Recent work in machine learning shows that deep neural networks can be used to solve a
wide variety of inverse problems arising in computational imaging. We explore the central …

This manuscript considers the problem of learning a random Gaussian network function
using a fully connected network with frozen intermediate layers and trainable readout layer …

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising
in high-dimensional inference tasks. Here one produces an estimator of an unknown …

We characterize the measurement complexity of compressed sensing of signals drawn from
a known prior distribution, even when the support of the prior is the entire space (rather than …

Approximate message passing (AMP) emerges as an effective iterative paradigm for solving
high-dimensional statistical problems. However, prior AMP theory--which focused mostly on …

In recent years, there have been significant advances in the use of deep learning methods in
inverse problems such as denoising, compressive sensing, inpainting, and super-resolution …

We consider the phase retrieval problem of reconstructing a $ n $-dimensional real or
complex signal $\mathbf {X}^\star $ from $ m $(possibly noisy) observations $ Y_\mu=|\sum …

We consider estimating a high dimensional signal in $\R^ n $ using a sublinear number of
linear measurements. In analogy to classical compressed sensing, here we assume a …

Compressive phase retrieval is a popular variant of the standard compressive sensing
problem in which the measurements only contain magnitude information. In this paper …

Recovering an unknown object from the magnitude of its Fourier transform is a phase
retrieval problem. Here, we consider a much difficult case, where those observed intensity …