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- Tim Groseclose, Jeffrey Milyo, +29 authors Barry Weingast
- 2003

We measure media bias by estimating ideological scores for several major media outlets. To compute this, we count the times that a particular media outlet cites various think tanks and policy groups, then compare this with the times that members of Congress cite the same groups. Our results show a strong liberal bias: all of the news outlets we examine,… (More)

- Deanna Needell, Rachel Ward
- SIAM J. Imaging Sciences
- 2013

This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization, and our results may be the first of this kind. In particular, we show that from O(s log(N)) nonadaptive linear measurements, an image can be reconstructed to within the best s-term approximation of… (More)

- Felix Krahmer, Rachel Ward
- SIAM J. Math. Analysis
- 2011

Consider an m×N matrix Φ with the Restricted Isometry Property of order k and level δ, that is, the norm of any k-sparse vector in R N is preserved to within a multiplicative factor of 1±δ under application of Φ. We show that by randomizing the column signs of such a matrix Φ, the resulting map with high probability embeds any fixed set of p = O(e k) points… (More)

- Massimo Fornasier, Holger Rauhut, Rachel Ward
- SIAM Journal on Optimization
- 2011

We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a minimal nuclear norm and an approximatively low-rank solution. Under the assumption that the linear measurements fulfill… (More)

- Rachel Ward
- IEEE Transactions on Information Theory
- 2009

Compressed sensing (CS) decoding algorithms can efficiently recover an N -dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = O(klogN/k) measurements y = Phi<sub>x</sub>. If the sparsity or approximate sparsity level of x were known, then this theoretical guarantee would imply quality assurance of the resulting… (More)

- Felix Krahmer, Rachel Ward
- IEEE Transactions on Image Processing
- 2014

In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence suggests that superior image reconstruction can be obtained through variable density sampling strategies that… (More)

- Yudong Chen, Srinadh Bhojanapalli, Sujay Sanghavi, Rachel Ward
- ICML
- 2014

Matrix completion concerns the recovery of a low-rank matrix from a subset of its revealed entries, and nuclear norm minimization has emerged as an effective surrogate for this com-binatorial problem. Here, we show that nuclear norm minimization can recover an arbitrary n ⇥ n matrix of rank r from O(nr log 2 (n)) revealed entries, provided that revealed… (More)

- Deanna Needell, Rachel Ward
- IEEE Transactions on Image Processing
- 2013

Consider the problem of reconstructing a multidimensional signal from an underdetermined set of measurements, as in the setting of compressed sensing. Without any additional assumptions, this problem is ill-posed. However, for signals such as natural images or movies, the minimal total variation estimate consistent with the measurements often produces a… (More)

- Massimo Fornasier, Rachel Ward
- Foundations of Computational Mathematics
- 2010

Free-discontinuity problems describe situations where the solution of interest is defined by a function and a lower dimensional set consisting of the discontinuities of the function. Hence, the derivative of the solution is assumed to be a 'small' function almost everywhere except on sets where it concentrates as a singular measure. This is the case, for… (More)

- Abhinav Nellore, Rachel Ward
- Inf. Comput.
- 2015

For a certain class of distributions, we prove that the linear programming relaxation of k-medoids clustering—a variant of k-means clustering where means are replaced by exemplars from within the dataset—distinguishes points drawn from nonoverlapping balls with high probability once the number of points drawn and the separation distance between any two… (More)