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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)
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)
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)
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)
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)
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)
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)
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)
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)