We present a survey paper on compressed sensing, which explores the theoretical and practical aspects of compressed sensing and its applications.Expand

One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between a… Expand

Compressed sensing (CS) is an exciting, rapidly growing, field that has attracted considerable attention in signal processing, statistics, and computer science, and hundreds of conferences, workshops, and special sessions have been dedicated to this growing research field.Expand

It is known that the Continuous Wavelet Transform of a distribution f decays rapidly near the points where f is smooth, while it decays slowly near the irregular points. This property allows the… Expand

In this paper we describe a new class of multidimensional representation systems, called shearlets, obtained by applying the actions of dilation, shear transformation and translation to a fixed function, and exhibit the geometric and mathematical properties, recently advocated by many authors for sparse image processing applications.Expand

We introduce the Haar wavelet-based perceptual similarity index (HaarPSI), a novel and computationally inexpensive similarity measure for full reference image quality assessment.Expand

We derive fundamental lower bounds on the connectivity and the memory requirements of deep neural networks guaranteeing uniform approximation rates for arbitrary function classes in $L^2(\mathbb{R}^d)$.Expand

AbstractDuality principles in Gabor theory such as the Ron–Shen duality principle and the
Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this
article we… Expand