This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …

This article presents novel results concerning the recovery of signals from undersampled
data in the common situation where such signals are not sparse in an orthonormal basis or …

We explore the redundancy of parameters in deep neural networks by replacing the
conventional linear projection in fully-connected layers with the circulant projection. The …

Non-local self-similarity is well-known to be an effective prior for the image denoising
problem. However, little work has been done to incorporate it in convolutional neural …

An oblivious subspace embedding (OSE) given some parameters ε, d is a distribution D over
matrices Π∈ R m× n such that for any linear subspace W⊆ R n with dim (W)= d, P Π~ D (∀ …

We give two different and simple constructions for dimensionality reduction in ℓ 2 via linear
map**s that are sparse: only an O (ε)-fraction of entries in each column of our embedding …

We propose Intermediate Layer Optimization (ILO), a novel optimization algorithm for solving
inverse problems with deep generative models. Instead of optimizing only over the initial …

We present a new bound for suprema of a special type of chaos process indexed by a set of
matrices, which is based on a chaining method. As applications we show significantly …

Transformer models have achieved great progress on computer vision tasks recently. The
rapid development of vision transformers is mainly contributed by their high representation …

In the theory of compressed sensing, restricted isometry analysis has become a standard
tool for studying how efficiently a measurement matrix acquires information about sparse …