There has been definite progress recently in proving the variational single-letter formula given by the heuristic replica method for various estimation problems. In particular, the replica formula for the mutual information in the case of noisy …

Compressed sensing (CS) demonstrates that sparse signals can be estimated from underdetermined linear systems. Distributed CS (DCS) further reduces the number of measurements by considering joint sparsity within signal ensembles. DCS with jointly …

This paper addresses fundamental scaling issues that hinder phase retrieval (PR) in high dimensions. We show that, if the measurement matrix can be put into a generalized block-diagonal form, a large PR problem can be solved on separate blocks, at …

We consider the estimation of a n-dimensional vector x from the knowledge of noisy and possibility non-linear element-wise measurements of xxT, a very generic problem that contains, e.g. stochastic 2-block model, submatrix localization or the spike …

We analyze the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications, such as dictionary learning, blind matrix calibration, sparse …

We consider the problem of the assignment of nodes into communities from a set of hyperedges, where every hyperedge is a noisy observation of the community assignment of the adjacent nodes. We focus in particular on the sparse regime where the number …

In this paper, we consider the phase recovery problem, where a complex signal vector has to be estimated from the knowledge of the modulus of its linear projections, from a naive variational Bayesian point of view. In particular, we derive an …

We study non-adaptive pooling strategies for detection of rare faulty items. Given a binary sparse N dimensional signal x, how to construct a sparse binary M × N pooling matrix F such that the signal can be reconstructed from the smallest possible …

In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a situation …

Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only “approximately sparse”, i.e. even though the signal contains only a small fraction of relevant (large) components the …

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