We consider recovery of low-rank matrices from noisy data by hard thresholding of singular
values, in which empirical singular values below a threshold are set to 0. We study the …

In this paper, we address the problem of estimating noise level from a single image
contaminated by additive zero-mean Gaussian noise. We first provide rigorous analysis on …

In a multivariate analysis problem, we are given a sample x1, x2,..., xn of random
observations of dimension p. Statistical methods such as Principal Components Analysis …

Although traditional subspace direction of arrival (DOA) algorithms enable super-resolution,
the algorithm performance declines sharply when the number of sources is incorrectly …

Sparse principal component analysis and iterative thresholding Page 1 The Annals of Statistics
2013, Vol. 41, No. 2, 772–801 DOI: 10.1214/13-AOS1097 © Institute of Mathematical Statistics …

In this paper, we propose a denoising method motivated by our previous analysis of the
performance bounds for image denoising. Insights from that study are used here to derive a …

We show that in a common high-dimensional covariance model, the choice of loss function
has a profound effect on optimal estimation. In an asymptotic framework based on the …

We consider the recovery of low-rank matrices from noisy data by shrinkage of singular
values, in which a single, univariate nonlinearity is applied to each of the empirical singular …

This paper addresses the statistical performance of subspace DoA estimation using a
sensor array, in the asymptotic regime where the number of samples and sensors both …

The truncated singular value decomposition of the measurement matrix is the optimal
solution to the representation problem of how to best approximate a noisy measurement …