing functions/data and has …

Wavelets and their associated transforms are highly efficient when approximating and
analyzing one-dimensional signals. However, multivariate signals such as images or videos …

It is a challenging task to reconstruct images from their noisy, blurry, and/or incomplete
measurements, especially those with important details and features such as medical …