approximate message-passing

Approximate Message-Passing Decoder and Capacity Achieving Sparse Superposition Codes

We study the approximate message-passing decoder for sparse superposition coding on the additive white Gaussian noise channel and extend our preliminary work. We use heuristic statistical-physics-based tools, such as the cavity and the replica …

Decoding from pooled data: Phase transitions of message passing

We consider the problem of decoding a discrete signal of categorical variables from the observation of several histograms of pooled subsets of it. We present an Approximate Message Passing (AMP) algorithm for recovering the signal in the random dense …

Statistical and computational phase transitions in spiked tensor estimation

We consider tensor factorizations using a generative model and a Bayesian approach. We compute rigorously the mutual information, the Minimal Mean Square Error (MMSE), and unveil information-theoretic phase transitions. In addition, we study the …

Performance Limits for Noisy Multimeasurement Vector Problems

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 …

Intensity-only optical compressive imaging using a multiply scattering material and a double phase retrieval approach

In this paper, the problem of compressive imaging is addressed using natural randomization by means of a multiply scattering medium. To utilize the medium in this way, its corresponding transmission matrix must be estimated. For calibration purposes, …

MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel

This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements. We derive the corresponding approximate message passing (AMP) algorithm and its state evolution. Relying on non-rigorous but …

Phase transitions in sparse PCA

We study optimal estimation for sparse principal component analysis when the number of non-zero elements is small but on the same order as the dimension of the data. We employ approximate message passing (AMP) algorithm and its state evolution to …

Adaptive damping and mean removal for the generalized approximate message passing algorithm

The generalized approximate message passing (GAMP) algorithm is an efficient method of MAP or approximate-MMSE estimation of x observed from a noisy version of the transform coefficients z = Ax. In fact, for large zero-mean i.i.d sub-Gaussian A, GAMP …