Blind calibration for compressed sensing: state evolution and an online algorithm

@article{Gabri2019BlindCF,
  title={Blind calibration for compressed sensing: state evolution and an online algorithm},
  author={Marylou Gabri{\'e} and Jean Barbier and Florent Krzakala and Lenka Zdeborov{\'a}},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2019},
  volume={53}
}
Compressed sensing allows for the acquisition of compressible signals with a small number of measurements. In experimental settings, the sensing process corresponding to the hardware implementation is not always perfectly known and may require a calibration. To this end, blind calibration proposes to perform at the same time the calibration and the compressed sensing. Schülke and collaborators suggested an approach based on approximate message passing for blind calibration (cal-AMP) in (Schülke… 
1 Citations

Mean-field inference methods for neural networks

  • Marylou Gabri'e
  • Computer Science
    Journal of Physics A: Mathematical and Theoretical
  • 2020
A selection of classical mean-field methods and recent progress relevant for inference in neural networks are reviewed, and the principles of derivations of high-temperature expansions, the replica method and message passing algorithms are reminded, highlighting their equivalences and complementarities.

References

SHOWING 1-10 OF 79 REFERENCES

Blind Calibration in Compressed Sensing using Message Passing Algorithms

This paper extends the approximate message passing (AMP) algorithm used in CS to the case of blind calibration, and shows that even in cases where convex relaxation is pos- sible, the algorithm requires a smaller number of measurements and/or signals in order to perform well.

Blind calibration for compressed sensing by convex optimization

This work considers the problem of calibrating a compressed sensing measurement system under the assumption that the decalibration consists in unknown gains on each measure, and shows that this formulation can be exactly expressed as a convex optimization problem, and can be solved using off-the-shelf algorithms.

Probabilistic reconstruction in compressed sensing: algorithms, phase diagrams, and threshold achieving matrices

A more thorough presentation of the probabilistic approach to reconstruction and the derivation of the message passing algorithm for reconstruction and expectation maximization learning of signal-model parameters are presented.

Blind sensor calibration using approximate message passing

This work proposes a message passing algorithm called calibration approximate message passing (Cal-AMP) that can treat a variety of such sensor-induced imperfections, and experimentally exhibits a phase transition between domains of success and failure.

A conjugate gradient algorithm for blind sensor calibration in sparse recovery

This work proposes a cost function on a suitable manifold, namely, the set of complex diagonal matrices with determinant one, which can enhance numerical stabilities of the proposed algorithm for blind sensor calibration in linear inverse problems, such as compressive sensing.

Message-passing algorithms for compressed sensing

A simple costless modification to iterative thresholding is introduced making the sparsity–undersampling tradeoff of the new algorithms equivalent to that of the corresponding convex optimization procedures, inspired by belief propagation in graphical models.

Signal recovery using expectation consistent approximation for linear observations

It is shown that EC recovery exhibits consistency with the replica theory for a wider class of random observation matrices, including Bayesian optimal signal recovery of compressed sensing using random row-orthogonal matrices.

Vector approximate message passing for the generalized linear model

Numerical experiments show that the proposed GLM-VAMP is much more robust to ill-conditioning in A than damped GAMP.

Combination of compressed sensing and parallel imaging for highly accelerated first‐pass cardiac perfusion MRI

Comp compressed sensing and parallel imaging are combined by merging the k‐t SPARSE technique with sensitivity encoding (SENSE) reconstruction to substantially increase the acceleration rate for perfusion imaging and a new theoretical framework is presented for understanding the combination of k-t SParSE with SENSE based on distributed compressed sensing theory.

Inference from correlated patterns: a unified theory for perceptron learning and linear vector channels

A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The
...