SignalNoise {RMT4DS}

Signal-Plus-Noise Models

Description

Estimation of signals, rank of signals.

Usage

StepWiseSVD(Y, threshold=NULL, B=1000, level=0.02, methods='kmeans',
    u_threshold=NULL, v_threshold=NULL, sparse=TRUE)
ScreeNot(Y, r1)
GetRank(Y, r1, type=c("1","2"), level=0.1, B=500)
signal_value(d, svr)
signal_vector(k1, k2, d1, d2, svr, left=TRUE)

Arguments

Y

matrix to be denoised.

B

repeat time of simulations.

threshold

threshold used in determining rank of signal.

level

significance level in determing ranks.

methods

methods used in determining sparse structure.

u_threshold, v_threshold

thresholds used in determining sparse structure if kmeans is not used.

sparse

whether signals have sparse structure.

r1

upper bound of rank.

type

type of test.

k1, k2

k-th eigenvector.

d, d1, d2

eigenvalues of corresponding signal matrix

left

whether to use left singular vectors.

svr

ndf/ndim of Y.

Details

StepWiseSVD works well in sparse setting and requires i.i.d normal noise and a lot simulation time.SreeNot is to pick the best TSVD result so works well in general setting.

When using signal-plus-noise related limits, make sure they are limits of signal-related values or vectors.

Value

StepWiseSVD performs step-wise SVD to denoise and returns decomposed strcuture,

ScreeNot performs ScreeNot to denoise and returns decomposed strcuture,

GetRank gives rank of signals.

signal_value gives corrected signal eigenvalue from SVD result,

signal_vector gives limiting inner product between signal vector and corresponding signal-plus-noise vector.

Author(s)

Xiucai Ding, Yichen Hu

References

[1] Ding, X. (2020). High dimensional deformed rectangular matrices with applications in matrix denoising. Bernoulli, 26(1), 387-417.

[2] Donoho, D. L., Gavish, M., & Romanov, E. (2020). Screenot: Exact mse-optimal singular value thresholding in correlated noise. arXiv preprint arXiv:2009.12297.

[3] Ding, X., & Yang, F. (2022). Tracy-Widom distribution for heterogeneous Gram matrices with applications in signal detection. IEEE Transactions on Information Theory, vol. 68, no. 10, pp. 6682-6715.