We consider faithfully combining phase retrieval with classical compressed sensing. Inspired by the recent novel formulation for phase retrieval called PhaseMax, we present and analyze SparsePhaseMax, a linear program for phaseless compressed sensing in the natural parameter space. We establish that when provided with an initialization that correlates with an arbitrary k-sparse n-vector, Sparse...

For various classes of Lipschitz functions we provide dimension free concentration inequalities for infinitely divisible random vectors with independent components and finite exponential moments. The purpose of this note is to further visit the concentration phenomenon for infinitely divisible vectors with independent components in an attempt to obtain dimension free concentration. Let X ∼ ID(γ...

Given n (discrete or continuous) random variables Xi, the (2 n − 1)-dimensional vector obtained by evaluating the joint entropy of all non-empty subsets of {X1,. .. , Xn} is called an entropic vector. Determining the region of entropic vectors is an important open problem with many applications in information theory. Recently, it has been shown that the entropy regions for discrete and continuo...

The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this literature, the structure is represented by sparsity in a well-chosen basis. We show how to achieve guarantees similar to standard compressed sensing but without emp...

We here provide additional proofs, definitions, lemmas and derivations omitted in the paper. Note that material contained in the latter are referred to by the captions used there (e.g. Theorem 1), whereas auxiliary statements contained exclusively in this supplement are preceded by a capital Roman letter (e.g. Theorem A.1). A Sub-Gaussian random variables and concentration inequalities A random...