We derive a formula for optimal hard thresholding of the singular value decomposition in presence correlated additive noise; although it nominally involves unobservables, we show how to apply even where noise covariance structure is not priori known or independently estimable. The proposed method, which call ScreeNOT, mathematically solid alternative Cattell’s ever-popular but vague scree plot ...

Abstract We compare two common methods for detecting functional connectivity: thresholding correlations and Singular Value Decomposition (SVD). We find that thresholding correlations is better at detecting focal regions of correlated voxels, whereas SVD is better at detecting extensive regions of correlated voxels. We apply these results to resting state networks in an fMRI data set, and to loo...

We compare two common methods for detecting functional connectivity: thresholding correlations and singular value decomposition (SVD). We find that thresholding correlations are better at detecting focal regions of correlated voxels, whereas SVD is better at detecting extensive regions of correlated voxels. We apply these results to resting state networks in an fMRI dataset to look for connecti...

In this paper, we present a fast implementation of the Singular Value Thresholding (SVT) algorithm for matrix completion. A rank-revealing randomized singular value decomposition (RSVD) algorithm is used to adaptively carry out partial singular value decomposition (SVD) to fast approximate the SVT operator given a desired, fixed precision. We extend the RSVD algorithm to a recycling rank reveal...

Time-resolved imaging in microscopy is important for the direct observation of a range of dynamic processes in both the physical and life sciences. However, the image sequences are often corrupted by noise, either as a result of high frame rates or a need to limit the radiation dose received by the sample. Here we exploit both spatial and temporal correlations using low-rank matrix recovery met...