• Corpus ID: 238259256

Spiked Covariance Estimation from Modulo-Reduced Measurements

@article{Romanov2022SpikedCE,
  title={Spiked Covariance Estimation from Modulo-Reduced Measurements},
  author={Elad Romanov and Or Ordentlich},
  journal={ArXiv},
  year={2022},
  volume={abs/2110.01150}
}
Consider the rank-1 spiked model: X = √ νξ u + Z , where ν is the spike in-tensity, u ∈ S k − 1 is an unknown direction and ξ ∼ N (0 , 1) , Z ∼ N ( 0 , I ) . Motivated by recent advances in analog-to-digital con-version, we study the problem of recovering u ∈ S k − 1 from n i.i.d. modulo-reduced measurements Y = [ X ] mod ∆ , focusing on the high-dimensional regime ( k (cid:29) 1 ). We develop and analyze an algorithm that, for most directions u and ν = poly( k ) , estimates u to high accuracy… 

Figures from this paper

References

SHOWING 1-10 OF 24 REFERENCES
Adaptive estimation of a quadratic functional by model selection
We consider the problem of estimating ∥s∥ 2 when s belongs to some separable Hilbert space and one observes the Gaussian process Y(t) = (s, t) + σ L(t), for all t ∈ H, where L is some Gaussian
Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
AbstractWe compute the limiting distributions of the largest eigenvalue of a complex Gaussian samplecovariance matrix when both the number of samples and the number of variables in each samplebecome
On Unlimited Sampling and Reconstruction
TLDR
An alternative paradigm for sensing and recovery, called the Unlimited Sampling Framework, which derives conditions when perfect recovery is possible and complement them with a stable recovery algorithm and guarantees extend to measurements affected by bounded noise, which includes round-off quantization.
Unlimited Sampling of Sparse Sinusoidal Mixtures
TLDR
This paper develops a method for recovery of $K-sparse, sum-of-sinusoids from finitely many wrapped samples, thus avoiding clipping or saturation, and obtains a parametric sampling theorem.
Numerical Reconstruction of the Covariance Matrix of a Spherically Truncated Multinormal Distribution
We relate the matrix of the second moments of a spherically truncated normal multivariate to its full covariance matrix and present an algorithm to invert the relation and reconstruct from . While
On unlimited sampling
TLDR
Numerical experiments that corroborate the theory indeed show that it is possible to perfectly recover function that takes values that are orders of magnitude higher than the ADC's threshold, and prove such sufficiency conditions and complement them with a stable recovery algorithm.
Integer-Forcing source coding
TLDR
This work develops the source coding dual of the IF approach to arrive at a new low-complexity scheme, IF source coding, for distributed lossy compression of correlated Gaussian sources under a minimum mean squared error distortion measure.
Unlimited Sampling From Theory to Practice: Fourier-Prony Recovery and Prototype ADC
TLDR
This paper studies the problem of recovering a bandlimited signal from point-wise modulo samples, aiming to connect theoretical guarantees with hardware implementation considerations, and provides a new Fourier domain recovery algorithm.
Outage Behavior of Integer Forcing With Random Unitary Pre-Processing
TLDR
The results are applied to obtain universal bounds on the gap-to-capacity of multiple-antenna closed-loop multicast, achievable via linear pre-processed integer forcing.
Concentration Inequalities - A Nonasymptotic Theory of Independence
TLDR
Deep connections with isoperimetric problems are revealed whilst special attention is paid to applications to the supremum of empirical processes.
...
...