Can we recover a complex signal from its Fourier magnitudes? More generally, given a set
of m measurements, y_k=\left| a _k^* x\right| yk= ak∗ x for k= 1, ..., mk= 1,…, m, is it possible …

This paper is concerned with finding a solution x to a quadratic system of equations yi=|< ai,
x>|^ 2, i= 1, 2,..., m. We prove that it is possible to solve unstructured quadratic systems in n …

In phase retrieval, the goal is to recover a signal x∈ CN from the magnitudes of linear
measurements Ax∈ C M. While recent theory has established that M≈ 4N intensity …

This paper develops a novel algorithm, termed SPARse Truncated Amplitude flow
(SPARTA), to reconstruct a sparse signal from a small number of magnitude-only …

Discriminative latent-variable models are typically learned using EM or gradient-based
optimization, which suffer from local optima. In this paper, we develop a new computationally …

Pooling operators construct non-linear representations by cascading a redundant linear
transform, followed by a point-wise nonlinearity and a local aggregation, typically …

The explosion of computational imaging has seen the frontier of image processing move
past linear problems, like denoising and deblurring, and towards non-linear problems such …

In this short note we propose a simple two-stage sparse phase retrieval strategy that uses a
near-optimal number of measurements, and is both computationally efficient and robust to …

Phase retrieval plays an important role in vast industrial and scientific applications. We
consider a noisy phase retrieval problem in which the magnitudes of the Fourier transform …

We investigate a compressive sensing framework in which the sensors introduce a distortion
to the measurements in the form of unknown gains. We focus on blind calibration, using …